## WORD PROBLEMS INVOLVING OPERATIONS OF WHOLE NUMBERS

Problem 1 :

What number must be increased by 293 to get 648?

Let x be the required number.

What must be increased by 293 to get 648

x + 293 = 648

x = 648 - 293

Problem 2 :

A woman has $255 in her purse. She gives $35 to each of her five children. How much money does she have left?

Amount she has in her purse = $255

Each child gets = $35

Amount distributed :

Amount she has left :

= $255 - $175

Problem 3 :

The Year 8 students at a school are split into 4 equal classes of 27 students each. The school decides to increase the number of classes to 6. How many students will there be in each of the new classes, if the students are divided equally between them?

Number of existing classes = 4

Number of students in total :

Number of classes increased = 6

Number of students in each class :

= ¹⁰⁸⁄₆

Problem 4 :

My bank account contains $3621 and I make monthly withdrawals of $78 for 12 months. What is my new bank balance.

My old balance = $3621

I make withfrawals $78 each month for 12 months.

Amount of withdrawal :

My new balance :

= old balance - withdrawal

= $3621 - $936

Problem 5 :

A contractor bought 34 loads of soil, each weighing 12 tonnes. If the soil cost $23 per tonne, what was the total cost ?

Number of loads = 34

Weight of 1 load = 12 tonnes

Cost of soil = $23 per tonne

Number of tonnes :

= 408 tonnes

Required cost :

= $9384

Problem 6 :

4 less than three times of a whole number is equal to 8. Find the whole number.

Let x be the required whole number.

From the given information,

Add 4 to both sides.

Divide both sides by 3.

The whole number is 4.

Problem 7 :

The sum of two whole numbers is 8 and that of the difference is 2. Find the two whole numbers.

Let x and y be the two required whole numbers such that x > y .

x + y = 8 ----(1)

x - y = 2 ----(2)

Add (1) and (2) :

Divide both sides by 2.

Substitute x = 5 into (1).

Subtract 5 from both sides.

The two whole numbers are 5 and 3.

Problem 8 :

In a two-digit whole number, the digit at the tens place is twice the digit at the ones place. If 18 is subtracted from it, the digits are reversed. Find the two-digit whole number.

Let x be the digit in ones place.

Then the two-digit number is (2x)(x).

(2x)(x) - 18 = (x)(2x)

(10 ⋅ 2x) + (1 ⋅ x) - 18 = (10 ⋅ x) + (1 ⋅ 2x)

20x + x - 18 = 10x + 2x

21x - 18 = 12x

Subtract 12x from both sides.

9x - 18 = 0

Add 18 to both sides.

The digit at the ones place is 2 and the digit at the tens place is 4.

So, the required two-digit number is 42.

Problem 9 :

A whole number consisting of two digits is four times the sum of its digits and if 27 be added to it, the digits are reversed. Find the whole number.

Let xy be the required two-digit whole number.

Given : The two-digit whole is equal four times the sum of its digits

xy = 4(x + y)

(10 ⋅ x) + (1 ⋅ y) = 4x + 4y

10x + y = 4x + 4y

6x - 3y = 0

y = 2x ----(1)

Given : If 27 be added to it, the digits are reversed.

xy + 27 = yx

(10 ⋅ x) + (1 ⋅ y) + 27 = (10 ⋅ y) + (1 ⋅ x)

10 x + y + 27 = 10y + x

9x - 9y + 27 = 0

x - y + 3 = 0

Substitute y = 2x.

x - 2x + 3 = 0

Substitute x = 1 into (1).

Therefore, the required two-digit whole number is 36.

Problem 10 :

What are the smallest and largest three-digit whole numbers which are evenly divisible by 7?

Steps to find the smallest three-digit whole number divisible by 7 :

The smallest three-digit whole number is 100. Divide 100 by 7 and get the quotient and remainder.

When 100 is divided by 7, the quotient is 14 and the remainder is 2.

Subtract the remainder 2 from the divisor 7.

Add 5 to the dividend 100.

105 is the smallest three-digit number divisible by 7.

Steps to find the largest three-digit whole number divisible by 7 :

The largest three-digit whole number is 999. Divide 999 by 7 and get the quotient and remainder.

When 999 is divided by 7, the quotient is 142 and the remainder is 5.

Subtract the remainder 5 from the dividend 999.

994 is the largest three-digit number divisible by 7.

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## Whole numbers

Here you will learn about whole numbers, including how to identify whole numbers, whole numbers on a number line, and the properties of whole numbers.

Students will first learn about whole numbers as part of counting and cardinality in Kindergarten and will expand their knowledge of whole numbers throughout elementary and middle school when learning about the properties of whole numbers and performing the four operations with whole numbers.

## What are whole numbers?

Whole numbers are a set of numbers starting at zero and increasing by one each time.

Whole numbers do not include fractions, decimals, or negative numbers. They are positive integers.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10….

All whole numbers are integers, but not all integers are whole numbers since integers also include negative numbers. Both whole numbers and integers are rational numbers.

For example,

0 \quad \quad \quad \quad 100 \quad \quad \quad \quad 857 \quad 1,524 \quad \quad 125,031 \quad \quad 1,000,000 | -5 \quad \quad \quad \quad \cfrac{1}{2} \quad \quad \quad \quad 0.75 \quad 0.\overline{88} \quad \quad \quad \;\, 2\cfrac{1}{4} \,\;\; \quad \quad \quad \quad \pi \quad \quad |

## Properties of whole numbers

Commutative property of whole numbers

- The commutative property of whole numbers states that the order of two numbers being added or multiplied together does not matter and that changing the order of the numbers will still give the same result.

a+b=b+a 4+5=5+4 | a \times b=b \times a 6 \times 3=3 \times 6 |

See also : Commutative property

Associative property of whole numbers

- The associative property of whole numbers states that, when adding or multiplying three numbers, the grouping of two numbers within the expression can change and still give the same result.

(a+b)+c=a+(b+c) (8+4)+6=8+(4+6) | (a \times b) \times c=a \times(b \times c) (2 \times 5) \times 7=2 \times(5 \times 7) |

See also : Associative property

Distributive property

- The distributive property of whole numbers says that multiplication is distributive over addition or subtraction. This means that when multiplying a number by a sum or difference of 2 numbers, you can multiply by each number separately and then add or subtract the products.

| |
---|---|

a(b+c)=(a \times b)+(a \times c) \begin{aligned} 5(3+9) & =(5 \times 3)+(5 \times 9) \\ & =15+45 \\ & =60 \end{aligned} | a(b-c)=(a \times b)-(a \times c) \begin{aligned} 8(10-1) & =(8 \times 10)-(8 \times 1) \\ & =80-8 \\ & =72 \end{aligned} |

See also : Distributive property

Closure property

- The closure property of whole numbers says that the sum or product of two whole numbers will always be a whole number.

a+b=c If a and b are whole numbers, c will be a whole number. 9+6=15 | a \times b=c If a and b are whole numbers, c will be a whole number. 8 \times 4=32 |

## Common Core State Standards

How does this relate to Kindergarten math through 6th grade math?

- Kindergarten – Counting and Cardinality (K.CC.1, K.CC.2, K.CC.3) Count to 100 by ones and by tens; Count forward beginning from a given number within the known sequence (instead of having to begin at 1 ); Write numbers from 0 to 20. Represent a number of objects with a written numeral 0-20 (with 0 representing a count of no objects).
- Grade 1 – Operations and Algebraic Thinking (1.0A.B.3 ) Apply properties of operations as strategies to add and subtract. Examples: If 8 + 3 = 11 is known, then 3 + 8 = 11 is also known. (Commutative property of addition). To add 2 + 6 + 4, the second two numbers can be added to make a ten, so 2 + 6 + 4 = 2 + 10 = 12. (Associative property of addition).
- Grade 2 – Operations and Algebraic Thinking (2.OA.C.3) Determine whether a group of objects (up to 20 ) has an odd or even number of members, for example, by pairing objects or counting them by 2 s; write an equation to express an even number as a sum of two equal addends.
- Grade 3 – Operations and Algebraic Thinking (3.OA.B.5) Apply properties of operations as strategies to multiply and divide. Examples: If 6 \times 4 = 24 is known, then 4 \times 6 = 24 is also known. (Commutative property of multiplication). 3 \times 5 \times 2 can be found by 3 \times 5 = 15, then 15 \times 2 = 30, or by 5 \times 2 = 10, then 3 \times 10 = 30. (Associative property of multiplication). Knowing that 8 \times 5 = 40 and 8 \times 2 = 16, one can find 8 \times 7 as 8 \times (5 + 2) = (8 \times 5) + (8 \times 2) = 40 + 16 = 56. (Distributive property).
- Grade 4 – Number and Operations Base Ten (4.NBT.B.5) Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.
- Grade 6 – Number Systems (6.NS.B.4) Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1–100 with a common factor as a multiple of a sum of two whole numbers with no common factor. For example, express 36 + 8 as 4 \, (9 + 2).

## How to use whole numbers

In order to identify whole numbers:

Recall the definition of the type of number needed.

Show whether the number fits or does not fit the definition.

In order to apply a property of whole numbers:

Recall the property.

Use the property to get an answer.

## [FREE] Types of Number Check for Understanding Quiz (Grade 2, 4 and 6)

Use this quiz to check your grade 6 students’ understanding of types of numbers. 10+ questions with answers covering a range of 2nd, 4th and 6th grade types of numbers topics to identify areas of strength and support!

## Identifying whole numbers examples

Example 1: identifying whole numbers.

Which of the following are whole numbers?

0, \, 8.5, \, -1, \, 32, \, 6 \cfrac{1}{4} \, , \, 3.05, \, 927

Since the set of whole numbers does not include decimals, fractions, and negative numbers, you can eliminate 8.5, -1, 6 \cfrac{1}{4} \, , and 3.05 from the list.

2 Show whether the number fits or does not fit the definition.

The remaining numbers are 0, 32, and 927. All three fit the definition and are whole numbers.

Answer: 0, 32, and 927

## Example 2: identifying whole numbers

Maya says -4 is a whole number since it doesn’t have a decimal or fractional part. Is she correct?

The set of whole numbers includes all positive integers starting at zero. Whole numbers do not include negative numbers, fractions, or decimals.

-4 is not a whole number since it is not a positive number. Negative numbers are not whole numbers. Therefore, Maya is incorrect.

## Example 3: identifying whole numbers

Which point on the number line represents a whole number?

The only point on the number line that shows a whole number is B, which represents 5.

Point A represents 3 \cfrac{1}{2} \, , point C represents 6 \cfrac{1}{2} \, and point D represents a fraction or decimal between 7 \cfrac{1}{2} and 8.

Since whole numbers do not include fractions or decimals, point B is the only whole number.

## Example 4: identifying whole numbers

Which whole number fills in the blank in the sequence?

26, \, 27, \, 28, \, \rule{0.5cm}{0.15mm} \, , \, 30, \, 31

26, \, 27, \, 28, \, {\bf{29}}, \, 30, \, 31

Although there are many fractions and decimals in between 28 and 30, there is only one whole number, which is 29.

## Example 5: apply a property of whole numbers

Fill in the blank using your knowledge of the commutative property of multiplication to make the equation true.

\rule{0.5cm}{0.15mm} \, \times 15=15 \times 3

The commutative property of multiplication states that the order of two numbers being multiplied together does not matter and that changing the order of the numbers will still give the same result.

a \times b = b \times a

\underline{3} \times 15=15 \times 3

The number 3 makes the equation true.

## Example 6: apply a property of whole numbers

Fill in the blank using your knowledge of the distributive property to make the equation true.

3 \times(7 + 9)= \, \rule{0.5cm}{0.15mm} \, +27

The distributive property states that multiplication is distributive over addition. This means that when multiplying a number by a sum of 2 numbers, you can multiply by each number separately and then add the products.

a(b + c) =(a \times b) + (a \times c)

Since this equation can also be solved as (3 \times 7) + (3 \times 9), I know that the missing number is 21.

3 \times(7 + 9)=\underline{21}+27

## Teaching tips for whole numbers

- Allow students to use concrete manipulatives to explore whole numbers when first building number sense.
- Use a number line to give students a visual representation of whole numbers. As they progress to higher grades, the number line can be partitioned into fractional and decimal parts as well, so students can see the difference between whole numbers and fractions/decimals. Later, a number line can also be extended past the number zero to show negative numbers. Students will gain better number sense when they are able to see non-examples of whole numbers.
- Display a chart or poster in the classroom showing the different types of numbers – whole numbers, natural numbers, integers, real numbers, etc. New types of numbers can be added to these displays in higher grade levels. This will help students differentiate between the sets of numbers.

## Easy mistakes to make

- Thinking that zero is not a whole number Zero is the first and smallest whole number. The set of whole numbers begins at zero and increases by one with each number.
- Thinking that whole numbers are the same as integers Whole numbers are a subset of integers. Integers include all negative numbers, positive numbers, and zero, while whole numbers include only non-negative integers.

## Related types of numbers lessons

This whole numbers topic guide is part of our series on types of numbers. You may find it helpful to start with the main types of numbers topic guide for a summary of what to expect or use the step-by-step guides below for further detail on individual topics. Other topic guides in this series include:

- Types of numbers
- Irrational numbers
- Rational numbers
- Prime numbers
- Natural numbers
- Prime and composite numbers
- Number sets
- Even numbers
- Odd numbers
- Absolute value

## Practice identifying whole numbers questions

1. What is the smallest whole number?

The set of whole numbers starts at zero. Whole numbers do not include negative numbers, fractions, or decimals. Therefore, the smallest whole number listed is zero.

2. Look at the number line. What is the missing whole number?

When counting whole numbers by ones, the number after 19 will be 20.

3. Colin wrote a set of whole numbers on the whiteboard using the numbers 0, 1, 3, and 9. What number should he not have included?

1.039 should not have been included because it is a decimal, not a whole number.

4. Select the group of numbers made up of only whole numbers.

101, \, 556, \, 18,000, \, 1 is the only group of numbers comprised of only whole numbers. The other groups include at least one fraction or decimal.

5. Which property is demonstrated by the following equation?

5(9+8)=(5 \times 9)+(5 \times 8)

Associative property

Commutative property

This shows the distributive property because multiplication is being distributed over addition. The distributive property allows you to perform the multiplication separately, then add the products.

6. Fill in the blank to make the equation true.

8 \times\left(6 \times \, \rule{0.5cm}{0.15mm} \, \right)=(8 \times 6) \times 4

This equation shows the associative property of multiplication, which states that when multiplying three numbers, the grouping of two numbers within the expression can change and still give the same result.

Therefore, since the right side shows 8, 6, and 4 being multiplied, I know the same 3 numbers are being multiplied on the left side of the equation.

## Whole numbers FAQs

Whole numbers are a set of numbers (also known as natural numbers or counting numbers) starting at the number zero and increasing by one each time. Whole numbers do not include fractions, decimals, or negative numbers.

Whole numbers and natural numbers are very similar but not the same. The set of natural numbers starts at one instead of zero.

Whole numbers are a subset of integers. Integers include positive whole numbers, negative whole numbers, and zero, while whole numbers only include non-negative integers.

If the fraction has the same numerator and denominator, or if its numerator is a multiple of its denominator, it can be written as a whole number. For example, the fraction \cfrac{4}{2} can be written as the whole number 2.

## The next lessons are

- Rounding numbers
- Factors and multiples

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## Solving problems with whole numbers

## 1.6 Solving problems with whole numbers

Order of operations.

If you use “BODMAS” or “BEDMAS” correctly to remember the order of operations, you will get the same answer. But, evaluating an expression using terms will help more with algebra later on!

## Worked Example 1.22: Using order of operations in calculations

Do not use a calculator. Follow the correct order of operations to find the answer.

## Separate the terms of the expression.

Thinking about “terms” is a useful way to help us to simplify. Terms are separated by addition and subtraction symbols, and joined into one by multiplication and division symbols, and brackets. To evaluate an expression, we must: separate it into terms simplify each term (if needed) add or subtract from left to right.

This expression has three terms: \(7\), \(−2 \times 1 \times 3\), and \(+3 \times 5\). We must simplify the second and third terms.

## Add and subtract from left to right

Worked example 1.23: using order of operations in calculations, separate the expression into terms..

Remember that terms are separated by addition and subtraction symbols, and joined into one by multiplication and division symbols, and brackets. First separate into terms, then simplify, and then add or subtract from left to right.

This expression has three terms: \(19\), \(−5\), and \(+ 1^{2}\). We must simplify the exponent in the third term.

## Simplify each term and calculate from left to right.

Instead of saying, for example “\(60\) calls per day”, people often say “at a rate of \(60\) calls per day”.

The word ‘per’ is often used to describe a rate and can mean for every , for , in each , in , out of , or every .

Speed is one example that describes the rate of movement over time. For example, a problem states that the invasive trees in the Western Cape are to be cut down in favour of natural vegetation. There are roughly \(3\ 000\ 000\) invasive trees in the area, and it is possible to cut them down at a rate of \(15\ 000\) trees per day with the labour available. The question could then be, “How many working days will it take before all the invasive trees have been cut down?”

To answer this rate question, you divide the total number of trees by the number that can be cut in one day:

So, it will take \(200\) days for all the trees to be cut down if the rate of cutting stays the same.

It is important to check that your answer makes sense. In this question we were looking for the number of days, so the answer must refer to days.

## Worked Example 1.24: Solving problems with rate

A car travels a distance of \(180 \text{ km}\) in \(2\) hours on a straight road. How many kilometres can it travel in \(3\) hours at the same speed?

## Understand the problem and summarise all the given information.

What we know:

- Distance = \(180 \text{ km}\)
- Time = \(2\) hours
- Speed = always the same

What we don’t know:

- Distance in \(3\) hours

## Find the distance in \(1\) hour.

If the car travels \(180 \text{ km}\) in \(2\) hours, then it will travel \(180 \div 2 = 90 \text{ km}\) in \(1\) hour.

## Find the distance in \(3\) hours (answer the question).

If the car travels \(90 \text{ km}\) in \(1\) hour, then it will travel \(90 \times 3 = 270 \text{ km}\) in \(3\) hours.

So, the car will travel \(270 \text{ km}\) in \(3\) hours.

Another useful concept is that of ratio . When we talk about ratio, we compare different amounts, such as the number of green apples and red apples in a bag, or the number of adults and children in a group. We might say, “there are two green apples for every red apple in the bag”, or “there are two children for every adult in the group”.

Look at these patterns.

Imagine if these are the beads and we continue the same pattern. In pattern A in the picture, there are \(5\) red beads for every \(4\) yellow beads. Try to describe patterns B and C in the same way.

You can either start with red beads or the yellow beads. It is equally correct to say “In pattern A there are \(4\) yellow beads for every \(5\) red beads.”

The patterns in question 4 can be described like this: In pattern A, the ratio of yellow beads to red beads is \(4\) to \(5\). This is written as \(4 : 5\). In pattern B, the ratio between yellow beads and red beads is \(3 : 6\). In pattern C the ratio is \(2 : 7\).

When solving problems with ratio, first look for the total number of parts. For example, in the pattern above, there are two parts: red beads and yellow beads. Then work out each quantity according to the ratio.

## Worked Example 1.25: Dividing amounts in the given ratio

If the number of hours that Nathi, Modi and Tim worked are in the ratio \(5 : 4 : 3\), then to be fair, the payment should also be shared in that ratio. What fraction of the payment should each person get?

## Work out the number that represents the total of the parts of the ratio.

Add the parts of the ratio: \(5 + 4 + 3 = 12\)

## Write the ratio of each person’s payment as a fraction.

Nathi should receive \(5\) parts, Modi \(4\) parts, and Tim \(3\) parts of the money. There are \(12\) parts altogether, so of the total payment:

- Nathi should receive \(\frac{5}{12}\),
- Modi should get \(\frac{4}{12}\),
- and Tim should get \(\frac{3}{12}\).

## Increasing and decreasing ratio

Sometimes you need to increase a ratio. For example, to increase \(40\) in the ratio \(2 : 3\) means that the \(40\) represents two parts and must be increased so that the new number represents \(3\) parts. If \(40\) represents two parts, then \(20\) represents \(1\) part. The increased number will therefore be \(20 \times 3 = 60\).

## Worked Example 1.26: Increasing a number in the given ratio

Increase \(56\) in the ratio \(2 : 5\).

## Find the number that represents \(1\) part.

If \(56\) represents \(2\) parts, then \(56 \div 2 = 28\) represents \(1\) part.

## Find the number that represent the unknown ratio.

The second number in the ratio is \(5\), so \(28 \times 5 = 140\).

So, the increased number is \(140\).

## Check your answer.

If the answer is correct, then \(56 : 140 = 2 : 5\).

Simplifying the ratio on the left-hand side should give us the ratio on the right-hand side.

When simplifying the ratio, you look for the highest common factor of both numbers. In this example, \(28\) is the highest common factor of \(56\) and \(140\).

## Worked Example 1.27: Decreasing a number in the given ratio

Decrease \(30\) in a ratio of \(2 : 3\).

We are decreasing in a ratio of \(2 : 3\), so the answer must be smaller than \(30\). Therefore, \(30\) must be equivalent to the bigger part of the ratio.

This new ratio should be equivalent to the original ratio. So, both sides should be multiplied or divided by the same whole number.

If \(30\) represents \(3\) parts, then \(30 \div 3 = 10\) represents \(1\) part.

## Find the number that represents the unknown ratio.

Our answer must be equivalent to the \(2\) part of the ratio.

Therefore, \(20 : 30\) is equivalent to \(2 : 3\).

\(30\) will decrease to \(20\).

## Whole Number Word Problems

Free video lessons on how to solve whole number word problems using the math models (tape diagrams/block models) taught in Singapore Math .

Related Topics: Whole Number Operations , Previous set of video math lessons in this series. , Next set of video math lessons in this series.

## Singapore Math: Primary 5 - Whole Numbers, Word Problem Q5

## Singapore Math: Primary 5 - Whole Numbers, Word Problem Q6

## Singapore Math: Primary 5 - Whole Numbers, Word Problem Q7

## Singapore Math: Primary 5 - Whole Numbers, Word Problem Q8

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## Whole Numbers Questions

Whole numbers questions are provided here, along with detailed explanations, so that students can practise these questions to improve their understanding. These questions are helpful for the students of Class 6 since whole numbers is one of the important topics for them. However, in this grade, they will learn the basic properties of whole numbers and simple arithmetic operations to be performed on them. In this article, you will learn how to solve various problems on whole numbers in simple methods and get accurate answers.

What are whole numbers?

In mathematics, whole numbers are defined as the set of numbers that include positive integers and 0. In other words, whole numbers are comprised of natural numbers and 0. The set of whole numbers is denoted by the English alphabet W.

Thus, whole numbers = W = {0, 1, 2, 3, 4, 5, 6, 7,….}

Click here to get more information about whole numbers and the properties of whole numbers .

## Whole Numbers Questions and Answers

1. Write the three whole numbers occurring just before 1001.

The three whole numbers occurring just before 1001 are 1000, 999 and 998.

2. How many whole numbers are there between 33 and 54?

The whole numbers between 33 and 54 are:

34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53

Thus, there are 20 whole numbers between 33 and 54.

3. Find the sum by suitable rearrangement.

197 + 234 + 103

This can be rearranged as:

(197 + 103) + 234

= 300 + 234

Therefore, 197 + 234 + 103 = 534.

4. The school canteen charges Rs. 20 for lunch and Rs. 4 for milk each day. How much money do you spend in 5 days on these things?

The cost of lunch per day = Rs. 20

The cost of milk per day = Rs. 4

Cost of lunch for 5 days = 5 × Rs. 20 = Rs. 100

Cost of milk for 5 days = 5 × Rs. 4 = Rs. 20

Total cost = Rs. (100 + 20) = Rs. 120

5. Simplify: 216 × 65 + 216 × 35.

216 × 65 + 216 × 35 = 216 × (65 + 35)

= 216 × 100

Thus, 216 × 65 + 216 × 35 = 21600

6. Find the product by suitable rearrangement:

(a) 2 × 1768 × 50

(b) 4 × 166 × 25

This expression can be rearranged as:

= (2 × 50) × 1768

= 100 × 1768

Therefore, 2 × 1768 × 50 = 176800

= (4 × 25) × 166

= 100 × 166

Therefore, 4 × 166 × 25 = 16600

7. A vendor supplies 32 litres of milk to a hotel in the morning and 68 litres in the evening. If the milk costs Rs. 45 per litre, how much money is due to the vendor per day?

Milk quantity supplied by a vendor in the morning = 32 litres

Milk quantity supplied by a vendor in the evening = 68 litres

The cost of milk per litre = Rs. 45

The total cost of milk per day = Rs. 45 × (32 + 68)

= Rs. 45 × 100

Therefore, the money due to the vendor per day is Rs. 4500.

8. Evaluate: 81265 × 249 – 81265 × 149.

81265 × 249 – 81265 × 149

= 81265 × (249 – 149)

= 81265 × 100

9. Find the product using suitable properties: 854 × 102.

= 854 × (100 + 2)

= 854 × 100 + 854 × 2 (Using distributive property)

= 85400 + 1708

Thus, 854 × 102 = 87108

10. Study the pattern:

1 × 8 + 1 = 9

12 × 8 + 2 = 98

123 × 8 + 3 = 987

1234 × 8 + 4 = 9876

12345 × 8 + 5 = 98765

Write the next two steps. Can you say how the pattern works?

(Hint: 12345 = 11111 + 1111 + 111 + 11 + 1).

From the given, we can write the next two steps as:

123456 × 8 + 6 = 987654

1234567 × 8 + 7 = 9876543

Using the pattern 12345 = 11111 + 1111 + 111 + 11 + 1, we have:

123456 = (111111 + 11111 + 1111 + 111 + 11 + 1)

123456 × 8 = (111111 + 11111 + 1111 + 111 + 11 + 1) × 8

= 111111 × 8 + 11111 × 8 + 1111 × 8 + 111 × 8 + 11 × 8 + 1 × 8

= 888888 + 88888 + 8888 + 888 + 88 + 8

123456 × 8 + 6 = 987648 + 6

Yes, here the pattern works.

Now, 1234567 × 8 + 7 = 9876543

1234567 = (1111111 + 111111 + 11111 + 1111 + 111 + 11 + 1)

1234567 × 8 = (1111111 + 111111 + 11111 + 1111 + 111 + 11 + 1) × 8

= 1111111 × 8 + 111111 × 8 + 11111 × 8 + 1111 × 8 + 111 × 8 + 11 × 8 + 1 × 8

= 8888888 + 888888 + 88888 + 8888 + 888 + 88 + 8

1234567 × 8 + 7 = 9876536 + 7

Yes, here also the pattern works.

## Practice Questions on Whole Numbers

- Which is the smallest whole number?
- Evaluate the following using the distributive property of whole numbers. 4275 × 125
- Find the sum 1962 + 453 + 1538 + 647 using suitable rearrangement.
- Find the value of 24 + 27 + 16 in two different ways.
- Match the following:

(i) 425 × 136 = 425 × (6 + 30 +100) (a) Commutativity under multiplication.

(ii) 2 × 49 × 60 = 2 × 60 × 39 (b) Commutativity under addition.

(iii) 70 + 1005 + 30 = 70 + 30 + 1005 (c) Distributivity of multiplication over addition.

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## 4th Grade Resources - Use the four operations with whole numbers to solve problems.

Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 x 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. Represent verbal statements of multiplicative comparisons as multiplication equations.

Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison.

Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.

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## Common Core: 4th Grade Math : Use the four operations with whole numbers to solve problems

Study concepts, example questions & explanations for common core: 4th grade math, all common core: 4th grade math resources, example questions, example question #1 : use the four operations with whole numbers to solve problems.

What equation is described below?

In this phrase, "is" represents equal and "times" means multiplication.

## Example Question #4 : Use The Four Operations With Whole Numbers To Solve Problems

## Example Question #5 : Use The Four Operations With Whole Numbers To Solve Problems

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## Example Question #7 : Use The Four Operations With Whole Numbers To Solve Problems

## Example Question #8 : Use The Four Operations With Whole Numbers To Solve Problems

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## 4 Operations word problems

Add / subtract / multiply / divide.

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## Course: 4th grade > Unit 2

- Addition, subtraction, and estimation: FAQ
- Rounding whole numbers to nearest hundred
- Rounding whole numbers to nearest thousand
- Round whole numbers
- Rounding whole numbers: missing digit
- Round whole numbers to different place values
- Rounding whole numbers word problems

## Round whole numbers word problems

- Your answer should be
- an integer, like 6
- a simplified proper fraction, like 3 / 5
- a simplified improper fraction, like 7 / 4
- a mixed number, like 1 3 / 4
- an exact decimal, like 0.75
- a multiple of pi, like 12 pi or 2 / 3 pi

## Word Problems on Addition and Subtraction of Whole Numbers

We will learn how to solve step-by-step the word problems on addition and subtraction of whole numbers. We know, we need to do addition and subtraction in our daily life. Let us solve some word problem examples.

Word problems on adding and subtracting of large numbers:

1. The population of a country in 1990 was 906450600 and next year it is increased by 9889700. What was the population of that country in the year of 1991?

The population of a country in 1990 = 906450600

Increased population by next year = + 9889700

Total population of that country in 1991 = 916340300

Therefore, the population of that country in the year of 1991 is 916340300.

2. Aaron bought two houses for $1668000 and $2454000. How much did he spend in all?

Cost of one house = $ 1668000

Cost of other house = + $ 2454000

Total cost of both houses = $ 4122000

Amount of money spent in all $4122000.

3. The sum of two numbers is 41482308. If one number is 3918695 then, find the other number.

Sum of two numbers = 41482308

One of the number = - 3918695

Second number = 37563613

Therefore, the other number is 37563613.

4. Mr. Jones deposited $278475 in a bank in his account. Later he withdrew $155755 from his account. How much money was left in the bank in his account?

Amount deposited = $ 278475

Amount withdrawn = - $ 155755

Amount left = $ 122720

Therefore, Mr. Jones has $ 122720in his bank account.

Note: We need to be careful while arranging the addends in columns.

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## Operations & Algebraic Thinking - 4th Grade

Use the four operations with whole numbers to solve problems..

CCSS.Math.Content.4.OA.A.3 Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.

Teacher Notes The focus in this standard is to have students use and discuss various strategies. It refers to estimation strategies, including using compatible numbers (numbers that sum to 10 or 100) or rounding. Problems should be structured so that all acceptable estimation strategies will arrive at a reasonable answer. Students need many opportunities solving multi-step story problems using all four operations.

This standard references interpreting remainders. Remainders should be put into context for interpretation. Ways to address remainders: • Remain as a left over • Partitioned into fractions or decimals • Discarded leaving only the whole number answer • Increase the whole number answer up one • Round to the nearest whole number for an approximate result

Student Knowledge Goals I know estimation strategies. I know mental math strategies. I know that a letter represents an unknown quantity. I can represent multi-step word problems using equations and a symbol for the unknown. I can interpret multi-step word problems and determine the appropriate operation to solve. I can use mental math and estimation to determine the reasonableness of an answer. I can interpret a remainder based on the context of a problem.

Teacher Lessons Engage NY Module 3-A Overview Engage NY Module 3-A1 - Includes printable classwork and homework *4.OA.A.1 & 4.OA.A.2 also covered Engage NY Module 3-D12 - Includes printable classwork and homework 4.OA.A.3 Lesson A - Includes printable classwork and homework 4.OA.A.3 Lesson B - Includes printable classwork and homework 4.OA.A.3 A&B Answers

Student Video Lessons Learn Zillion Video Lessons Study Jams - Word Problems to Equations Study Jams - Reasonableness & Estimation Study Jams - Equations & Word Problems

Online Problems, Games, and Assessments Khan Academy - Questions and Video Lessons Multi-Step Word Problems Multi-Step Word Problems & Video Lessons Multi-Step Word Problems with Estimating - Upper Level

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## Whole numbers

The set of whole numbers include the natural numbers and 0. Suppose we call this set W, then W = { 0,1,2,3,4,5,6,......}. Natural number, also called counting numbers, are 1, 2, 3, 4...

The number line below only shows whole numbers from 0 to 10.

However, not all numbers are shown!

50 is also a whole number.

Similarly, 2000 is also a whole number as the following figure shows.

## See below two graphs showing what whole numbers are

## Physical representations of whole numbers

1 cube: physical representation of 1 |

1 long : physical representation of 10 Made of 10 cubes. |

1 flat : physical representation of 100 Made of 100 cubes. |

1 block: physical representation of 1000 Made of 1000 cubes. |

## Why do we need whole numbers?

## What types of numbers are out there besides whole numbers?

Whole numbers quiz. check your understanding of this lesson..

Ways of writing whole numbers

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100 Tough Algebra Word Problems. If you can solve these problems with no help, you must be a genius!

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## IMAGES

## VIDEO

## COMMENTS

Problem 6 : 4 less than three times of a whole number is equal to 8. Find the whole number. Solution : Let x be the required whole number. From the given information, 3x - 4 = 8. Add 4 to both sides. 3x = 12. Divide both sides by 3. x = 4. The whole number is 4. Problem 7 : The sum of two whole numbers is 8 and that of the difference is 2.

Multi-step word problems with whole numbers. Google Classroom. Microsoft Teams. After collecting eggs from his chickens, Dale puts the eggs into cartons to sell. Dale fills 15 cartons and has 7 eggs left over. Each carton holds 12 eggs.

Use Place Value to Write Whole Numbers. In the following exercises, write each number as a whole number using digits. six hundred two. fifteen thousand, two hundred fifty-three. three hundred forty million, nine hundred twelve thousand, sixty-one. two billion, four hundred ninety-two million, seven hundred eleven thousand, two.

This video provides several examples of solving word problems using whole number operations.Complete Video List: http://www.mathispower4u.yolasite.com

The four basic operations on whole numbers are addition; subtraction; multiplication and division. We will learn about the basic operations in more detailed explanations along with the examples. Worked-out problems related to Operations on whole numbers. 1. Solve using rearrangement: = (784 + 216) + 127. = 1000 + 127. = 1127. (b) 25 × 8 × 125 ...

Singapore Maths: Primary 5 - Whole Numbers, Word Problem Q4. Learn how to use models to understand and solve word problems on whole numbers. Example: Dave and Eli bought some DVDs and paid $96 altogether. If Eli bought 10 more DVDs than Dave and paid $20 more than him, find the number of DVDs that Dave bought. Next set of videos in this series.

Q9 . Write these statements 0 using the symbols >, = or <. (a) 25 is less than 90 (b) 50 is equal to five times 10 (c) twelve is greater than five . Q10 . Complete each of the following using the symbols >, = or <. (a) 7 + 12 4 (b) 84 79 (c) 32 50 (d) 7 x 8 56 . Q11. Use written methods to work out the following:

Example 5: apply a property of whole numbers. Fill in the blank using your knowledge of the commutative property of multiplication to make the equation true. \rule {0.5cm} {0.15mm} \, \times 15=15 \times 3 × 15 = 15 × 3. Recall the property. Show step.

Number Word Problems Worksheets and Solutions. Objective: I can solve whole number word problems. Example: At a football match, there were 11 820 spectators. 8 256 of the spectators were adults. Of the remaining spectators, there were 3 times as many teenagers as young children. How many teenagers were there?

1.6 Solving problems with whole numbers Order of operations. If you use "BODMAS" or "BEDMAS" correctly to remember the order of operations, you will get the same answer. But, evaluating an expression using terms will help more with algebra later on!

Solving a word problem on whole numbers using models. Example: Each month Li pays bills for electricity and water. If she pays $36 a month for electricity, and $720 a year for electricity and water together, find the amount of money she pays for water each month. Show Step-by-step Solutions.

In this article, you will learn how to solve various problems on whole numbers in simple methods and get accurate answers. What are whole numbers? In mathematics, whole numbers are defined as the set of numbers that include positive integers and 0. In other words, whole numbers are comprised of natural numbers and 0.

4th Grade Resources - Use the four operations with whole numbers to solve problems. Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 x 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. Represent verbal statements of multiplicative comparisons as multiplication equations. Multiply or divide to ...

Example Question #1 : Use The Four Operations With Whole Numbers To Solve Problems. What equation is described below? is times as many as. Possible Answers: Correct answer: Explanation: is times the amount of. In this phrase, "is" represents equal and "times" means multiplication. So we have.

Add / subtract / multiply / divide. These grade 5 math word problems involve the 4 basic operations: addition, subtraction, multiplication and division. Some questions will have more than one step. The last question on each worksheet asks students to write an equation with a variable representing the unknown quantity.

Solve multistep word problems posed with whole numbers and having whole-number answers using the four . operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation

Round whole numbers word problems. The distance to the moon is an average of 384,400 kilometers. Round the distance to the nearest ten thousand. Learn for free about math, art, computer programming, economics, physics, chemistry, biology, medicine, finance, history, and more. Khan Academy is a nonprofit with the mission of providing a free ...

Hi! Welcome to iQuestionPH!The today's lesson is about Solving Word Problems Involving Whole Numbers. 💡Visual representations are powerful ways to access ab...

We know, we need to do addition and subtraction in our daily life. Let us solve some word problem examples. Word problems on adding and subtracting of large numbers: 1. The population of a country in 1990 was 906450600 and next year it is increased by 9889700. What was the population of that country in the year of 1991?

Practice Solving a Word Problem with the Addition of Whole Numbers with practice problems and explanations. Get instant feedback, extra help and step-by-step explanations. Boost your Algebra grade ...

Practice Solving Word Problems Using Multiplication of Whole Numbers with practice problems and explanations. Get instant feedback, extra help and step-by-step explanations. Boost your Algebra ...

CCSS.Math.Content.4.OA.A.3. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental ...

The numeral that we use to represent the set above is 4 When using numbers to count how many elements a set has, it is referred to as cardinal numbers. For instance, 4 or four is a cardinal number. What types of numbers are out there besides whole numbers? These are integers, rational numbers, irrational numbers real numbers, and complex numbers.