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Dividing Whole Numbers by Fraction

dividing whole numbers by fractions

What do we do when we divide whole numbers by fractions? On dividing a whole number by a fraction, we find the number of groups of the fraction we can fit in the whole. The most common method for dividing a whole number by fraction is multiplying the given whole number by the reciprocal fraction. The following article will help you understand how do you divide a whole number by a fraction. Learn the different ways to divide whole numbers by fractions.

Multiplying the Reciprocal of the Fraction

The first method is the most common method wherein we multiply the whole number with the fraction reciprocal. The following example will help you completely understand the steps of dividing a whole number by a fraction. 

Step 1: Begin by converting the whole number into a fraction. We can do this by placing the whole number as the numerator of the fraction. In the place of the denominator, we will place  1.

For example, if we have to calculate 3 ÷ 2/5 

We will change 3 to 31

Step 2: Next, we will find the reciprocal of the fraction given as a divisor. The reciprocal of any number is its inverse. So, in the case of a fraction, the given numerator will become the denominator, and the denominator will be the new numerator. 

For example, the reciprocal of 2/5 will be  5/2

Step 3: Now that we have two fractions, we will multiply them. For multiplication, we will first multiply the numerators and then the denominators. 

For example, 3/1 * 5/2 = 15/2

Step 4: Lastly, we will simplify the fraction, if required. So, we will reduce it to the lowest terms. If we have an improper fraction, i.e., the numerator of the fraction is larger than the denominator, we will change it to a mixed number. 

For example, 15/2 = 7*1/2

Multiplying the Bottom Number of the Fraction 

There is an easier way to divide whole numbers by fractions for those who wish to have fewer steps of calculations. 

Step 1. We will multiply the denominator of the fraction (i.e., the bottom number) with the whole number. 

Step 2. After we obtain the product, we will simplify the fraction. If the answer is an improper fraction, we will change it into a mixed form. 

For example, 32   ÷ 7

First, we will multiply the bottom number, i.e., 2, with the whole number.    

So,   3/2 * 7 = 3/1 * 4

Since this fraction cannot be further simplified, it is the answer. 

Division of a Whole Number by A Decimal

Now, let us learn the process of the division of whole numbers by decimal numbers. One of the most popular methods of dividing a whole number by a decimal is by converting the decimal number into a fraction. 

So, we will first convert the decimal into a fraction by removing the decimal point and adding 10x in the denominator, wherein x represents the number of digits after the decimal point. 

For example, 2 ÷ 0.05

We can convert 0.05 into a fraction as follows:

 2 ÷ 005/100

Next, we will follow the same steps we use to divide whole numbers by fractions. 

2 * 100/5

200/5 = 40 

The answer is 40.

Activity:
This activity will help you study the division of fractions by a whole number. 

Take two strips of paper. Ensure that both the strips are of equal length. Cut one of the strips into 3 equal parts. 

Now you will be left with 1/3 part of the strip. Next, you have to cut that one-third part into 4 equal parts. 

Finally, you will be left with a certain portion. Compare that part with the other strip. Hint: 1/3 ÷ 4

How To Divide A Fraction by Whole Number?

Now that we know how to divide whole numbers by fractions, let us check the vice versa. Here is how to divide a fraction by a whole number. 

The steps for dividing a fraction by a whole number remain the same. So, we will first convert the whole number into a fraction. The following steps will help you understand the method of division of a fraction by a whole number. 

For example, divide 2/5 ÷ 4

Step 1: First, we will write the problem and then convert the whole number into a fraction. We add 1 as the denominator of the whole number. So, the whole number becomes the numerator. 

For example,   2/5 ÷ 4/1

Step 2: Next, we will multiply the two fractions, and to do this, we will write the reciprocal of the whole number. So, the numerator, which is our whole number, will become the denominator, and the denominator will become the numerator. 

For example,  2/5 * 1/4

Step 3: We will multiply the two fractions. We will first find the product of the two numerators and then the two denominators as given below:

2/20

Step 4: Now, we can simplify the product obtained and reduce it to the lowest terms. 

So, 2/20 can be reduced to 1/10

So the answer will be 1/10.

Real-Life Applications of Division of Whole Numbers by Fractions

The division of whole numbers by fractions or the division of fractions by whole numbers has several applications in our day to life. Here are the most common examples of applications of the division of whole numbers by fractions and vice versa.

  • While distributing pizza slices amongst family members or friends
  • When we divide a loaf of bread into pieces.
  • Dividing paper into strips when doing craft activities
  • In games and activities

Solved Examples on Division of Whole Numbers by Fractions

Example 1: Divide the following whole numbers with fractions:

  1. 22 ÷ 2/3
  2. 40 ÷ 1/2
  3. 44 ÷ 6/3

Solution: a.) 22 ÷ 2/3

First, we will convert the whole number into a fraction by adding 1 as the denominator.

22/1 ÷ 2/3

Now, we will write the reciprocal of the fraction.  

22/1 * 3/2

We will multiply the two fractions to obtain a product.

22/1 ÷ 2/3 = 44/3

Since the product is an improper fraction, we will convert it into a mixed fraction.

The answer is 14÷2/3.

b. )  40 ÷ 1/2

First, we will convert the whole number into a fraction by adding 1 as the denominator.

40/1 ÷ 1/2

Now, we will write the reciprocal of the fraction.  

22/1 ÷ 2/1

We will multiply the two fractions to obtain a product.

22/1 ÷ 2/1 = 44/1

The answer is 44.

c.) 44 ÷ 6/3

First, we will convert the whole number into a fraction by adding 1 as the denominator.

44/1 ÷ 6/3

Now, we will write the reciprocal of the fraction.  

22/1 * 3/6

We will multiply the two fractions to obtain a product.

22/1 * 3/6 = 66/6

Since the product is an improper fraction, we usually convert it into a mixed fraction, but we can simplify it here. 

The answer is 11.

Example 2: Hazel organizes a spaghetti night at her place. She has ½ a cup of toppings to sprinkle equally over 3 bowls. How many toppings (in terms of cups) does she put in each bowl?

Solution: Hazel has ½ a cup of toppings 

Number of bowls = 3 

Given: Each bowl has an equal amount of toppings

The number of toppings Hazel puts in each bowl = 1/2 ÷ 3

So, we will first convert the whole number into a fraction by adding 1 as the denominator. Then we will write the inverse of the divisor and multiply the two fractions to obtain a product. 

1/2 ÷ 3/1 

= 1/2 *1/3 = 1/6

 Answer: Hazel puts ⅙ of toppings into each bowl.

Practice ProblemsQuestion

1: Divide the following:

a. 5 ÷ 4/6

b. 6 ÷ 1/2

c. 3 ÷ 2/4

d. 11 ÷ 2/5

e. 8 ÷ 11/2

f. 67 ÷ 1/2

g. 45 ÷ 2/3

h. 9 ÷ 8/12

I. 4 ÷ 1/8

j. 5 ÷ 8/9

Question 2: David bought a packet of chocolates. It weighs 1/6 of a pound. He fills 3 bowls with these chocolates. Calculate the weight of each bowl if he fills the bowls equally.

Question 3: Syra had 1/2 of a pound of biscuits. She distributed the biscuits equally amongst her 2 daughters. What is the share of each daughter? 

Frequently Asked Questions

1. What is Dividing Fractions with Whole Numbers?

Ans. When you divide a fraction by a whole number, you’re just taking the top number and dividing it by the bottom number. For example, if you have 1/3 and you want to divide it by 2, then you’d multiply 1 times 2 and get 2. Then you’d multiply 3 times 2 and get 6. So your final answer would be 1/3 divided by 2, which is equal to 1/6.

2. What is the Rule for Dividing Fractions with Whole Numbers?

Ans. The rule for dividing fractions with whole numbers is simple:

Divide the numerator by the denominator.

That’s it! Let’s look at an example. Suppose you want to divide 1/2 by 8. The first step is to divide the numerator of your fraction (1) by the denominator of your fraction (8). This gives you 1 divided by 8 = 0.125, or 0 1/8, which is pronounced: “one-eighth.”

3. How do you Divide Fractions with Whole Numbers?

Ans. There are a few different ways to divide fractions with whole numbers, but the easiest way is to make sure that both sides of your equation are in the same denominator. Let’s say you have 1/4 and 5/8. To divide them, we need to turn them into fractions that have a denominator of 2. We can do this by multiplying the top number by 2 and then dividing it by the bottom number. So for our example, we would get:2(1/4) / 8 = ½

4. How to Solve Dividing Fractions with Whole Numbers?

Ans. 1. Divide the numerator by the denominator.

2. Write down the answer and simplify if necessary.

3. If you have a decimal point in your answer, round it up or down to the nearest whole number.

5. How do you Divide a Whole Number by a Fraction?

Ans. To divide a whole number by a fraction, you just have to do the same thing you would do if you were dividing any other number by another number. Let’s say we want to divide 45 by 5. So we write it like this: 45/5. Now let’s multiply both sides of that equation by 10: 4500/50=4500/5. Now we can subtract the other side from both sides and continue until we get rid of all those extra zeroes: 4500-4500=0/5=0.

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