The process of dividing fractions with whole numbers is different than what it seems. Even though you are dividing whole numbers, the most effective way to solve these kinds of math problems is to use a multiplication sign. Let's explain why.
How Division of Fractions Work
Before explaining why dividing fractions with whole numbers requires you to multiply fractions, let’s learn how to divide fractions. Any time you are asked to divide fractions, you have to flip or invert the fraction. Here's an example:
As you can see, dividing the first fraction by the second fraction of one-half is actually the same thing as multiplying the numerator (the top part of the fraction) by 2.
The result is an improper fraction, which means the numerator is larger than the denominator (the bottom number of the fraction.) This improper fraction can also be converted into a mixed number:
So 6/5 and 1 1/5 are equivalent fractions. Use this fractions worksheet to learn how to turn improper fractions into mixed fractions.
Dividing Fractions With Whole Numbers: A Step-by-Step Guide
Now that we know how multiplying and dividing fractions work, let's learn how to divide whole numbers by fractions.
Anytime a whole number is the divisor of a fraction, you are further dividing this fraction into multiple equal parts. Let's break this process down step by step:
1. Inverse the the Whole Number
To start, you must convert the whole number into a fraction by inversing it. This means that the value of 1 will become the numerator and the whole number will become the denominator. A fraction with a numerator value of 1 is called a unit fraction.
2. Multiply the Fractions
You will now multiply the numerators and denominators.
3. Simplify the Fraction
Find the lowest common denominator, the smallest number that both numbers can be divided by. In this case, the number is 3.
Why Is Dividing Fraction With Whole Numbers Important?
When you enter 5th grade and 6th grade math, you start exploring math worksheets and word problems that involve adding and subtracting fractions. This prepares you for middle school math, where you start multiplying and dividing fractions with whole numbers.
Building a strong fraction foundation helps you with more complex fractional concepts that you'll learn in high school math.
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Dividing fractions with whole numbers is done by multiplying the whole number with the denominator of the given fraction. In the general form, it can be understood as, x/y ÷ a = x/ya, where x/y is the fraction and 'a' is any whole number. Let us learn about dividing fractions with whole numbers in this article along with interesting games, worksheets, and examples.
Steps of Dividing Fractions with Whole Numbers
Dividing fractions with whole numbers results in a value less than the given fraction. It is because we are dividing it into smaller equal parts and the quotient obtained will be the value of one part out of those. For example, if we say that divide 2/3 into 4 equal parts. It means we are breaking 2/3 into 4 equal parts and the answer will be the value of one such part. So, 2/3 ÷ 4 = 2/3 × 1/4 = 2/12 = 1/6. Here, you can observe that 1/6 < 2/3.
How to Divide Fractions by Whole Numbers?
To divide fractions by whole numbers, one should be aware of the concept of reciprocal. For dividing fractions with whole numbers, follow the steps given below:
- Step 1: Write the division fact as dividend ÷ divisor, where the given fraction will be the dividend and the given whole number will be the divisor.
- Step 2: Change the division sign into multiplication and write the reciprocal of the divisor (whole number).
- Step 3: Find the product by multiplying numerator with numerator and denominator with denominator. That will be the required answer.
For example, let us divide 11/8 by 2.
Step 1: 11/8 ÷ 2
Step 2: 11/8 × 1/2 (as the reciprocal of 2 is 1/2)
Step 3: 11/8 × 1/2 = 11/16.
Therefore, 11/8 ÷ 2 = 11/16.
Another way to understand this method of dividing fractions with whole numbers is that we can simply multiply the given whole number to the denominator of the fraction. In the above example, we are actually doing the same in step 2. We multiply 2 to 8, and then the denominator of the answer becomes 2 × 8 = 16.
Look at the image given below to understand the division of fractions by whole numbers in a better way.
Dividing Fractions with Whole Numbers Games
There are a number of games and activities for learning dividing fractions with whole numbers in an easy way. Some of the games are given below:
- Ask learners to take two strips of paper of equal length. Ask them to cut one of the strips into 3 equal parts. This way they will be left with 1/3 part of the strip. Now, ask them to cut that 1/3 part into 4 equal parts. Finally, they will be left with some portion. Ask learners to compare that part with the other strip. This way they will find that it is 1/12th part of the original which is nothing but the answer of the division fact of 1/3 ÷ 4.
- The other game can be around activity cards of the division of fractions with whole numbers. Write a division fact (for example, 8/5 ÷ 3) in some cards (a different question in each of the cards, obviously!) and distribute it among learners. Draw an image of a blank strip or a circle along with the division fact to make it more visually attractive.
Division of Whole Number by Fraction
Now, let us learn how to do the division of whole numbers by fractions. To divide a whole number by a fraction, follow the steps mentioned below:
- Step 1: Find the reciprocal of the given fraction.
- Step 2: Multiply the reciprocal with the given whole number. The product will be required answer.
For example, to divide 3 by 2/5, we just need to multiply 3 by 5/2 (reciprocal of 2/5). This implies, 3 × 5/2 = 15/2.
► Also Check:
- Division of Fractions
- Fractions
- Whole Numbers
- Multiplication of Fractions
FAQs on Dividing Fractions with Whole Numbers
What is Dividing Fractions with Whole Numbers?
While learning about the division of fractions, one may find questions based on a special case which is dividing fractions with whole numbers. In dividing fractions by whole numbers, we need to multiply the fraction with the reciprocal of the whole number. That product will be the answer to the division.
What is the Rule for Dividing Fractions with Whole Numbers?
The rule for dividing fractions by whole numbers is that we need to multiply the reciprocal of the whole number to the given fraction. By this simple rule, we can solve any problem based on this concept.
How do you Divide Fractions with Whole Numbers?
To divide fractions with whole numbers, follow the steps listed below:
- Find the reciprocal of the whole number. The reciprocal of x is 1/x.
- Multiply the reciprocal value to the fraction.
- That product will be the required answer.
How to Solve Dividing Fractions with Whole Numbers?
In order to solve dividing fractions with whole numbers, we need to multiply the given whole number to the denominator of the fraction. It always results in a number less than the value of the fraction given.
How do you Divide a Whole Number by a Fraction 5th Grade?
For dividing whole numbers with fractions, we need to multiply the reciprocal of the fraction with the whole number. In mathematics, this concept is generally learnt in grade 5 when learners get to know about the division of fractions.