Introduction
There are many situations in life where we might have to divide a fraction by a whole number.
Say we have of a cake left and we want to split it between 4 people. What fraction will each individual get?
To solve for the amount of cake each individual will get, we need to divide by 4.
When doing division involving fractions, we will usually have to use something called the reciprocal.
A reciprocal is the flip of a fraction. For example, the reciprocal of is .
In general, to solve the division of two fractions, we multiply the top fraction by the reciprocal of the bottom.
Dividing Fractions by Whole Numbers
Let's solve the problem from earlier.
Dividing Fractions by Whole Numbers
We want to divide by 4.
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First, convert our whole number 4 into the fraction .
Keep the first fraction how it is, flip the second fraction and then multiply them together.
÷ =
Finally, we simplify our answer.
We successfully divided by 4 and the result is that each individual will get a slice of the original cake.
Dividing Whole Numbers by Fractions
The procedure for dividing a whole number by a fraction is very similar to what we just saw previously.
While baking the cake earlier, the recipe called for cups of flour.
If our bag of flour contains 25 cups of flour, how many cakes can we make with one bag of flour?
To solve for how many cakes we can make with one bag of flour, we will need to divide 25 by .
Dividing Whole Numbers by Fractions
We want to divide 25 by .
Before we begin, let's convert the mixed number into an improper fraction.
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Convert the whole number 25 into a fraction with a denominator of 1.
Since we are dividing by , keep the first fraction how it is, flip and multiply the two fractions together.
÷ =
We will turn our 25 on top into a fraction with a denominator of 1.
We are at the point where we should multiply the top fraction by the reciprocal of the bottom.
We have enough flour to make exactly 31 whole cakes.
To recap, we usually begin by changing our whole number into a fraction with a denominator of 1.
When we divide two fractions by eachother, we simply multiply the top fraction by the reciprocal of the bottom one.

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