Imagine you have 1/4 of a pie to slip with your friend. Explain how you would divide fractions to figure our how much of the pie each of you will have.
To divide the 1/4 pie equally between you and your friend, you need to divide the fraction 1/4 by the number of people, which is 2 (one for you and one for your friend).
To do this, you can multiply the fraction 1/4 by its reciprocal, which is 2/1 because dividing by a fraction is the same as multiplying by its reciprocal.
So, multiplying 1/4 by 2/1:
(1/4) × (2/1) = (1 × 2) / (4 × 1)
= 2/4
Therefore, each of you will have 2/4 of the pie. However, this fraction can be simplified. Both 2 and 4 can be divided by their greatest common divisor, which is 2. Dividing both the numerator and denominator of 2/4 by 2:
(2 ÷ 2) / (4 ÷ 2) = 1/2
Hence, each of you will have 1/2 of the pie.
To divide fractions and determine how much of the pie each of you will have, you would follow the steps below:
Step 1: Write down the fraction representing the amount of pie you have, which is 1/4.
Step 2: Invert the fraction of your friend's share. Since you are dividing fractions, you need to find the reciprocal of the fraction. So, if your friend's share is 1, you would write it as 1/1, and then invert it to become 1/1.
Step 3: Multiply the two fractions together. Multiply the numerator of the first fraction (1) with the numerator of the second fraction (1), which gives you 1. Multiply the denominator of the first fraction (4) with the denominator of the second fraction (1), which also gives you 4. Therefore, the result of 1/4 multiplied by 1/1 is 1/4.
Step 4: Simplify the resulting fraction if possible. In this case, 1/4 is already in its simplest form, so no further simplification is needed.
Step 5: Interpret the resulting fraction. The resulting fraction, 1/4, represents the share of the pie each of you will have. Since the denominator is 4, it means that each of you will have 1 part out of 4 parts of the whole pie.
Therefore, both you and your friend will have 1/4 (or 1 out of 4) of the pie.