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Lesson 5: Dividing fractions and whole numbers word problems

# Divide fractions: FAQ

## What does it mean to divide fractions?

When we divide one fraction by another, we're finding out how many times one fraction fits into another. For example, start fraction, 1, divided by, 2, end fraction, divided by, start fraction, 1, divided by, 4, end fraction tells us how many one-fourths are in one-half.
Try it yourself with these exercises:

## How is dividing fractions related to multiplying fractions?

When we divide fractions, we can use the reciprocal of the divisor (the fraction we are dividing by) to multiply instead.
For example, start fraction, 1, divided by, 2, end fraction, divided by, start fraction, 1, divided by, 4, end fraction, equals, start fraction, 1, divided by, 2, end fraction, times, start fraction, 4, divided by, 1, end fraction, equals, 2.
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## How can we use visuals to help us understand fraction division?

We can use pictures, models, or diagrams to show how dividing fractions works. For example, we can show start fraction, 1, divided by, 2, end fraction, divided by, start fraction, 1, divided by, 4, end fraction by drawing a half circle and dividing it into four equal parts to see that there are two one-fourths in one-half.
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## What is a unit fraction and how do we divide with them?

A unit fraction is a fraction with a numerator of 1. For example, start fraction, 1, divided by, 2, end fraction, start fraction, 1, divided by, 3, end fraction, and start fraction, 1, divided by, 4, end fraction are all unit fractions.
When we divide a unit fraction by a whole number, we multiply the denominator by the whole number. For example, start fraction, 1, divided by, 2, end fraction, divided by, 2, equals, start fraction, 1, divided by, 4, end fraction.
When we divide a whole number by a unit fraction, we multiply the whole number by the reciprocal of the unit fraction. For example, 2, divided by, start fraction, 1, divided by, 2, end fraction, equals, 2, times, start fraction, 2, divided by, 1, end fraction, equals, 4.
Try it yourself with these exercises:

## What are some common mistakes people make when dividing fractions?

Some common mistakes include:
• forgetting to find the reciprocal of the divisor when using the multiplication method
• dividing the numerators instead of multiplying them when using the multiplication method
• forgetting to simplify the answer when possible