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Lesson 6: Multiplying fractions word problems

# Multiply fractions: FAQ

## How do we multiply fractions and whole numbers visually?

There are many different ways to multiply fractions visually. We can use area models, groups of objects, tape diagrams, or number lines. All of these methods help us to see how the multiplication works.
For example, we can use a number line to show how we multiply start fraction, 4, divided by, 5, end fraction, times, 10 by drawing a number line from 0 to 10 and then splitting the number line into 5 equal parts.
Next, we can find start fraction, 4, divided by, 5, end fraction of 10 on the number line by counting 4 lengths of 2:
So, start fraction, 4, divided by, 5, end fraction, times, 10, equals, 8.
Try it yourself with these exercises:

## What are the strategies we can use to multiply fractions by fractions?

Just like multiplying fractions and whole numbers, we can use different visuals to help us multiply fractions. Some popular strategies are using area models, tape diagrams, or number lines.
We can use an area model to multiply start color #543b78, start fraction, 3, divided by, 10, end fraction, end color #543b78, times, start color #0c7f99, start fraction, 1, divided by, 4, end fraction, end color #0c7f99. First, we can create a striped rectangle by multiplying its start color #7854ab, start text, w, i, d, t, h, end text, end color #7854ab, times, start color #11accd, start text, h, e, i, g, h, t, end text, end color #11accd.
The striped rectangle would show start color #7854ab, start fraction, 3, divided by, 10, end fraction, end color #7854ab of a unit wide and start color #11accd, start fraction, 1, divided by, 4, end fraction, end color #11accd of a unit high. The amount overlapping would be our product. In this example, the product is start fraction, 3, divided by, 40, end fraction.
Try it yourself with these exercises:

## How do we multiply mixed numbers?

To multiply mixed numbers, we can convert them to improper fractions and then multiply the fractions as we normally would. For example, to multiply 1, start fraction, 1, divided by, 2, end fraction by 2, start fraction, 1, divided by, 4, end fraction, we first convert them to improper fractions: start fraction, 3, divided by, 2, end fraction, times, start fraction, 9, divided by, 4, end fraction. Then, we multiply the numerators and denominators: start fraction, 27, divided by, 8, end fraction.
Try it yourself with this exercise:

## How do we find the area of rectangles with fraction side lengths?

To find the area of any rectangle, we can multiply the length times the width. If the rectangle has fractional side lengths, we multiply the two fractions together.
For example, to find the area of a rectangle with side lengths start fraction, 1, divided by, 2, end fraction and start fraction, 2, divided by, 3, end fraction, we multiply start fraction, 1, divided by, 2, end fraction, times, start fraction, 2, divided by, 3, end fraction, equals, start fraction, 2, divided by, 6, end fraction, equals, start fraction, 1, divided by, 3, end fraction.
Try it yourself with this exercise:

## Why do we need to learn how to multiply fractions?

Multiplying fractions is a key skill in math that you'll use throughout your academic career and in the real world. For example, if you need to scale a recipe up or down, you might need to multiply fractions in order to adjust the quantities of the ingredients.