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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.
A number line labeled 0 to 10 with tick marks every 1 unit. Above the number line is a tape diagram divided into 5 equal parts, each labeled one-fifth. A curved bracket across the tape diagram is labeled 10.
Next, we can find start fraction, 4, divided by, 5, end fraction of 10 on the number line by counting 4 lengths of 2:
A number line labeled 0 to 10 with tick marks every 1 unit. An arrow moves right along the number line from 0 to tick mark 8. Above the number line is a tape diagram divided into 5 equal parts. 4 parts are shaded. The shaded parts of the tape diagram are between tick mark 0 and tick mark 8 of the number line. A curved bracket above the shaded part of the tape diagram is labeled four-fifths times ten.
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.
A rectangle that has been split into 40 parts, set in 4 rows of 10 parts each. The parts in the top row has been shaded blue. The parts in the left 3 columns have been shaded purple. The first 3 parts in the top row are striped to show they are shaded both blue and purple. Along the top of the rectangle, the columns are labeled one-tenth. A bracket across the first 3 columns is labeled three-tenths. Along the left side of the rectangle, the rows are labeled one-fourth. A bracket across the top row is labeled one-fourth.
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.

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• Thanks that helps, I understand it more.