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This lesson helps you interpret and compute products and quotients and solve word problems involving **division of fractions** by fractions. Visual representations such as fraction models and equations would serve as guides to represent the problem.

**See the fact file below for more information on the multiplying and dividing fractions or alternatively, you can download our 29-page Multiplying and Dividing Fractions worksheet pack to utilise within the classroom or home environment.**

## Key Facts & Information

### MULTIPLYING FRACTIONS

- How do we multiply fractions? Let us start with an example. What is the product of 4 and 1/3? This means it’s 4 wholes of one third.
- The concept is the same as when we multiply whole numbers, for example:
- 4 x 5 = 5 + 5 + 5 + 5 = 20

- Now, when we multiply numbers, we often use the fact that when we multiply numbers, order does not matter; it is commutative. This means, for example, 4 x 5 = 5 x 4, so that:
- 5 + 5 + 5 + 5 = 4 + 4 + 4 + 4 + 4
- 20 = 20

- Let us examine what this means when we are studying fractions. We expect to find that 6 x 1/3 = 1/3 x 6. Now:
- 6 x 1/3 = 1/3 + 1/3 + 1/3 + 1/3 + 1/3 + 1/3

- And (1/3 + 1/3 + 1/3) + (1/3 + 1/3 + 1/3) equals 1 + 1 = 2.
- On the other hand, 1/3 x 6 means one-third of 6, and that is just 6 divided by 3, so that we have 6 wholes split into 3 equal parts, giving us a product of 2.
- Let’s take a look at another example. Calculate the product of 5 and 2/3.
- This is just the same as two-thirds of 5. Now, one-third of 5 is 5/3, so two-thirds of 5 is 2 x 5/3 which is equal to 10/3.
- Any whole number can be written as a fraction. For example, 2 can be written as 2/1, 4/2, 6/3, and so on. Any number can be used, as long as the numerator is twice the denominator.
- Now, let us take a look at multiplying fractions by other fractions. For example, what is the product of 1/3 and 1/2? This means we are getting one third of one half.
- If we take a half and divide it into 3, we have 1/6 of a whole. We can see this if we also partition the other half into 3 pieces. So, we have:
- 1/3 x 1/2 = (1×1)/(3×2) = 1/6

- The product of 1/3 and 1/2 is 1/6, and we obtained it by multiplying the two numerators and then the two denominators.
- What happens if we have mixed fractions? We turn them into improper fractions first, then multiply.
- For example, find the product of 2 1/3 and 3/4.
- To multiply fractions, multiply the numerators and denominators separately. To multiply mixed fractions, turn them into improper fractions first before performing multiplication.

### DIVIDING FRACTIONS

- Let’s now look at what happens when we divide fractions. For example, divide 1/4 by 2.
- Dividing by 2 and multiplying by a half are the same thing. Therefore, we could write it as: (1/4) / 2 = 1/4 x 1/2 = 1/8
- Here’s another example. What is the quotient of 1/3 and 4?
- Dividing 4 by 1/3 is the same as multiplying 1/3 by 1/4. Hence, we get a quotient of 1/12.
- In both cases, we noticed that in dividing fractions by a number, we can instead multiply the denominator by that number. Another way of saying this is we write the divisor, the number we are dividing by, as a fraction, given that it is a whole number. Upon doing so, we turn that fraction upside-down and multiply instead.
- Let’s now try to divide fractions by fractions. For example, find the quotient of 1/2 and 1/4.
- Following the rule, we get:
- 1/2 x 4/1 = (1×4)/(2×1) = 4/2 = 2

- To divide fractions, turn the second fraction upside-down and multiply. To divide mixed fractions, turn them into improper fractions first.

**Multiplying and Dividing Fractions Worksheets**

This is a fantastic bundle which includes everything you need to know about the multiplying and dividing fractions across 29 in-depth pages. These are** ready-to-use Multiplying and Dividing Fractions worksheets that are perfect for teaching students how to interpret and compute products and quotients and solve word problems involving division of fractions by fractions. Visual representations such as fraction models and equations would serve as guides to represent the problem. **

### Complete List Of Included Worksheets

- Lesson Plan
- Multiplying and Dividing Fractions
- Multiply or Divide
- Fraction Times a Number
- Fraction Times a Fraction
- Filling In
- Multiplication Word Problems
- Fraction Divided By a Number
- Fraction Divided By a Fraction
- Filling In 2.0
- Division Word Problems
- Real Wor(l)d Problems

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**Use With Any Curriculum**

These worksheets have been specifically designed for use with any international curriculum. You can use these worksheets as-is, or edit them using Google Slides to make them more specific to your own student ability levels and curriculum standards.