# Operations with fractions · Grade 6

> Operations with fractions, Grade 6: A whole number times a fraction and more. Explanation, worked examples and free practice following the Israeli curriculum.

In Operations with fractions (Grade 6) you practise 7 skills: A whole number times a fraction · A fraction of a fraction · Dividing by a fraction · Bigger or smaller? · Expanding is not multiplying · Part, whole and which part · Fraction word problems.

To multiply a whole number by a fraction, multiply the number by the numerator and keep the denominator. For example, 3 lots of 2/5 make 6/5, which is 1 1/5.

A fraction of a fraction is a multiplication: multiply the numerators and multiply the denominators. Half of 3/4 is 3/8.

Dividing by a fraction asks how many times the fraction goes into the number. There are 12 quarters in 3, so 3 divided by 1/4 is 12. To divide by a fraction you can multiply by its reciprocal.

Multiplying by a fraction less than 1 makes a number smaller, and multiplying by a fraction greater than 1 makes it bigger. Expanding a fraction is not multiplying: expanding 3/4 by 2 gives 6/8, which has the same value. Multiplying 3/4 by 2 gives 6/4, which is bigger.

**Tip:** Before you calculate, ask yourself whether the answer should be bigger or smaller than the number you started with.

## What you learn

### A whole number times a fraction

- Example: Work out: 6 × 3/8
- Answer: 2 1/4
- Solution: 6 × 3/8 = 18/8 18/8 = 2 1/4

### A fraction of a fraction

- Example: Work out: 1/2 × 3/4 (A square divided into 8 equal squares, 2 rows and 4 columns. In one row, 3 squares are shaded.)
- Answer: 3/8
- Solution: One row is 1/2 of the square, and 3/4 of it is shaded: 3 squares out of 8. 1/2 × 3/4 = 3/8

### Dividing by a fraction

- Example: Work out: 5 ÷ 5/6
- Answer: 6
- Solution: 5 ÷ 5/6 = 5 × 6/5 = 30/5 = 6

### Bigger or smaller?

- Example: Is the product 12 × 2/3 bigger than 12, smaller than 12 or equal to 12?
- Options: smaller than 12 · equal to 12 · bigger than 12
- Answer: smaller than 12
- Solution: 2/3 is less than 1, so multiplying by it makes the number smaller. The product is smaller than 12.

### Expanding is not multiplying

- Example: Expand the fraction 5/12 by 2.
- Answer: 10/24
- Solution: 5 × 2 = 10 12 × 2 = 24 5/12 = 10/24 The value of the fraction has not changed: the parts are smaller, and there are more of them.

### Part, whole and which part

- Example: What part is 11 out of 20? Write it as a fraction.
- Answer: 11/20
- Solution: 11/20

### Fraction word problems

- Example: A library has 99 books, and 5/9 of them are science books. How many science books does it have?
- Answer: 55
- Solution: 99 ÷ 9 = 11 11 × 5 = 55

## Not on the site yet

- The hidden factor
- Matching a question to a calculation

The exercises are made by rules and the answers are worked out in code. The topic follows the new Israeli elementary programme (2023).

[Practise on the site](https://kixplo.com/il/en/) · [All Grade 6 topics](https://kixplo.com/il/en/math/grade-6/2023/)