# Fractions: meaning and operations · Grade 5

> Fractions: meaning and operations, Grade 5: A fraction is a division and more. Explanation, worked examples and free practice following the Israeli curriculum.

In Fractions: meaning and operations (Grade 5) you practise 11 skills: A fraction is a division · A part of a whole · A part of a quantity: three meanings · Improper fractions and mixed numbers · Fractions on the number line · Expanding and reducing · Comparing fractions · Between two fractions · Adding and subtracting fractions · Fraction equations · Fraction word problems.

A fraction is also the answer to a division: 25 ÷ 4 = 25/4 = 6 1/4. A ribbon 25 metres long can be cut into 4 equal parts, and each part is 6 1/4 metres long. But 25 books cannot be shared equally into 4 boxes: each box gets 6 books, and one book is left over.

A fraction as a part of a quantity has three meanings. Find the part: 3/4 of 20 children is 15 children. Find the whole: if 6 children are 1/5 of a group, the group has 30 children. And find which part: 4 out of 20 is 4/20, that is 1/5.

A fraction has many names: expand or simplify it by multiplying or dividing the numerator and the denominator by the same number. That is how to compare fractions: write them with a common denominator. A fraction greater than 1 can be written as a mixed number: 7/4 = 1 3/4. And between any two different fractions there is another fraction, so there are infinitely many between them.

To add or subtract fractions, write them with a common denominator. There are three cases: one denominator is a multiple of the other (1/2 + 1/4 = 2/4 + 1/4 = 3/4); the denominators have a common factor (1/4 + 1/6 = 3/12 + 2/12 = 5/12); or they have no common factor except 1 (1/2 + 1/3 = 3/6 + 2/6 = 5/6). Equations are solved the same way: to find the missing number in ☐ + 1/3 = 5/6, subtract: 5/6 − 1/3 = 1/2.

**Tip:** Before you compare two fractions, check whether you can compare each of them with a half.

## What you learn

### A fraction is a division

- Example: One pizza is shared equally among 5 children. What part of a pizza does each child get?
- Answer: 1/5
- Solution: Each child got one part of 1/5 of a pizza, so: 1 ÷ 5 = 1/5

### A part of a whole

- Example: What part of the rectangle is shaded? Write it as a fraction. (A rectangle divided into 4 equal parts. One part is shaded.)
- Answer: 1/4
- Solution: The rectangle is divided into 4 equal parts, and one part is shaded. 1/4

### A part of a quantity: three meanings

- Example: What part is 4 out of 15? Write it as a fraction.
- Answer: 4/15
- Solution: 4/15

### Improper fractions and mixed numbers

- Example: Write as a mixed number: 4/3
- Answer: 1 1/3
- Solution: One whole has 3 parts: 1 × 3 = 3 One more part is left: 4/3 = 1 1/3

### Fractions on the number line

- Example: Which number is marked on the number line? (A number line from 0 to 1. Between each pair of consecutive whole numbers there are 4 equal steps, and a point is marked on the line.)
- Options: 2/8 · 2/5 · 4/2 · 2/4
- Answer: 2/4
- Solution: The point is 2 steps after 0, and each step is 1/4, so it is: 2/4

### Expanding and reducing

- Example: Fill in the numerator: 1/5 = ☐/10
- Answer: 2
- Solution: The denominator got 2 times bigger: 5 × 2 = 10 so the numerator does too: 1 × 2 = 2 1/5 = 2/10

### Comparing fractions

- Example: Fill in the sign: 5/10 ☐ 3/10
- Answer: >
- Solution: 5/10 > 3/10

### Between two fractions

- Example: Which picture marks this fraction? 1/5
- Options: A (A number line from 0 to 1, cut into ten equal steps, with a point on the eighth mark after 0.) · B (A number line from 0 to 1, cut into ten equal steps, with a point on the sixth mark after 0.) · C (A number line from 0 to 1, cut into ten equal steps, with a point on the third mark after 0.) · D (A number line from 0 to 1, cut into ten equal steps, with a point on the second mark after 0.)
- Answer: D
- Solution: The fraction 1/5 equals 2/10, so its point is on that mark: picture D.

### Adding and subtracting fractions

- Example: Work out: 3/9 − 2/9
- Answer: 1/9
- Solution: 3/9 − 2/9 = 1/9

### Fraction equations

- Example: Find the missing number: 1 = ☐ + 10/11
- Answer: 1/11
- Solution: To find a missing addend, take the known addend away from the total: 1 − 10/11 = 11/11 − 10/11 = 1/11 Check: 1 = 1/11 + 10/11

### Fraction word problems

- Example: A cake was cut into 8 equal pieces. Noa ate 2 pieces, and Itai ate 2 pieces. What part of the cake is left?
- Answer: 1/2
- Solution: 2/8 + 2/8 = 4/8 8/8 − 4/8 = 4/8

## Not on the site yet

- Two numbers on the marked part of a line
- Finding the whole from a pictured part
- Who shot better? Not enough information

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 5 topics](https://kixplo.com/il/en/math/grade-5/2023/)