# Fractions · Grade 4

> Fractions, Grade 4: Part of a whole, Part of a set, Equivalent fractions and more. Explanation, worked examples and free practice following the Israeli curriculum.

In Fractions (Grade 4) you practise 11 skills: Part of a whole · Part of a set · Fractions on the number line · Fractions equal to 1 and to 0 · Improper fractions and mixed numbers · Equivalent fractions · Comparing fractions · Adding and subtracting fractions · A whole number times a fraction · Fraction equations · Fraction word problems.

A fraction is part of a whole cut into equal parts: the denominator says how many parts the whole is cut into, and the numerator how many are taken. 3/5 is three fifths: a fifth and a fifth and a fifth. A fraction is also a point on the number line: cut the line from 0 to 1 into equal parts and count parts from 0.

When the numerator equals the denominator, the fraction equals 1, for example 4/4 = 1. When the numerator is 0, the fraction equals 0. When the numerator is greater than the denominator, the fraction is greater than 1 and can be written as a mixed number: 7/4 = 1 3/4.

A fraction has more than one name: 1/2 and 2/4 cover the same part of the same whole. With the same denominator, the fraction with the greater numerator is greater. To add or subtract fractions with the same denominator, add or subtract the numerators; the denominator stays: 2/7 + 3/7 = 5/7. When one denominator is double the other, the bars show how to write both in the same parts: 1/2 = 2/4, so 1/2 + 1/4 = 3/4.

A whole number times a fraction is repeated addition: 3 × 2/5 = 2/5 + 2/5 + 2/5 = 6/5 = 1 1/5. Addition and subtraction undo each other, so a missing number is found with the other operation: in ☐ + 2/5 = 4/5 the missing number is 4/5 − 2/5 = 2/5.

**Tip:** When you compare a fraction with a whole or with a half, ask: how much is missing to make a whole?

## What you learn

### 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

### Part of a set

- Example: What is 1/3 of 6?
- Answer: 2
- Solution: One part out of 3: 6 ÷ 3 = 2

### Fractions on the number line

- Example: Which fraction does the dot mark? (A number line from 0 to 1, cut into 4 equal parts, with a dot on tick 3 after 0.)
- Options: 3/4 · 1/4 · 2/4
- Answer: 3/4
- Solution: The line is cut into 4 equal parts, so each part is 1/4 . The dot is 3 parts after 0, so it marks: 3/4

### Fractions equal to 1 and to 0

- Example: Which fraction equals 1?
- Options: 12/13 · 1/12 · 12/12
- Answer: 12/12
- Solution: The numerator equals the denominator, so: 12/12 = 1

### Improper fractions and mixed numbers

- Example: Write as a mixed number: 5/2
- Answer: 2 1/2
- Solution: 2 wholes have 4 parts: 2 × 2 = 4 One more part is left: 5/2 = 2 1/2

### Equivalent fractions

- Example: The two bars are the same whole. Fill in the numerator: 2/4 = ☐/2 (A bar divided into 4 equal parts, 2 parts shaded.) (A bar of the same length, divided into 2 equal parts.)
- Answer: 1
- Solution: The shaded part is covered exactly by one part out of 2: (The second bar, one part shaded.) 2/4 = 1/2

### Comparing fractions

- Example: Fill in the sign: 3/6 ☐ 5/6
- Answer: <
- Solution: The denominators are the same, and 5 parts are more than 3 parts. 3/6 < 5/6

### Adding and subtracting fractions

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

### A whole number times a fraction

- Example: Work out: 2 × 3/7
- Answer: 6/7
- Solution: Multiplying by a whole number is repeated addition: 3/7 + 3/7 = 6/7 2 × 3/7 = 6/7

### Fraction equations

- Example: Find the missing number: ☐ + 1/4 = 3/4
- Answer: 1/2
- Solution: 3/4 − 1/4 = 2/4 . Check: 2/4 + 1/4 = 3/4

### Fraction word problems

- Example: A cake was cut into 7 equal pieces. Sophie ate one piece, and Ben ate 3 pieces. What part of the cake did they eat together?
- Answer: 4/7
- Solution: 1/7 + 3/7 = 4/7

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 4 topics](https://kixplo.com/il/en/math/grade-4/2023/)