Fractions · Grade 4
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
For example: What part of the rectangle is shaded? Write it as a fraction.
Answer and solution
The answer: 1/4
The rectangle is divided into 4 equal parts, and one part is shaded. 1/4
Part of a set
For example: What is 1/3 of 6?
Answer and solution
The answer: 2
One part out of 3: 6 ÷ 3 = 2
Fractions on the number line
For example: Which fraction does the dot mark?
- 3/4
- 1/4
- 2/4
Answer and solution
The answer: 3/4
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
For example: Which fraction equals 1?
- 12/13
- 1/12
- 12/12
Answer and solution
The answer: 12/12
The numerator equals the denominator, so: 12/12 = 1
Improper fractions and mixed numbers
For example: Write as a mixed number: 5/2
Answer and solution
The answer: 2 1/2
2 wholes have 4 parts: 2 × 2 = 4 One more part is left: 5/2 = 2 1/2
Equivalent fractions
For example: The two bars are the same whole. Fill in the numerator: 2/4 = ☐/2
Answer and solution
The answer: 1
The shaded part is covered exactly by one part out of 2: 2/4 = 1/2
Comparing fractions
For example: Fill in the sign: 3/6 ☐ 5/6
Answer and solution
The answer: <
The denominators are the same, and 5 parts are more than 3 parts. 3/6 < 5/6
Adding and subtracting fractions
For example: Work out: 1/3 + 2/3
Answer and solution
The answer: 1
1/3 + 2/3 = 1
A whole number times a fraction
For example: Work out: 2 × 3/7
Answer and solution
The answer: 6/7
Multiplying by a whole number is repeated addition: 3/7 + 3/7 = 6/7 2 × 3/7 = 6/7
Fraction equations
For example: Find the missing number: ☐ + 1/4 = 3/4
Answer and solution
The answer: 1/2
3/4 − 1/4 = 2/4 . Check: 2/4 + 1/4 = 3/4
Fraction word problems
For 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 and solution
The answer: 4/7
1/7 + 3/7 = 4/7
The exercises are made by rules and the answers are worked out in code, so there are new exercises every time. The topic follows the new Israeli elementary programme (2023).