Operations with fractions · Grade 6
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
For example: Work out: 6 × 3/8
Answer and solution
The answer: 2 1/4
6 × 3/8 = 18/8 18/8 = 2 1/4
A fraction of a fraction
For example: Work out: 1/2 × 3/4
Answer and solution
The answer: 3/8
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
For example: Work out: 5 ÷ 5/6
Answer and solution
The answer: 6
5 ÷ 5/6 = 5 × 6/5 = 30/5 = 6
Bigger or smaller?
For example: Is the product 12 × 2/3 bigger than 12, smaller than 12 or equal to 12?
- smaller than 12
- equal to 12
- bigger than 12
Answer and solution
The answer: smaller than 12
2/3 is less than 1, so multiplying by it makes the number smaller. The product is smaller than 12.
Expanding is not multiplying
For example: Expand the fraction 5/12 by 2.
Answer and solution
The answer: 10/24
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
For example: What part is 11 out of 20? Write it as a fraction.
Answer and solution
The answer: 11/20
11/20
Fraction word problems
For example: A library has 99 books, and 5/9 of them are science books. How many science books does it have?
Answer and solution
The answer: 55
99 ÷ 9 = 11 11 × 5 = 55
Not on the site yet
Parts of this topic that are not built yet: The hidden factor · Matching a question to a calculation.
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).