Fractions: meaning and operations · Years 5–6
In Fractions: meaning and operations (Years 5–6) you practise 10 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 · 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
For example: One pizza is shared equally among 5 children. What part of a pizza does each child get?
Answer and solution
The answer: 1/5
Each child got one part of 1/5 of a pizza, so: 1 ÷ 5 = 1/5
A 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
A part of a quantity: three meanings
For example: What part is 4 out of 15? Write it as a fraction.
Answer and solution
The answer: 4/15
4/15
Improper fractions and mixed numbers
For example: Write as a mixed number: 4/3
Answer and solution
The answer: 1 1/3
One whole has 3 parts: 1 × 3 = 3 One more part is left: 4/3 = 1 1/3
Fractions on the number line
For example: Which number is marked on the number line?
- 2/8
- 2/5
- 4/2
- 2/4
Answer and solution
The answer: 2/4
The point is 2 steps after 0, and each step is 1/4, so it is: 2/4
Expanding and reducing
For example: Fill in the numerator: 1/5 = ☐/10
Answer and solution
The answer: 2
The denominator got 2 times bigger: 5 × 2 = 10 so the numerator does too: 1 × 2 = 2 1/5 = 2/10
Comparing fractions
For example: Fill in the sign: 5/10 ☐ 3/10
Answer and solution
The answer: >
5/10 > 3/10
Adding and subtracting fractions
For example: Work out: 3/9 − 2/9
Answer and solution
The answer: 1/9
3/9 − 2/9 = 1/9
Fraction equations
For example: Find the missing number: 1 = ☐ + 10/11
Answer and solution
The answer: 1/11
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
For 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 and solution
The answer: 1/2
2/8 + 2/8 = 4/8 8/8 − 4/8 = 4/8
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 national curriculum in England: mathematics (key stages 3 and 4).