Fractions: meaning and operations · Grade 5
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
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
Between two fractions
For example: Which picture marks this fraction? 1/5
Answer and solution
The answer: D
The fraction 1/5 equals 2/10, so its point is on that mark: picture D.
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
Not on the site yet
Parts of this topic that are not built 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, so there are new exercises every time. The topic follows the new Israeli elementary programme (2023).