Fractions: Make, Compare and Calculate
Year 6 | Ages 10–11 | Beginner
Instructions: Work through each activity and show your method in the answer boxes. Use common factors to simplify and common multiples to find common denominators. Check that your answers are sensible; simplify each fraction where possible.
Simplify and Find Common Denominators
For Questions 1–3, divide the numerator and denominator by the same common factor to simplify. For Questions 4–5, find a common denominator and write each equivalent fraction. Show your working.
1. Simplify 12/18.
2. Simplify 15/25.
3. Simplify 21/28.
4. Write 2/3 and 3/4 as equivalent fractions with denominator 12.
5. Write 5/6 and 1/4 as equivalent fractions with denominator 12.
Compare and Order Fractions
Use equivalent fractions or a common denominator to compare the fractions. For Questions 1–3, write <, > or = in the box. For Questions 4–5, write the fractions in the requested order.
1. 3/4 5/8
2. 2/3 4/6
3. 7/6 5/4
4. Order from smallest to largest: 1/2, 3/4, 2/3.
5. Order from largest to smallest: 5/4, 7/6, 3/2.
Add and Subtract Fractions
Find a common denominator before adding or subtracting fractions with different denominators. Convert mixed numbers to improper fractions if that helps. Give each answer in its simplest form.
1. 1/2 + 1/3 =
2. 3/4 − 1/6 =
3. 2 1/3 + 1 1/6 =
4. 3 1/4 − 1 1/2 =
5. 5/6 + 3/8 =
Multiply and Divide Fractions
To multiply, multiply the numerators and multiply the denominators, then simplify. To divide a proper fraction by a whole number, divide the fraction by that number and simplify your result.
1. 2/3 × 3/5 =
2. 4/7 × 1/2 =
3. 3/4 × 2/5 =
4. 1/2 ÷ 3 =
5. 3/5 ÷ 2 =
Fractions, Decimals and Percentages
Use familiar equivalences to complete each conversion. For example, 1/2 = 0.5 = 50%. Write a fraction in its simplest form where needed.
1. Write 1/4 as a decimal and a percentage.
2. Write 3/5 as a decimal and a percentage.
3. Write 0.75 as a fraction in its simplest form and as a percentage.
4. Write 40% as a fraction in its simplest form and as a decimal.
5. Complete the equivalence: 7/10 = ___ = ___%.
Activity 1: 2/3 ; 3/5 ; 3/4 ; 8/12 and 9/12 ; 10/12 and 3/12
Activity 2: > ; = ; < ; 1/2, 2/3, 3/4 ; 3/2, 5/4, 7/6
Activity 3: 5/6 ; 7/12 ; 3 1/2 ; 1 3/4 ; 29/24 (or 1 5/24)
Activity 4: 2/5 ; 2/7 ; 3/10 ; 1/6 ; 3/10
Activity 5: 0.25 and 25% ; 0.6 and 60% ; 3/4 and 75% ; 2/5 and 0.4 ; 0.7 and 70%
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