Fractions Practice Set 2
Extra fraction practice, page 14 style.
This booklet is extra practice on fractions. It matches page 14 of your CGP book.
What you’ll practise
There are five sections. You’ll practise:
- Equivalent fractions — fill in the missing number to make pairs equivalent.
- Ordering fractions — compare and pick the smallest.
- Adding and subtracting fractions, including when one is a whole numberA number with no fractional part: 0, 1, 2, 3, 4, ….
- Mixed number arithmetic — adding and subtracting mixed numbers.
- Finding a fraction of a number — like 3/4 of 28.
How to use the booklet
The five sections are all on the same level. Work through them in order.
If you get stuck on any section, that’s OK — that’s what your tutor is here for. The section you stop on tells them exactly where you need help.
The five exercises:
· Section A — Equivalent fractions. Find the missing number to make pairs equivalent.
· Section B — Ordering fractions. Compare and pick the smallest.
· Section C — Add and subtract proper fractions. Including whole minus fraction.
· Section D — Mixed number arithmetic. Always convert to improper first.
· Section E — Fraction of a number. Divide by the denominator, multiply by the numerator.
· Section A — Equivalent fractions. Find the missing number to make pairs equivalent.
· Section B — Ordering fractions. Compare and pick the smallest.
· Section C — Add and subtract proper fractions. Including whole minus fraction.
· Section D — Mixed number arithmetic. Always convert to improper first.
· Section E — Fraction of a number. Divide by the denominator, multiply by the numerator.
TUTOR — MATERIALS TO HAVE READY
For this paper:
- Pen and paper for working longhand.
- Times tables — this paper is non-calculator. If pupil is shaky on tables, that bottleneck will show up in Sections C, D, and E.
- Watch the conversion to mixed numbers — pupils often get the improper fraction right and then mess up the final conversion. Common error: getting the whole part right but mis-stating the remainderWhat’s left over after dividing. 7 ÷ 2 = 3 with remainder 1..
SECTION A · EQUIVALENT FRACTIONS
Find the missing number
Aim: Find an equivalent fraction by scaling top and bottom by the same factorA whole number that divides another exactly, with no remainder. 3 is a factor of 12 because 12 ÷ 3 = 4..
Rule: Multiply (or divide) BOTH the numerator AND the denominator by the same number. Value stays the same.
3/4 = 6/8 = 9/12 = 15/20 = …
3/4 = 6/8 = 9/12 = 15/20 = …
Worked example
2/7 = ?/35. Find the numerator.
- Denominator goes from 7 to 35: multiply by 5.
- Apply to numerator: 2 × 5 = 10.
- So 2/7 = 10/35. ✓
SECTION B · ORDERING
Compare fractions
Aim: Decide which of two or three fractions is smallest.
Find a common denominator (the LCMLowest common multiple. The smallest number that is a multiple of both a and b. LCM(4, 6) = 12.). Convert each fraction. Compare numerators.
Worked example
Which is smaller: 2/5 or 1/4?
- LCMLowest common multiple. The smallest number that is a multiple of both a and b. LCM(4, 6) = 12.(5, 4) = 20.
- 2/5 = 8/20. 1/4 = 5/20.
- 5/20 < 8/20, so 1/4 is smaller. ✓
SECTION C · ADD AND SUBTRACT
Add and subtract proper fractions
Aim: Fluent addition and subtraction with different denominators, and with a whole numberA number with no fractional part: 0, 1, 2, 3, 4, … on one side.
Common denominator first. Add or subtract numerators only. Simplify if possible.
For a whole numberA number with no fractional part: 0, 1, 2, 3, 4, …, write it over the denominator: 5 = 15/3.
For a whole numberA number with no fractional part: 0, 1, 2, 3, 4, …, write it over the denominator: 5 = 15/3.
Watch out
1/3 + 1/6 is NOT 2/9. You can’t just add tops and bottoms. Common denominator first: 1/3 = 2/6, then 2/6 + 1/6 = 3/6 = 1/2.
SECTION D · MIXED NUMBERS
Mixed number arithmetic
Aim: Add and subtract mixed numbers reliably, including the conversion back at the end.
The process:
1. Convert both mixed numbers to improper fractions.
2. Find a common denominator.
3. Add or subtract numerators.
4. Convert the result back to a mixed number.
5. Simplify the fractional part if needed.
1. Convert both mixed numbers to improper fractions.
2. Find a common denominator.
3. Add or subtract numerators.
4. Convert the result back to a mixed number.
5. Simplify the fractional part if needed.
Watch out
Don’t try to add the whole parts separately and the fractions separately when subtracting — you’ll often need to “borrow” from the whole part. The improper-fraction route avoids this entirely.
SECTION E · FRACTION OF A NUMBER
Find a fraction of a number
Aim: Calculate “X/Y of N” with no calculator.
Two steps:
1. Divide N by the denominator Y.
2. Multiply the result by the numerator X.
So 3/4 of 20 = (20 ÷ 4) × 3 = 5 × 3 = 15.
1. Divide N by the denominator Y.
2. Multiply the result by the numerator X.
So 3/4 of 20 = (20 ÷ 4) × 3 = 5 × 3 = 15.
Worked example
Find 5/6 of 42.
- Divide by 6: 42 ÷ 6 = 7.
- Multiply by 5: 7 × 5 = 35. ✓
VOCABULARY
- Numerator
- The top number of a fraction.
- Denominator
- The bottom number of a fraction.
- Equivalent fraction
- A fraction with a different look but the same value.
- Lowest terms
- Top and bottom share no common factor other than 1.
- Improper fraction
- Top is bigger than (or equal to) the bottom. 7/3.
- Mixed number
- Whole number plus a proper fraction. 2 1/3.
- Common denominator
- The LCM of two or more denominators. Used to compare or add/subtract fractions.
Recap
- Equivalent: multiply top and bottom by the same number.
- Compare: common denominator, then compare numerators.
- Add/subtract: common denominator, then numerators only.
- Mixed numbers: convert to improper first.
- Fraction of: divide by denominator, multiply by numerator.
Part Two
Now try the practice questions
45 questions across three sections, 30 minutes when you’re ready. The step-by-step walkthroughs unlock after you mark.
Instructions
- Type each numeric answer in the box. For sign questions, use a minus sign (e.g.
-7). For radio questions, tap your choice. - You can start the 30-minute timer or work untimed.
- When finished, click Mark My Work. Your answers will then be locked, the correct answers will appear under each wrong question with the working, and you will get 5 similar practice questions inline for each one you missed.
Timed practice · 30 minutes
When you’re ready, start the timer
This practice is designed to take 30 minutes. Your tutor will see how long you took. You can work untimed if you prefer.
Section A · Equivalent fractions
Find the missing numerator or denominator to make pairs equivalent.
Q1.
3/4 = ?/12. Find the missing numerator.
Your answer:
(2 marks)
Q2.
3/4 = 15/?. Find the missing denominator.
Your answer:
(2 marks)
Q3.
3/4 = ?/100. Find the missing numerator.
Your answer:
(2 marks)
Q4.
5/6 = ?/18. Find the missing numerator.
Your answer:
(2 marks)
Q5.
5/6 = 25/?. Find the missing denominator.
Your answer:
(2 marks)
Q6.
5/6 = ?/48. Find the missing numerator.
Your answer:
(2 marks)
Q7.
8/9 = ?/18. Find the missing numerator.
Your answer:
(2 marks)
Q8.
8/9 = 64/?. Find the missing denominator.
Your answer:
(2 marks)
Q9.
8/9 = 80/?. Find the missing denominator.
Your answer:
(2 marks)
Section B · Ordering fractions
Compare fractions with different denominators. Pick the smallest.
Q10.
Which is the smaller: 2/3 or 5/6?
Your answer:
(2 marks)
Q11.
Which is the smaller: 3/8 or 1/3?
Your answer:
(3 marks)
Q12.
Which is the smallest of 5/8, 2/3, 3/4?
Your answer:
(3 marks)
Q13.
Which is the smallest of 2/9, 5/18, 1/3?
Your answer:
(3 marks)
Section C · Add and subtract proper fractions
Including whole minus fraction.
Q14.
Calculate 5/12 + 1/12. Express in lowest terms as 1/?. Find the denominator.
Your answer:
(2 marks)
Q15.
Calculate 1/6 + 1/4. Express as ?/12. Find the numerator.
Your answer:
(3 marks)
Q16.
Calculate 3/5 + 1/4. Express as ?/20. Find the numerator.
Your answer:
(3 marks)
Q17.
Calculate 7/3 - 1/2. Express as ?/6. Find the numerator.
Your answer:
(3 marks)
Q18.
Calculate 6 - 3/4. Express as an improper fraction a/4. Find a.
Your answer:
(3 marks)
Q19.
Calculate 5 - 2/3. Express as an improper fraction a/3. Find a.
Your answer:
(3 marks)
Section D · Mixed number arithmetic
Add and subtract mixed numbers. Always convert to improper first.
Q20.
Calculate 2 1/4 + 1 1/2. Express as a mixed number A b/c. Find A.
Your answer:
(4 marks)
Q21.
Calculate 3 2/5 - 1 1/2. Express as a mixed number A b/c. Find A.
Your answer:
(4 marks)
Q22.
Calculate 2 5/6 + 1 1/3. Express as a mixed number A b/c. Find A.
Your answer:
(4 marks)
Q23.
Calculate 5 1/3 - 2 1/4. Express as a mixed number A b/c. Find A.
Your answer:
(4 marks)
Q24.
Calculate 1 5/8 + 3 3/4. Express as a mixed number A b/c. Find A.
Your answer:
(4 marks)
Q25.
Calculate 4 1/6 - 5/12. Express as a mixed number A b/c. Find A.
Your answer:
(4 marks)
Section E · Fraction of a number
Divide by the denominator, multiply by the numerator.
Q26.
Calculate 1/6 of 42.
Your answer:
(2 marks)
Q27.
Calculate 1/9 of 81.
Your answer:
(2 marks)
Q28.
Calculate 3/4 of 28.
Your answer:
(3 marks)
Q29.
Calculate 5/8 of 56.
Your answer:
(3 marks)
Q30.
Calculate 2/7 of 49.
Your answer:
(3 marks)
Q31.
Calculate 4/9 of 81.
Your answer:
(3 marks)
Q32.
Calculate 5/12 of 60.
Your answer:
(3 marks)
Q33.
Calculate 3/11 of 88.
Your answer:
(4 marks)