Fractions and ratios
Describe parts of a whole and compare quantities without confusing the two.
Before you begin
- Multiplication tables
- Equivalent fractions
Compare fractions using equal-sized parts
A denominator tells you the size of each equal part; a numerator counts those parts. To add fractions, first express them in a common unit. For 1/3 + 1/4, twelfths work because both denominators divide 12. Rewriting as 4/12 + 3/12 gives 7/12. The value of each fraction stays unchanged when its numerator and denominator are multiplied by the same nonzero number.
Use a ratio to share a total
A ratio compares quantities in the stated order. Red:blue = 2:3 means five equal parts in total, not that red is two-thirds of the collection. Red is 2/5 of the whole. Find the value of one part by dividing the total by the sum of the ratio parts, then multiply by each part count. Check that the shares add back to the total.
Worked example
Share 35 counters in the ratio red:blue = 2:3.
Show the worked solution
- There are 2 + 3 = 5 equal ratio parts.
- One part represents 35 ÷ 5 = 7 counters.
- Red has 2 × 7 = 14; blue has 3 × 7 = 21. Their sum is 35.
14 red counters and 21 blue counters.
Try it yourself
If red:blue = 2:3, what fraction of all counters is blue?
Common mistakes
- Do not add denominators when adding fractions.
- A part-to-part ratio is different from a part-to-whole fraction.
What can you explain now?
A 48 cm ribbon is cut in the ratio 3:5. Find both lengths and explain your method.
Compare with the explanation
18 cm and 30 cm.
Eight parts share 48 cm, so each part is 6 cm. Multiply by 3 and 5. The lengths sum to 48 cm and simplify to the required ratio.
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Original StudyForA content. AI-assisted checks completed; subject-teacher review is still pending. These lessons are not endorsed by an exam board.
Common Core mathematics standards ↗