Understanding ratios — part-to-part sharing
The two amounts being compared don't have to be equal (here, 2 vs 3) — but each part represents the same-sized unit. The total number of parts here is 2 + 3 = 5.
Key Idea
To split a total by a ratio, first count the parts, then find what one part is worth. If you have 10 drops to split in the ratio 2:3, that's 5 parts, so one part = 10 ÷ 5 = 2 drops; then blue = 2 parts = 4 drops, yellow = 3 parts = 6 drops. (Check: 4 + 6 = 10. ✓)
Seeing it in action
Worked example
Split 20 marbles in the ratio 2:3, blue to yellow.
Parts: 2 + 3 = 5. One part = 20 ÷ 5 = 4. → blue = 2×4 = 8, yellow = 3×4 = 12. (8 + 12 = 20 ✓)
2 + 3 = 5 equal parts, so one part is 20 ÷ 5 = 4 marbles.
Worked example 2: equal shares
Split 10 drops in the ratio 1:1.
Parts: 1 + 1 = 2. One part = 10 ÷ 2 = 5. → 5 and 5.
A common mistake, and the fix
Treating one part as the whole.
In a 2 : 3 ratio of red to blue, red is 2 parts out of 5, so 2/5 of the total, not 2/3. Add the parts to find the whole first.
Try a few
Split 12 in the ratio 1:2.
Split 15 in the ratio 2:1.
Split 21 in the ratio 3:4.
Try it in Numeris.
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Put the reasoning on paper.
Try six fraction, angle, perimeter and area questions with explained answers, for grades 4–6.
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