Foundation and Higher · ratios and fractions
Ratio to fraction.
Add the parts
first.
3 : 2 is not
three halves of the total
a ratio compares part with part —
3 : 2
a fraction is part of the whole
so you need the total number of parts
step 1 of 4
Ratio to fraction
1. Draw 3 parts for boys and 2 for girls.
2. Add the parts: 3 + 2 = 5.
✓ Boys are 35 of the class, not 32
boys : girls = 3 : 2
5 parts altogether
step 2 of 4
Fraction to ratio
1. 2 parts out of 7 are red.
2. So 7 − 2 = 5 parts are not red.
✓ 2 : 5, not 2 : 7
27 of the sweets are red
the other 5 parts are not
step 3 of 4
Use it to share
1. 5 parts share 35: each part is 7.
2. Boys have 3 parts: 3 × 7 = 21.
✓ Check: girls 14, and 21 + 14 = 35
35 students, boys : girls = 3 : 2
step 4 of 4
Part against part
1. 32 does mean something: boys ÷ girls.
2. Part to part, not part to whole.
✓ Of the total, or of the girls?
boys : girls = 3 : 2
boys = 32 × girls
girls = 23 × boys
10 girls: 15 boys
ratios and fractions —
Add the parts
that is the denominator
Part ÷ total
fraction of the whole
Part ÷ part
one part as a fraction of another
Draw the bar.
It answers most ratio questions.
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