Foundation and Higher · fraction arithmetic
Four operations
with fractions.
Four short rules.
+ and − need a
common denominator
the bottom number of a fraction —
Denominator
it names the size of the pieces
same size? then you can add
rule 1 of 4
Add: match bottoms
1. 3 and 4 both go into 12.
2. Multiply top and bottom by the same.
✓ Add the tops. The bottom stays 12.
rule 2 of 4
Subtract: the same way
1. 6 and 4 both go into 12.
2. Change both fractions, then subtract.
✓ Never subtract the bottoms
rule 3 of 4
Multiply: top × top
1. Tops together, bottoms together.
2. No common denominator needed.
✓ Simplify at the end if you can
23 × 45
= 2 × 43 × 5
= 815
rule 4 of 4
Divide: flip, multiply
1. Keep the first. Flip the second.
2. Change ÷ to ×, then multiply.
✓ 15 eighths is 1 whole and 7 eighths
34 ÷ 25
= 34 × 52
= 158 = 178
fraction arithmetic —
Add, subtract
common denominator first
Multiply
top × top, bottom × bottom
Divide
flip the second, then multiply
Mixed number? Make it
top-heavy before you start.
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