Definition
Fraction of a quantity
A fraction of a quantity is the amount found by multiplying that quantity by the fraction.
What it means
The denominator tells how many equal groups to split the quantity into. One group is one unit fraction of the quantity. The numerator tells how many of those groups to take. This is multiplication by a fraction, not a new kind of fraction.
Remember it
Divide by the bottom to find one share; multiply by the top to take the needed shares.
Example
To find 3/5 of 20 counters, split 20 into 5 equal groups: 20 ÷ 5 = 4 counters in each group. Take 3 groups: 4 × 3 = 12. So 3/5 of 20 is 12.
Watch for
3/5 of 20 is not 20 ÷ 3. The denominator makes the equal groups; the numerator tells how many groups to take.
Common mix-up
The word “of” signals multiplication here: 3/5 of 20 means 20 × 3/5.
Exact meaning
For a fraction a/b and a quantity Q, the fraction a/b of Q is the product Q × a/b. It can be found by dividing Q by b and multiplying by a, with the unit of Q preserved unless the context changes it.