A fraction of a fraction
When we multiply two fractions, the word of is often the easiest way to think about it. Start with the blue fraction, then shade a fraction of that amount using yellow. Where yellow and blue overlap, the picture turns green.
13 × 15
In words: One third of one fifth
Start with 15 of a whole. Then take 13 of that one fifth.
Start with 1/5. Look at the blue rectangle: it is one of five equal parts of the whole.
We want one third of the blue fifth.
The denominator tells us how many equal pieces
Split the whole into fifths, then split each fifth into 3 equal pieces. That makes 5 × 3 = 15 equal pieces altogether.
23 of 17
Start with one seventh of the whole, then take two thirds of that part. The green pieces show what you have taken.
3 columns × 7 rows = 21 equal pieces. 2 selected columns × 1 selected row = 2 green pieces.
Numerators count selected pieces; denominators count total pieces
For a fraction of a fraction, both of those counts multiply.
3 columns × 5 rows = 15 equal pieces. 2 selected columns × 4 selected rows = 8 green pieces.
“Of” and “×” are describing the same operation here
The word of helps us picture what multiplication is doing: take a fraction of the amount we already have.
What fraction of the whole is selected?
Start with the blue fraction, then click to add the yellow fraction. Count all the equal pieces and find the green overlap.
A fraction of a fraction
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You have learned
A fraction of a fraction means taking part of an amount that is already a fraction.
Multiply the numerators to count selected pieces, and multiply the denominators to count the total equal pieces.