Multiplying fractions by whole numbers
Maths · Key Stage 2 · The School
Multiplying is repeated adding
Two fifths times 3 means three lots of two fifths, added together. That is two fifths, plus two fifths, plus two fifths. Add the tops: 2 add 2 add 2 makes 6. The bottom number stays the same. The answer is six fifths. Seeing it written out this way makes the shortcut that follows feel far less mysterious.
The shortcut
You do not need to write it out as three additions every time. Just multiply the top number by the whole number, and leave the bottom number alone. Two fifths times 3: multiply 2 by 3 to get 6. The bottom stays 5. The answer is six fifths, exactly as before. The shortcut and the long way always agree. Checking one against the other is a good habit while the method is still new.
Turning the answer into a mixed number
Six fifths is bigger than a whole one. Five fifths make one whole. That leaves one fifth over. So six fifths is the same as one whole and one fifth, written as 1 and one fifth. An answer bigger than the bottom number should usually be converted this way.
A word problem to solve
A recipe needs three quarters of a cup of flour for one batch. You want to make 5 batches. Multiply three quarters by 5. Multiply the top: 3 times 5 makes 15. The bottom stays 4. That gives fifteen quarters. Fifteen quarters is the same as 3 whole cups and three quarters of a cup.