Multiply a Fraction by a Whole Number

Four gifts, and each one needs three sevenths of a yard of ribbon. How much ribbon do you need in all?

Three sevenths means a yard cut into seven equal pieces, with three of them taken.

Four gifts means four copies of three sevenths. You could add them all up — but there is a faster way.

Write it as multiplication: four times three sevenths.

Multiply the whole number by the numerator only. Four times three is twelve, so the numerator becomes twelve.

Here is the mistake to avoid. Do not multiply the denominator. The pieces did not change size — they are still sevenths. Seven stays seven.

So four times three sevenths is twelve sevenths. Twelve sevenths is more than one whole, so we are not finished yet.

Seven sevenths fill one whole yard, and five sevenths are left over. That makes one and five sevenths.

Four times three sevenths is twelve sevenths, or one and five sevenths yards. Multiply the top, keep the bottom, then check whether your answer is more than a whole.