How to see it
To multiply fractions, multiply the tops and multiply the bottoms. Then simplify. To divide by a fraction, ask how many of that fraction fit. How many fifths in one? Five. In three? Fifteen. Dividing by a fraction less than one makes the answer bigger. The shortcut: flip the second fraction and multiply.
A worked example
Two thirds times three quarters. Tops: 6. Bottoms: 12. Six twelfths, which is one half. Quicker: cancel the 3 diagonally first.
The common mistake: believing division always makes a number smaller
The trap is thinking dividing always shrinks things. 3 divided by one fifth is not three fifths. It is fifteen. Flip the fraction you divide by, not the first one.
Try one
Two fifths times five sixths.
- A1/3
- B10/11
- C7/30
- D2/5
Show the answerHide the answer
Right: A, 1/3
10 over 30 simplifies by 10.