Multiply Fractions in Two Moves

Multiplication usually makes numbers bigger, right? But multiply three quarters by two thirds... and the answer is only one half. Smaller than BOTH fractions! How can that possibly work? Watch the picture closely - the secret is hiding in the overlap.

Start with one rectangle. Split it into four equal columns, then shade three of them blue for three quarters. Now split that SAME rectangle into three equal rows, and shade two rows amber. The pieces must be equal-sized - uneven pieces do not represent fair fractional parts. Look at the grid. Four columns times three rows makes twelve equal pieces altogether. That gives the denominator: four times three equals twelve. The overlap covers three columns times two rows, which is six pieces. That gives the numerator: three times two equals six. So, multiply the top numbers together, and multiply the bottom numbers together. Three quarters times two thirds becomes six twelfths. Then simplify. Six and twelve can both be divided by six, so six twelfths becomes one half. Same amount. Neater name.

Now you try an 11+ style example: calculate three fifths multiplied by five eighths. Give your answer in its simplest form. First, keep the top numbers and bottom numbers in their own lanes. Never add across the fractions - this question says multiply. Multiply the numerators: three times five equals fifteen. Multiply the denominators: five times eight equals forty. That gives fifteen fortieths. The multiplication is finished... but the answer is not yet in its simplest form. Both numbers share a factor of five. Divide fifteen by five to get three. Divide forty by five to get eight. So fifteen fortieths simplifies to three eighths. Check it: three and eight share no factor greater than one. Final answer... three eighths. Clean, simple, done!

Remember: top times top, bottom times bottom, then simplify if you can. Keep every fractional piece equal, keep numerators and denominators in their lanes, and you can multiply proper fractions with confidence. Two quick moves... one tidy answer.