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Fraction Classroom · 2.2.0 · Student pages

Why can a decimal product be smaller?

Interpret multiplying by a decimal below one as taking only part of the other factor.

Anonymous group code: __________   Date: __________

The whole remains the same size. Taking half changes the selected amount, not the reference whole.Original amount: 0.8Half of the amount: 0.4
The whole remains the same size. Taking half changes the selected amount, not the reference whole.

Discuss the opening question

start. Why is 0.5 × 0.8 less than 0.8?

Work through the explanation

example. Why is 0.5 × 0.8 less than 0.8?

  1. Interpret 0.5 as one half. The question asks for half of the eight-tenths amount.
  2. Show eight tenths of a whole, then split that shaded amount into two equal shares.
  3. Each share contains four tenths. Record 0.5 × 0.8 = 0.4 and compare it with the original 0.8.
  4. Keep the comparison rule precise: for positive amounts, multiplying by a factor below one shrinks, by one preserves, and by a factor above one enlarges. Zero needs its own case.

Worked example: Multiplying by 0.5 takes one half of 0.8. Half of eight tenths is four tenths, so the product is 0.4.

Practise, then check independently

Use p1–p3 for practice. Try e1 without help. Show how your place-value units or model support the result.

p1. Calculate 0.5 × 0.6.

p2. Calculate 0.25 × 0.8.

p3. Calculate 1.5 × 0.4.

e1. Compare 0.3 × 0.7 with 0.7. Enter the product.

Explain a new situation

transfer. Without calculating, explain whether 0.9 × 0.65 is greater than, equal to, or less than 0.65.