Practice 1
Answer & reasoning
0.3 · Half of six tenths is three tenths.
Why can a decimal product be smaller?
Interpret multiplying by a decimal below one as taking only part of the other factor.
Try the practice questionsStart with this question
Why is 0.5 × 0.8 less than 0.8?
The key idea: Multiplying by 0.5 takes one half of 0.8. Half of eight tenths is four tenths, so the product is 0.4.
Make the idea visible
- Interpret 0.5 as one half. The question asks for half of the eight-tenths amount.
- Show eight tenths of a whole, then split that shaded amount into two equal shares.
- Each share contains four tenths. Record 0.5 × 0.8 = 0.4 and compare it with the original 0.8.
- 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.
A useful error to discuss
A learner might say: Multiplication always makes numbers larger.
That pattern holds for a positive number multiplied by a factor greater than one. A positive factor between zero and one takes only part of the amount.
Practise, then check
Try the first three questions with the model. Try the final check without help. A correct value is a starting point: explain how your units or drawing support it.
Practice 2
Answer & reasoning
0.2 · One quarter of eight tenths is two tenths.
Practice 3
Answer & reasoning
0.6 · One and a half copies of four tenths is six tenths.
Independent check
Answer & reasoning
0.21 · Three tenths of seven tenths is twenty-one hundredths, less than 0.7.
Explain a new situation
Without calculating, explain whether 0.9 × 0.65 is greater than, equal to, or less than 0.65.
Discuss the explanation
It is less: 0.9 takes nine tenths of the positive amount 0.65. The missing tenth makes the product smaller.
Materials for your group
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Choose the next step
If the learner only recalls whole-number multiplication, compare one copy, half a copy and two copies of the same amount.
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