Explain Decimal Products and Quotients
For multiplication, connect the digit product to its fractional units.
About 25 minutes, plus any extended practice
Supplied materials
- Paper and a pencil; drawing and spoken explanations are welcome. An adult may read directions and options aloud.
- Supplied worked-case record: For 1.5×0.4, fifteen tenths times four tenths gives sixty hundredths, or 0.60.
- All quantities and shape descriptions are supplied in the worked example and questions; no purchase or personal information is needed.
Learn the idea
Decimal multiplication combines fractional place values: a tenth times a tenth is a hundredth. Division can be made equivalent by scaling both dividend and divisor by the same power of ten. A size estimate and inverse operation check the decimal placement, preventing an unexamined string of digit rules.
For multiplication, connect the digit product to its fractional units. For division, scale both quantities equally to make the divisor whole, then divide. Check every quotient by multiplication and each product with a reasonable size estimate.
Check a quotient by multiplying it by the original divisor. Scaling only one input of a division changes the quotient. Write an equivalent fraction-unit product or an equally scaled division beside the original.
- Write an equivalent fraction-unit product or an equally scaled division beside the original.
- Follow the worked example. Point to each number or shape feature and say what it tells you.
- For multiplication, connect the digit product to its fractional units.
- Try the question and then the three practice questions. Check your answers and explain any change you make.
See the method in action
For 1.5×0.4, fifteen tenths times four tenths gives sixty hundredths, or 0.60. For 4.8÷0.6, scale both by ten to get 48÷6=8. Multiplying 8×0.6=4.8 verifies the quotient; scaling only the divisor would change the calculation. Check a quotient by multiplying it by the original divisor. Scaling only one input of a division changes the quotient. Write an equivalent fraction-unit product or an equally scaled division beside the original.
Check your reasoning
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Helpful tips
- Check a quotient by multiplying it by the original divisor.
- Scaling only one input of a division changes the quotient.
See the answer and explanation
0.42
Use place-value units for products or scale both dividend and divisor for division. The result is 0.42.
Take it further
Calculate 2.4×0.25 and 6.3÷0.9. Expected: 0.6 and 7.
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More practice: try new cases
Choose an answer for each problem. Explain your method on paper, then use the feedback to decide what to revisit.
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Check the subject sources
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