Use Decimal Algorithms and Exact Checks

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 12.48÷0.24, scale both by one hundred to get 1248÷24=52.
• All quantities and shape descriptions are supplied in the worked example and questions; no purchase or personal information is needed.

Learn the idea

Decimal algorithms preserve place value in all four operations. Align equal places for addition or subtraction, account for the fractional units of products, and scale both quantities equally for division. An inverse check catches a decimal point placed incorrectly even when the digit computation looks correct.

Choose the rule that matches the supplied operation. Calculate while preserving places, then use the inverse operation to reconstruct the input. Estimate the size first so that a factor-of-ten error is evident in the final result.

Choose a method for the actual operation, not one decimal rule for every calculation. In division, scale both the dividend and divisor by the same factor. Write a matching inverse equation beneath the original calculation.

1. Write a matching inverse equation beneath the original calculation.
2. Work through the supplied example and label what each number or attribute represents.
3. Choose the rule that matches the supplied operation.
4. Answer the check, then try the three changed-input practice questions and explain one correction.

Check your reasoning

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Take it further

Calculate 7.56÷0.18 and 2.75×1.2. Expected: 42 and 3.3.

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