4.5 Making decimal calculations easier · Unit 4 Decimals

1 · Teaching slidesuse ← → keys

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2 · Key words

equivalent fractionA fraction with the same value written a different way; 0.06 = 6/100.

place valueThe value a digit has because of its position.

partitioningSplitting a number into parts that are easier to work with.

compensateAdjusting after rounding a number to make a calculation easier.

3 · Summary of the sectionrevise from this

A decimal can be rewritten as a division: 0.06 = 6 ÷ 100.
Then reorder the calculation: 0.06 × 3500 = 6 × (3500 ÷ 100) = 6 × 35 = 210.
Multiplication and division may be done in any order, so choose the easy order.
Partition a number: 1.5 × 48 = 48 + 24 = 72.
Round and compensate: 8.2 × 9 = 8.2 × 10 − 8.2 = 73.8.
Double and halve: 2.5 × 16 = 5 × 8 = 40. The product does not change.
Learn the common ones: 0.5 = ½, 0.25 = ¼, 0.75 = ¾, 0.125 = ⅛, 0.1 = ÷10.
Dividing by a number less than 1 makes the answer bigger: 45 ÷ 0.5 = 90.

PDFPrintable worksheet All 56 questions, space to work PDFWorked answers Full solutions, not just the answer

Video lessons2 videos

Math Antics - Decimal Arithmetic

American mathantics

Watch again with 4.5 in mind: it shows why place value lets you rewrite a calculation more simply.

Multiplying and Dividing by Powers of 10

American Math with Mr. J

The idea behind most of the 4.5 shortcuts: 0.06 × 3500 is really 6 × 3500 ÷ 100.

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Making decimal calculations easier