One-page revision sheet

• Compare the whole-number parts first.
• If they are equal, compare the tenths; then the hundredths; then the thousandths.
• Work from the left, one place at a time — stop as soon as they differ.
• More digits does not mean bigger: 2.816 < 2.82.
• Filling with zeros makes the columns line up: 4.6 = 4.60, so 4.60 < 4.66.
• A zero on the end never changes the value: 0.5 = 0.50 = 0.500.
• Convert to the same unit before comparing measurements: 450 g = 0.45 kg.

Key words: compare  ·  order  ·  decimal number  ·  whole-number part  ·  tenths  ·  hundredths  ·  thousandths

• In a written method, line up the decimal points — that lines up the place values.
• Fill any gaps with zeros: 10 becomes 10.00 before subtracting 4.83.
• Mental method 1 — partition. Add the whole-number parts and the decimal parts separately, then combine: 2.3 + 7.8 = (2 + 7) + (0.3 + 0.8) = 9 + 1.1 = 10.1.
• Mental method 2 — round and adjust. 6.9 + 12.4 = 7 + 12.4 − 0.1 = 19.3.
• For subtraction, round and adjust the other way: 13.3 − 5.8 = 13.3 − 6 + 0.2 = 7.5.
• Decimal parts can carry into the units: 0.3 + 0.8 = 1.1, not 0.11.
• Always estimate first — 2.3 + 7.8 must be about 10.

Key words: decimal part  ·  whole-number part  ·  mental method  ·  written method  ·  partition

• Step 1. Do the multiplication ignoring the decimal point.
• Step 2. Count the decimal places in the question.
• Step 3. Put the same number of decimal places in the answer.
• 0.002 × 4: 2 × 4 = 8, and the question has 3 decimal places, so the answer is 0.008.
• 30 × 0.06: 30 × 6 = 180, and the question has 2 decimal places, so the answer is 1.80 = 1.8.
• You can drop a zero at the end of the answer, but never one in the middle.
• Multiplying by a number less than 1 makes the answer smaller: 0.4 × 0.7 = 0.28.
• Estimate first to check the point is in the right place.

Key words: decimal place  ·  product  ·  estimate

• Set the division out so the decimal point in the answer sits directly above the point in the question.
• Then divide exactly as you would with whole numbers.
• If there is a remainder, add zeros after the decimal point and carry on: 7 = 7.00, so 7 ÷ 4 = 1.75.
• Some divisions never stop, such as 2 ÷ 3 = 0.6666… — those must be rounded.
• When an answer must be rounded, work to one more decimal place than you need, then round.
• 8.46 ÷ 7 = 1.208… , so to 2 decimal places the answer is 1.21.
• Dividing by a whole number greater than 1 always makes the answer smaller.

Key words: divide  ·  remainder  ·  degree of accuracy  ·  decimal place

• 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.

Key words: equivalent fraction  ·  place value  ·  partitioning  ·  compensate