Multiplying decimals by whole numbers
Multiply one-digit numbers with up to two decimal places by whole numbers (e.g. 3.47 × 6)
What a learner can do afterwards
- Correctly compute 4.56 × 7 using a written method
- Use place-value reasoning to explain why 3.2 × 5 = 16.0
- Model a decimal multiplication using an area diagram or expanded form
1 · Read
Say a bag of sweets costs £1.35 and you want to buy 6 of them for a party. You already know how to do long multiplication with whole numbers. Decimals use the exact same steps, plus one extra move at the end. Multiply the digits as if the decimal point were not even there. Then count how many digits come after the point in the decimal number, and put the point back that many places from the right in your answer.
Work out 4.56 × 7. First, multiply as whole numbers: 456 × 7 = 3192. Now count the digits after the point in 4.56: there are 2 (the 5 and the 6). Put the point 2 places from the right in 3192, and you get 31.92.
You can also split the decimal before you multiply. For 3.4 x 2, think (3 x 2) + (0.4 x 2) = 6 + 0.8 = 6.8.
A common slip is lining up the decimal points like you would for adding. Don't do that here. Multiply first, then count the decimal digits in the question to place the point in the answer.
Multiply the digits like whole numbers, then move the decimal point in from the right by the same number of digits that followed the point in the question.
More to read
5.1 Decimals
Decimals name tenths, hundredths and thousandths by place. The 2 in 3.2 means 2 tenths, so 3.2 is 32 tenths. Multiplying 3.2 by 5 means 32 tenths times 5, which is 160 tenths or 16.0. Place value turns every decimal multiplication into whole number work.
5.2 Decimal Operations
Written decimal multiplication follows three moves: ignore the point and multiply, count the decimal places in the question, then put the point back. For 4.56 times 7, compute 456 times 7 = 3,192, then restore two places for 31.92. Estimating first guards the point: 4.56 times 7 must sit near 35. An answer like 3.192 fails the estimate test instantly.
1.7 Decimals
Area models and expanded forms show why decimal multiplication works. Splitting 4.56 times 7 into 4 times 7, 0.5 times 7 and 0.06 times 7 gives 28 + 3.5 + 0.42 = 31.92. Each part is easy mental maths. Adding the parts rebuilds the exact answer.
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2 · Watch
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Where it sits
18 questions wait behind this lesson, each with its answer explained. Every answer feeds the sky: stars light as they are learned, and dim when it is time to come back.