Decimal × whole number

1Summary 重點摘要

0.5 × 3 = 1.5. Multiply as integer, then place decimal point.

2Vocabulary cards Vocabulary

3Step by step Steps

1. Part 1: Start from repeated addition0.5 × 3 means adding three 0.5s: 0.5 + 0.5 + 0.5 = 1.5. Picture three 0.5 blocks joined together, making exactly 1.5. Multiplication is repeated addition, and decimal multiplication follows the same rule; this is the starting point of decimal times whole number. Why begin with addition? Addition can be seen and worked out concretely, so it verifies the product. Take care that 0.5 is half of one, so three halves are 1.5, not 0.15; the decimal point is decided by the meaning, never placed at random.
2. Part 2: The two-step methodWork out 0.8 × 3 in two steps, the basic method for a decimal times a whole number. Step one: ignore the decimal point and multiply as whole numbers, 8 × 3 = 24. Step two: count decimal places, 0.8 has only one, so the answer keeps one; set the dot inside 24 to get 2.4. The chant: multiply first, then place the dot. Why treat it as whole numbers first? Without the dot the working is exactly the old knowledge, so the familiar part is settled first. The usual error is skipping the count of decimal places and writing 24, ten times too big.
3. Part 3: Two decimal placesFor 0.25 × 3: step one gives 25 × 3 = 75; step two notes that 0.25 has two decimal places, so count two digits from the right of 75 and set the dot, giving 0.75. However many places the decimal has, the answer keeps exactly that many, counted from the right. Why does the answer keep the same number of places? The multiplier is a whole number, and whole numbers do not change the count of decimal places. Take care that the whole part of 0.75 is 0 and this 0 may not be dropped; when no whole digit stands before the dot, write a 0, for a bare .75 is incomplete and not the standard form.
4. Part 4: Decimals bigger than 1For 1.2 × 4: first treat it as 12 × 4 = 48; since 1.2 has one decimal place, the answer is 4.8. When the whole part is bigger than 1, the method stays exactly the same: multiply first, then place the dot. Estimate to check: 1.2 is near 1, and 1 × 4 is a little over 4, so 4.8 is sensible; an answer of 48 is plainly too big at a glance. Take care that estimation catches a dot placed in the wrong place; spending a few seconds estimating after each sum is a habit worth building, and many big errors fail to pass it.
5. Part 5: Money applicationA pack of biscuits costs 6.5 dollars; how much for 3 packs? 6.5 × 3: first 65 × 3 = 195, then restore one decimal place to get 19.5, that is 19.5 dollars. Pay 20 dollars and the change is 20 - 19.5 = 0.5 dollars. Money is the most common application of decimal multiplication, and a skill daily life demands. Take care to write the unit with the amount, and in giving change subtract the total from the money paid; reversed, a negative result means the money brought is not enough, and this should be noticed first.
6. Part 6: When the answer is whole0.5 × 2 = 1.0, which is written simply as 1; the trailing .0 need not stay. But while working, the decimal point must still sit in the right place: ten 0.1s make exactly 1. Set the dot correctly first and simplify afterwards, never reversing the order. Why may the .0 go? 1.0 and 1 are equal in value, differing only in form. Take care that simplifying touches only the trailing 0; a 0 in the middle of the decimal stays, and rewriting 1.05 as 1.5 is completely wrong — the value no longer matches.

4Diagrams Diagrams

5Worked example Example

6Common mistakes Mistakes

7Quick check Quick check

8Recap Recap

• Multiply as whole numbers first
• Count the original decimal places and restore the dot
• 0.25 × 3 = 0.75: two decimal places
• Check by repeated addition: 0.5 × 3 = three lots of 0.5
• Money answers keep the $ and the dot