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Multiplying with decimals
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Remember: Multiplication by a whole number is repeated addition!
For example:
It's easy! Just remember your answer will have tenths too so you will not get fooled. Compare these problems:
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1. Multiply by a whole number and compare the problems. Think of the addition - but you can get help from knowing your multiplication tables too.
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2. Continue the patterns!
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a. 7 × 0.1 = ____7 × 0.2 = ____ 7 × 0.3 = ___ 7 × 0.4 = ___
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e. 1 × 1.5 = ____2 × 1.5 = ____ 3 × 1.5 = ___ 4 × 1.5 = ___
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3. Explain why 5 × 0.3 is NOT
0.15.
4. 0.5 is one half. How can you easily find the answers to these? Compare the problems.
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5. Find the missing factor.
| a. 2 × ___ = 0.6 | d. __ × 0.7 = 5.6 | e. __ × 1.1 = 9.9 |
| f. __ × 1.2 = 2.4 | i. __ × 1.3 = 3.9 | j. __ × 1.3 = 13.0 |
| 6. Which of the decimals
0.1, 0.2, 0.3, ..., 0.8, 0.9 are closer to 0 than to 1? |
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| Which one is as close to 0 as it is to 1? | |||
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Rounding to the nearest whole number Remember? When rounding to whole tens, 45 ≈ 50, and 275 ≈ 280. In other words, numbers ending in 5 are rounded up. In the same way 0.5 is rounded up to 1, 1.5 is rounded up to 2, etc. |
7. Round the following decimals to the nearest whole number.
| a. 0.6 ≈ | e. 1.2 ≈ | f. 1.8 ≈ |
| g. 5.3 ≈ | k. 4.2 ≈ | l. 10.4 ≈ |
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6 × 1.6 Estimation: 1.6 is between 1 and 2 but closer to 2. So 6 × 1.6 will be between 6 × 1 and 6 × 2, or between 6 and 12, but closer to 12.
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| When estimating, you can round the number to the biggest
place value it has. For example, 48 is rounded to nearest ten up
(to 50), and 74 to the nearest ten down (to 70). In case of decimals, you can often simply round to the nearest
whole number.
For example, to estimate 27 × 3.3, round 27 to 30 and 3.3 to 3. You get 27 × 3.3 ≈ 30 × 3 = 90 |
8. Multiply in columns. Estimate first!
| a. 6 × 2.7 | c. 12 × 4.5 |
| Estimation: | Estimation: |
| d. 4 × 15.5 | f. 32 × 6.3 |
| Estimation: | Estimation: |
| j. 21 × 8.6 | l. 39 × 13.2 |
| Estimation: | Estimation: |
9. Word problems.
| a. A lawn mower gas tank capacity is 1.6 quarts. You keep a
small 2-gallon bucket of gas in the garage for the lawn mower. How
many times can you fill its tank from this bucket? Remember one
gallon is four quarts (or quart is fourth part of a gallon - the
word quart signifying quarter or 1/4).
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| b. Lucy jogs 1.2 miles five times a week, and Sharon jogs 1 1/2
miles four times a week. Who jogs more total during one week?
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| g. A baby weighs seven and a half pounds. Express this as a
decimal. Is it the same as saying, "Baby weighs seven pounds five
ounces" ?
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Next lesson: Decimals with hundredths
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The ideas in this decimals lesson are taken from Math Mammoth Decimals 1 book ($4.00 download). Only a few examples of each problem type are shown. |
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Find solutions to these puzzles.