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Multiplying hundredths
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Multiplication by a whole number is repeated addition!
Try these problems. Don't get fooled!
Remember, when you add hundredths, your answer also will have hundredth parts. And multiplying by a whole number is essentially adding. Compare:
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Example problem types
1. Multiply by a whole number and compare the problems. Think of addition - and you get help from multiplication tables too.
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2. Continue the patterns! Use adding to multiply by a whole number, or your multiplication tables.
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a. 9 × 0.01 =9 × 0.02 = 9 × 0.03 = 9 × 0.04 =
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d. 5 × 0.00 =10 × 0.01 = 15 × 0.02 = 20 × 0.03 =
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3. Explain why 6 �0.3 is NOT 0.18. Then find two numbers (not 1) whose product is 0.18.
4. Imagine nine little lines between each of the decimals on the number line below.
Which numbers do they represent?
Which of those are closer to 0 than to 1? Which are closer to 1?
5. Round the following decimals to the nearest whole number. Remember 0.50 is same as 0.5, so is rounded up to 1.
| a. 0.18 ≈ | b. 0.51 ≈ | f. 4.35 ≈ |
| m. 7.7 ≈ | n. 8.32 ≈ | r. 4.3 ≈ |
6. Estimate the result of the multiplication problem by rounding the decimal number to the nearest whole number.
| a. 2 × 3.24 ≈ 6 (since 3.24 ≈ 3) |
d. 13 × 2.24 ≈ |
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But when estimating, don't round anything to zero! Look how silly estimations you would get: 0.32 ≈ 0, so 7 × 0.32 ≈ 0 !!! This does not make any sense. Instead, round 0.32 to 0.30, and get 7 × 0.30 ≈ 2.10 |
| e. 6 × 0.24 ≈ |
h. 3 × 1.05 ≈ |
| i. 9 × 4.52 ≈ |
l. 13 × 1.21 ≈ |
7. Find the missing factor.
| a. 2 × ___ = 0.08 | d. __ × 0.09 = 0.63 |
| e. 3 × ___ = 0.36 | h. 4 × ___ = 0.84 |
| i. __ × 0.11 = 0.77 | l. 12 × ___ = 0.6 |
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4 × 2.14 Estimation: 2.14 is between 2 and 3 but closer to 2. So 4 × 2.14 will be between 4 × 2 and 4 × 3, or between 8 and 12, but closer to 8.
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3 × 2.27 Estimation: 2.27 is close to 2. Calculation:
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| When estimating, one method is to round the number to the biggest
place value it has. For example, 56 would be rounded to nearest
ten, and 228 to the nearest hundred.
In case of decimals, you can often simply round to the nearest whole number. For example, 3.87 would be rounded to 4. 15.26 would be rounded to 15. |
8. Multiply in columns. Estimate first!
| a. 4 × 6.37 | d. 6 × 15.85 |
| Estimation: | Estimation: |
| i. 22 × 8.06 | l. 9 × 4.95 |
| Estimation: | Estimation: |
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Money In the USA, money comes in dollars and cents. The word cent comes from from the Latin word cent"simus which means hundredth. Cents are hundredth parts of a dollar. That is why 1 dollar has 100 cents. In many countries of the world, the main money unit is also divided into 100 parts. Usually money amounts are given in dollars, using the decimal digits to tell how many hundredths, or how many cents. For example: $14.59 means 14 whole dollars, and 59 cents (59 hundredth parts) You can now apply your knowledge of how to add and multiply decimals to various money problems. |
9. Times 25 cents. Note the pattern.
| 1 × $0.25 = 2 × $0.25 = 3 × $0.25 = 4 × $0.25 = |
5 × $0.25 = 6 × $0.25 = 7 × $0.25 = 8 × $0.25 = |
9 × $0.25 = 10 × $0.25 = 11 × $0.25 = 12 × $0.25 = |
13 × $0.25 = 14 × $0.25 = 15 × $0.25 = 16 × $0.25 = |
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Mental math ideas 1) 7 × $8.99. Since $8.99 is just one cent less than $9, first calculate 7 × $9, and subtract from that 7 × 1 cent. Result $ _____ 2) 6 × $4.05. Just multiply separately the dollars and cents: 6 × $4 is $24, and 6 × 5 cents is 30 cents. Total $ _____ 3) 4 × $3.25. Multiply dollars and cents separately. Remember 4 × 25 cents is 1 whole dollar. Total $ _____ 4) 5 × $6.25. Multiply dollars and cents separately. Since 4 × 25 cents is 1 dollar, then 5 × 25 cents make $1.25. Total $ _____ 5) 2 × $1.75. Two times 75 cents is $1.50. Total $ _____ 6) 4 × $3.75. Calculate 4 × $4, and subtract from that 4 × 25 cents. Total $ _____ 7) $100 - $34.57. Subtract each of the digits 3, 4, and 5 from 9. The last one, 7, subtract from 10. To see the reason for this rule, subtract in columns and do all the borrowings. 8) $10 - $5.38. Subtract the digits 5 and 3 from 9. The last one, 8, subtract from 10. Result $_____ 9) Subtraction itself may be easier by thinking of the difference or "adding up to". For example $10 - $3.76. Difference of 3 and 9 - six. Difference of 7 and 9 - two. Difference of 6 and 10 - four. Result $_____ 10) $1 - $0.73. Subtract or find the difference of 7 and 9. The last one, 3, subtract from 10. Result $ _____ |
10. Find the change for items with these prices. Use the mental
math rule "Subtract all digits from 9 except the last one from 10."
| from $10:
a. $4.76 b. $2.38 c. $9.23 |
from $100:
m. $24.35 n. $81.95 o. $45.54 |
11. Word problems.
a. A pencil costs $0.45, an eraser $0.30, and a pencil sharpener $0.30. What is the cost of all three?You give $5 for the purchase. What is your change?
c. Lucy bought two pairs of jeans for $15.99 each, and two
sweaters for $8.75 each. What was her total bill? Estimate the
bill first.
If yes, calculate the change. If no, calculate how much more he would need.
h. Take a grocery store receipt, and imagine you're going through the store picking the items. Estimate the cost of each item and add them up as you go. How close does your estimation come to the actual cost? ( It is very good to practice this with several receipts, in fact.)
Example:
| tomatoes $0.45 cucumber $0.19 butter $2.35 eggs $2.57 honey $3.89 celery $1.03 -------------- total $10.48 |
estimation → |
tomatoes $0.50 cucumber $0.20 (sum 0.70) butter $2 (sum 2.70) eggs $2.50 (sum 5.20) honey $4 (sum 9.20) celery $1 (sum 10.20) --------------------------- estimated total $10.20 |
Next lesson: Comparing decimal numbers
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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. |
The fast, FUN, and easy way to learn multiplication. Learn the upper times tales in two sittings using mnemonic stories.
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