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May 2013

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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.

Multiplying with decimals
Free decimals lesson plan from HomeschoolMath.net

Remember: Multiplication by a whole number is repeated addition! For example:

4 × 105 = 105 + 105 + 105 + 105 = ___

4 × 0.2 = 0.2 + 0.2 + 0.2 + 0.2 = ____

2 × 1.6 = 1.6 + 1.6 = ____

3 × 0.5 = 0.5 + 0.5 + 0.5 = ____

It's easy! Just remember your answer will have tenths too so you will not get fooled. Compare these problems:

3 × 40 = 40 + 40 + 40 = ____

3 × 4 = 4 + 4 + 4 = ___

3 × 0.4 = 0.4 + 0.4 + 0.4 = ___

6 × 70 =

6 × 7 =

6 × 0.7 =

Example problem types

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.

a.	5 × 100 = ____ 5 × 10 = ____ 5 × 1 = ___ 5 × 0.1 = ___

b.	3 × 200 = ____ 3 × 20 = ____ 3 × 2 = ___ 3 × 0.2 = ___

d.	7 × 800 = ____ 7 × 80 = ____ 7 × 8 = ___ 7 × 0.8 = ___

2. Continue the patterns!

7 × 0.1 = ____

7 × 0.2 = ____

7 × 0.3 = ___

7 × 0.4 = ___

1 × 1.5 = ____

2 × 1.5 = ____

3 × 1.5 = ___

4 × 1.5 = ___

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.

a.	8 × 1 = ____ 8 × 0.5 = ____

d.	22 × 1 = ____ 22 × 0.5 = ____

e.	6 × 0.5 = ____ 7 × 0.5 = ____ 8 × 0.5 = ____ 9 × 0.5 = ____

h.	100 × 0.5 = ____ 101 × 0.5 = ____ 102 × 0.5 = ____ 103 × 0.5 = ____

i.	46 × 0.5 = ____

l.	21 × 0.5 = ____

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?
Which are closer to 1?

Which one is as close to 0 as it is to 1?

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 ≈

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.

*Think*. 6 × 1.6 is the same as 1.6 + 1.6 + 1.6 + 1.6 + 1.6 + 1.6		3 16 × 6 96
If 6 × 16 is 96, how could you use that to find the answer to 6 × 1.6?

4	×	3.7	= 3.7 + 3.7 + 3.7 + 3.7	= 14.8
whole number	times	a decimal with tenths	is the same as adding decimals with tenths,	so the answer will have tenths too!

You can use the standard algorithm of multiplying in columns, when multiplying a decimal with tenths by a whole number. Just put the decimal point in the right place since you know the answer will have tenths. Compare:

3 × 9.4

Estimate: 9.4 is between 9 and 10. So 3 × 9.4 is between 3 × 9 and 3 × 0 - between 27 and 30.

Calculation:

1 9.4 9.4 + 9.4 28.2		1 9.4 × 3 28.2
When you add, the answer has tenths	...	So when you multiply, the answer must have tenths too.

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).

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?

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" ?

Find solutions to these puzzles.

	×		=	0.8		×		=	2.4
×		×			×		×
	×		=	4.2		×		=	4.0
= 1.2		= 2.8			= 3.2		= 3.0

Next lesson: Decimals with hundredths

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.

New! Times Tales is now on DVD!

The fast, FUN, and easy way to learn multiplication. Learn the upper times tales in two sittings using mnemonic stories.

Multiplying with decimals Free decimals lesson plan from HomeschoolMath.net

Example problem types

Multiplying with decimals
Free decimals lesson plan from HomeschoolMath.net