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May 2013

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How to help students with multiplication tables?

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(easy hangman)
(difficult)

The ideas in this decimals lesson are taken from Math Mammoth Decimals 2 book ($4.00 download). The book has more problems than shown in this online lesson.

Dividing Decimals

Do you remember that multiplication and division are opposite operations?
From any multiplication equation we can write two corresponding division
equations. Look at the example to the right: →

3 × 0.9 = 2.7

2.7 ÷ 3 = 0.9

2.7 ÷ 0.9 = 3

When a decimal is divided by a whole number, as for example in the problem 4.5 ÷ 5, you can
think of multiplication: What number multiplied by 5 will give you 4.5? The answer is 0.9.

Remember that you can also think in terms of tenths, hundredths, and thousandths:

For example, 200 thousandths divided by 5 is 40 thousandths. (You could replace the word “thou-
sandths” in that sentence with “dollars,” “millions,” “kilograms,” or anything else, and it stays true!)

Written as fractions, this is

200

1000

÷ 5 =

1000

. Written as decimals, it is 0.200 ÷ 5 = 0.040 = 0.04.

When a decimal is divided by another decimal, think about how many times the divisor goes into
the dividend. For 0.24 ÷ 0.03, you can think, “How many times does 0.03 go into 0.24?” Just
as 3 apples goes into 24 apples 8 times, 3 hundredths goes into 24 hundredths 8 times

1. First shade the parts. Then divide and write a division sentence.

a. Shade 0.3.
Divide it into 3 parts.

b. Shade 0.64.
Divide it into 2 parts.

2. Write the division problems with numbers, and solve.

a. 54 hundredths divided by 6 equals ...

b. 72 thousandths divided by 9 equals ...

3. Write two division problems and two multiplication problems with the same numbers - a fact family!

a. 8 × 0.04 = 0.32

____ × ____ = _____

____ ÷ ____ = _____

(More problems available in the book.)

4. Divide. Think of backwards multiplication.

a. 0.024 ÷ 6 =

b. 0.24 ÷ 6 =

c. 2.4 ÷ 6 =

(More problems available in the book.)

Trick! Remember how sometimes, when multiplying, you end up with an extra
zero at the end: 10 ÷ 0.004 = 0.040, and we can omit the last zero and write it as 0.04.

When dividing by a whole number, it may help you to “tag” additional decimal zeros
to the number before dividing:

0.8 ÷ 100

= 0.800 ÷ 100 = 0.008

(Think: 800 thousandths divided
by 100 equals 8 thousandths.)

0.7 ÷ 10

= 0.70 ÷ 10 = 0.07

(Think: 70 hundredths divided
by 10 equals 7 hundredths.)

4 ÷ 8

= 4.0 ÷ 8 = 0.5

(Think: 40 tenths divided
by 8 equals 5 tenths.)

5. Divide. Use the trick above.

a. 0.3 ÷ 5 =

b. 0.3 ÷ 10 =

c. 3 ÷ 5 =

(More problems available in the book.)

7. If each heartbeat takes 0.8 seconds, how
long do five heartbeats take? Ten heartbeats?

In many practical situations we use the idea of how many times one number
goes into another. You can always write a division sentence from it.

Example 1: Mom cuts 0.4 meter pieces from a 1.2-meter piece of material.
How many pieces does she get?

Think, “How many times does 0.4 go into 1.2?”

The division 1.2 ÷ 0.4 = 3 gives us the answer: 3 pieces.

Example 2: 0.45 ÷ 0.005 = ?

First, tag a zero to 0.45 so that it has three decimals: 0.450 ÷ 0.005 = ?

Now think, “How many times does 0.005 fit into 0.450?”

This is the same as asking, “How many times does 5 fit into 450?”

The answer: 90 times.

8. Write a division sentence for each problem, and solve.

a. How many 0.3 m pieces do you get from 1.8 m of cloth?

9. Divide. Think: how many times does the divisor go into the dividend?

a. 2 ÷ 0.5 =

b. 3 ÷ 0.5 =

c. 7 ÷ 0.5 =

(More problems available in the book.)

Write a division sentence for each problem, and solve.

10. The asphalt team does a 1.2-mile stretch each day.

a. How many days does it take for them to cover a distance of 6 miles?

(More problems available in the book.)

15. Solve in the right order.

a. 3 ÷ 0.04 + 1.1

b. 5 − 0.3 ÷ 0.06

16. Figure out the pattern and continue it for two more problems.

a. 0.025 ÷ 0.005 =

0.25 ÷ 0.05 =

2.5 ÷ 0.5 =

(More problems available in the book.)