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 =
40
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!
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.)
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.
February 2010 newsletter
