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Adding and Subtracting Decimals

NS11

RECALL -Place Value

1,0001,000 101000

1010 11 0.10.1 0.010.01 0.000.0011

0.0000.00011

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Recall that when we add or subtract money, we write the numbers so that the decimal points are vertically aligned.

This way we are sure to add digits with the same place value.

We insert the decimal point in the answer below the other decimal points, as shown above.

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We use the same procedure to add or subtract any decimal numbers.

We keep the decimal points in line. This way, we add or subtract digits with

the same place value. The decimal points stay in a straight line,

as shown above.

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Let’s practice!

Find the perimeter of the triangle. Units are in centimeters.

How do we find perimeter? We keep the decimal points

aligned in the problem so we can add digits with the same place value.

We add the digits column by column, just as we would add whole numbers or money.

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Another Example:

The roof was 6.37 meters above the ground. The ladder could reach only 4.2 meters. The roof was how much higher than the ladder could reach?

We line up the decimal points vertically so that we subtract digits with the same place value.

We attach a zero to 4.2 so that there are no empty places in the problem. Then we subtract.

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Add: 6.2+3+ 4.25

To add digits with the same place value, we align decimal points.

In this problem the whole number 3 has the same place value as the 6 and the 4.

We place a decimal point to the right of the 3 and align decimal points.

We may fill empty decimal places with zeros if we wish.

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For some subtraction problems we need to add decimal places to perform the subtraction.

If we subtract 0.23 from 0.4, we find there is an “empty” place in the problem.

We fill the empty place with a zero. Then we subtract.

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Subtract: 0.4 – 0.231

We set up the problem by lining up the decimal points, remembering to write the first number on top.

We fill empty places with zeros.

Then we subtract.

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Subtract: 3 – 1.23

This problem is similar to subtracting $1.23 from $3.

We place the decimal point to the right of the 3, fill the decimal places with zeros, and subtract.

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a. 4.5

b. 6.3

c. 4.1

d. 2.3

4.3 + 2

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4 + 1.3 + 0.6

a.2.3

b.5.3

c.5.9

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4.75 – 2

a. 2.75

b. 4.73

c. 6.75

d. 4.77

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0.3 – 0.15

a. 0.25

b. 0.15

c. 0.12

d. 0.18

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1 – 0.1

a. 0.9

b. 1.1

c. 0

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2.5 – 1

a. 2.4

b. 2.6

c. 1.6

d. 1.4

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1 – 0.25

a. 0.24

b. 0.75

c. 1.25

d. 0.15

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The end!