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Chapter 9

Signed Numbers

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Subtracting Signed Numbers

9.2

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Opposite Numbers

The opposite of a positive number is a negative number with the same absolute value.

2– 2 0 1 3 4 5– 1– 3– 4– 5

The opposite of 4 is – 4.

4 + (– 4) = 0The sum of a number and its opposite is zero.

10 – 4 = 6 10 + (–4) = 6

15 – 8 = 7 15 + (–8) = 7

12 – 2 = 10 12 + (–2) = 10

Subtracting is the same as adding the opposite.

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Subtraction of Signed Numbers

Subtraction of Signed NumbersTo subtract signed numbers, add the opposite of the second number to the first number.

Example:Subtract. –6 – 14

–6 + (–14)

–20

The opposite of 14 is –14.

Change the subtraction to addition.

Perform the addition of the two negative numbers.

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Subtraction of Signed Numbers

Example:Subtract. –21 – (–13)

–21 + (13)

–8

The opposite of –13 is 13.

Change the subtraction to addition.

Perform the addition.

Remember when subtracting two signed numbers:1. The first number does not change.2. The subtraction sign is changed to addition.3. Write the opposite of the second number.4. Find the result of the addition problem.

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Subtraction of Signed Numbers

Example: Subtract. 5 1

11 5

5 1 5 111 5 11 5

5 5 1 1111 5 5 11

Subtraction changed to addition.

The LCD is 55.

25 1155 55

1455

Multiply the fractions.

Add the fractions.

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Applied Problems with Signed Numbers

Example:Find the difference in altitude between a mountain 5628 feet high and a gorge 350 feet below sea level.

5628 – (–350) = 5628 + 350 = 5978

= 5978 feet

5628 feet

Sea level

350 feet

5628 feet – (–350 feet )Difference

in altitude