evaluating algebraic expressions 1-5subtracting integers ns1.2 add, subtract, multiply, and divide...
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Evaluating Algebraic Expressions
1-5 Subtracting Integers
NS1.2 Add, subtract, multiply, and divide rational numbers (integers, fractions, and terminating decimals) and take positive rational numbers to whole-number powers.
NS2.5 Understand the meaning of the absolute value of a number; interpret the absolute value as the distance of the number from zero on a number line; and determine the absolute value of real numbers.
California Standards
Evaluating Algebraic Expressions
1-5 Subtracting Integers
When you subtract a positive integer, the difference is less than the original number. Therefore, you move to the left on the number line. To subtract a negative integer, you move to the right.
You can also subtract an integer by adding its opposite. You can then use the rules for addition of integers.
Evaluating Algebraic Expressions
1-5 Subtracting IntegersAdditional Example 1: Subtracting Integers
A. –7 – 4
–7 – 4 = –7 + (–4)
B. 8 – (–5)
8 – (–5) = 8 + 5
C. –6 – (–3)
–6 – (–3) = –6 + 3
= –11
= 13
= –3
Add the opposite of 4.
Add the opposite of –5.
Add the opposite of –3.
Same sign; use the sign of the integers.
Same sign; use the sign of the integers.
6 > 3; use the sign of 6.
Subtract.
Evaluating Algebraic Expressions
1-5 Subtracting IntegersCheck It Out! Example 1
A. 3 – (–6)
3 – (–6) = 3 + 6
B. –4 – 1
–4 – 1 = –4 + (–1)
C. –7 – (–8)
–7 – (–8) = –7 + 8
= 9
= –5
= 1
Add the opposite of –6.
Add the opposite of 1.
Add the opposite of –8.
Same signs; use the sign of the integers.
Same sign; use the sign of the integers.
8 > 7; use the sign of 8.
Subtract.
Evaluating Algebraic Expressions
1-5 Subtracting Integers
n – 6 for n = –2
n – 6
–2 – 6 Substitute –2 for n.
Evaluate the expression for the given value of the variable.
–2 + (–6)
–8
Add the opposite of 6.
Same sign; use the sign of the integers.
Additional Example 2B: Evaluating Expressions with Integers
Evaluating Algebraic Expressions
1-5 Subtracting Integers
–5 – r for r = –2
–5 + 2
–3
Evaluate the expression for the given value of the variable.
–5 – r
–5 – (–2) Substitute –2 for r.
Add the opposite of –2.
5 > 2; use the sign of 5.
Check It Out! Example 2A
Evaluating Algebraic Expressions
1-5 Subtracting Integers
a – 7 for a = –9
a – 7
–9 – 7 Substitute –9 for a.
Evaluate the expression for the given value of the variable.
–9 + (–7)
–16
Add the opposite of 7.
Same sign; use the sign of the integers.
Check It Out! Example 2B
Evaluating Algebraic Expressions
1-5 Subtracting Integers
The distance from the high dive to the swimming pool is 10 feet. The pool is 12 feet deep. What is the total distance from the high dive to the bottom of the pool?
Check It Out! Example 3
10 – (–12) Subtract the depth of the pool from the height of the high dive.
10 + 12 Add the opposite of –12.
22 Same sign; use the sign of the integers.
It is 22 feet from the diving board to the bottom of the pool.