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Evaluating Algebraic Expressions
1-3 Integers and Absolute Value
Warm UpWarm Up
California StandardsCalifornia Standards
Lesson PresentationLesson Presentation
PreviewPreview
Evaluating Algebraic Expressions
1-3 Integers and Absolute Value
Warm UpEvaluate each expression for the given values of the variables.
1. 2x – 3y for x = 17 and y = 62. 5(x + 3) + 4y for x = 3 and y = 23. 6.9(x – 2.7) + 7.1 for x = 5.14. 5x – 4y for x = 0.3 and y = 0.2
1638
23.660.7
Evaluating Algebraic Expressions
1-3 Integers and Absolute Value
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.Also covered: NS1.1
California Standards
Evaluating Algebraic Expressions
1-3 Integers and Absolute Value
Vocabularyintegeroppositeabsolute value
Evaluating Algebraic Expressions
1-3 Integers and Absolute Value
Integers are the set of whole numbers and their opposites. Opposites are numbers that are the same distance from 0 on a number line, but on opposite sides of 0.
Evaluating Algebraic Expressions
1-3 Integers and Absolute Value
Numbers on a number line increase in value as you move from left to right.
Remember!
Evaluating Algebraic Expressions
1-3 Integers and Absolute Value
Use <, >, or = to compare the scores.
Additional Example 1A: Sports Application
Aaron’s score is 4, and Felicity’s score is –1.
Place the scores on the number line.
–1 < 4
–5 –4 –3 –2 –1 0 1 2 3 4 5
–1 is to the left of 4.
Felicity's score is less than Aaron's score.
Evaluating Algebraic Expressions
1-3 Integers and Absolute Value
Use <, >, or = to compare the scores.
Additional Example 1B: Sports Application
List the golf scores in order from the lowest to the highest. The scores are –4, 2, 5, and –3.
Place the scores on the number line and read them from left to right.
In order from the lowest score to the highest score, the scores are –4, –3, 2, and 5.
–5 –4 –3 –2 –1 0 1 2 3 4 5
Evaluating Algebraic Expressions
1-3 Integers and Absolute Value
Use <, >, or = to compare the scores.
Check It Out! Example 1A
Francie’s score is –2, and Joaquin's score is –3.
Place the scores on the number line.
–3 < –2
–5 –4 –3 –2 –1 0 1 2 3 4 5
–3 is to the left of –2.
Joaquin's score is less than Francie's score.
Evaluating Algebraic Expressions
1-3 Integers and Absolute Value
Use <, >, or = to compare the scores.
Check It Out! Example 1B
List the golfer’s scores in order from the lowest to the highest. The scores are –3, 1, 0, and –2.
Place the scores on the number line and read them from left to right.
In order from the lowest score to the highest score, the scores are –3, –2, 0, and 1.
–5 –4 –3 –2 –1 0 1 2 3 4 5
Evaluating Algebraic Expressions
1-3 Integers and Absolute Value
Write the integers 8, –5, and 4 in order from least to greatest.
Additional Example 2: Ordering Integers
Graph the integers on a number line. Then read them from left to right.
The integers in order from least to greatest are –5, 4, and 8.
–5 –4 –3 –2 –1 0 1 2 3 4 5 6 7 8
Evaluating Algebraic Expressions
1-3 Integers and Absolute Value
Write the integers –4, –5, and 4 in order from least to greatest.
Check It Out! Example 2
Graph the integers on a number line. Then read them from left to right.
The integers in order from least to greatest are –5, –4, and 4.
–5 –4 –3 –2 –1 0 1 2 3 4 5 6 7 8
Evaluating Algebraic Expressions
1-3 Integers and Absolute Value
–5 –4 –3 –2 –1 0 1 2 3 4 5
A number’s absolute value is its distance from 0 on a number line. Absolute value is always positive because distance is always positive. “The absolute value of –4” is written as |–4|. Opposites have the same absolute value.
4 units 4 units
|–4| = 4 |4| = 4
Evaluating Algebraic Expressions
1-3 Integers and Absolute Value
Simplify each expression.
Additional Example 3: Simplifying Absolute-Value Expressions
A. |–3|
B. |17 – 6|
Subtract first: 17 – 6 = 11.
–3 is 3 units from 0, so |–3| = 3.
–5 –4 –3 –2 –1 0 1 2 3 4 5
3 units
|17 – 6| = |11|
= 11 Then find the absolute value: 11 is 11 units from 0.
Evaluating Algebraic Expressions
1-3 Integers and Absolute Value
Simplify each expression.
Additional Example 3: Simplifying Absolute-Value Expressions
C. |–8| + |–5| Find the absolute values first: –8 is 8 units from 0. –5 is 5 units from 0. Then add.= 13
D. |5 + 1| + |8 – 6|
5 + 1 = 6, 8 – 6 = 2.
= 6 + 2
|–8| + |–5| = 8 + 5
|5 + 1| + |8 – 6| = |6| + |2|
6 is 6 units from 0, 2 is 2 units from 0. Add.= 8
Evaluating Algebraic Expressions
1-3 Integers and Absolute Value
Simplify each expression.
Check It Out! Example 3
A. |–5|
B. |12 – 4|
Subtract first: 12 – 4 = 8.
–5 is 5 units from 0, so |–5| = 5.
–5 –4 –3 –2 –1 0 1 2 3 4 5
5 units
|12 – 4| = |8|
= 8 Then find the absolute value: 8 is 8 units from 0.
Evaluating Algebraic Expressions
1-3 Integers and Absolute Value
Simplify each expression.
C. |–2| + |–9|Find the absolute values first: –2 is 2 units from 0. –9 is 9 units from 0. Then add.= 11
D. |3 + 1| + |9 – 2|
3 + 1 = 4, 9 – 2 = 7.
= 4 + 7
|–2| + |–9| = 2 + 9
|3 + 1| + |9 – 2| = |4| + |7|
4 is 4 units from 0, 7 is 7 units from 0. Add.= 11
Check It Out! Example 3
Evaluating Algebraic Expressions
1-3 Integers and Absolute Value
Lesson Quiz1. At the end of the course, your golf score was
–2. Your friend’s score was 7. Use <, >, or = to compare your scores.
Write the integers in order from least to greatest.
2. –17, –26, 23
3. 0, 5, –4
Simplify each expression.
4. |–4| + |–2|
5. |6 + 13| – |7 – 5|
–2 < 7
–26, – 17, 23
–4, 0, 5
6
17