Lesson Warm Up 3 1. exponent 2. False 3. 81 Lesson
Lesson
3
Warm Up 3 1. exponent 2. False 3. 81 Lesson Practice 3 a. 8 1 b. _ 16 1 c. -_ 4 1 d. - _ 8 1 e. - _ 16
f. x7y-5 g. x5y2 x h. _ 6 y
i. x ab-2by ab+1 j. 8 × 1017 k. 1.60 × 10 3 pounds
© 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved.
LSN 3–1
Saxon Algebra 2
Lesson
3
1 5. _ 12 2
Practice 3
16x y 1 _ 5 3 a b c
1. -24
6.
2. 31
2x2 _ 7. 10 y
3. Commutative Property
9
4y 8. _ 6 x
4. Distributive Property
9. 9π m2 10. 74°
11. Let the circumference be C, the number of girls be g, and the average height be h. Then, C = g × h = 7 -3 3 × 10 × 1.4 × 10 . The Commutative Property of Multiplication allows for these numbers to be multiplied 7 -3 in any order to give C = 10 × 10 × 3 × 1.4. The exponents of 10 can be added mentally to give C = 10 4 × 3 × 1.4. Let 1.4 = 1 + 0.4. Then, 3 × 1.4 = 3(1 + 0.4) = 3 + 1.2 = 4.2 by the Distributive 4 Property and mental math. Therefore, C = 10 × 4.2 = 4.2 × 10 4 km by the Commutative Property of Multiplication. 12. a. Think of $18 as $20 - $2. Write an expression: 0.1(20 - 2). Use the distributive property: 0.1(20) - 0.1(2). Multiply: 2 - 0.2. Subtract: 1.8. A 10% tip is $1.80. b. A 15% tip equals a 10% tip plus one-half of the 10% tip. So, a 15% tip equals $1.80 + $0.90 = $2.70. 13. The first step should be labeled “Distributive Property.” The second step should be labeled “Multiply.” © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved.
LSN 3–2
Saxon Algebra 2
Lesson
3
14. a. -5 b. The result would increase by 2y c. 1 15. 3(33) + 2(75) = 99 + 150 = 249 mg 16. The first square has one side of length 5u - u = 4u. So, 2 the area of the first square = (4u)(4u) = 16u . The second square has one side of length 4u - 2u = 2u. So, the area 2 of the second square = (2u)(2u) = 4u . The combined area = 16u 2 + 4u 2 = 20u 2. 17. (17, 14) 18. 3(-1) - 2(1) + (1)(-1)2 - 5(-1) + 4(1)(-1)2 + 6(1) = -3 - 2 + 1 + 5 + 4 + 6 = 11 2 -2g + 4f + 5fg = -2(-1) + 4(1) + 5(1)(-1)2 = 2 + 4 + 5 = 11 19. A 20. Calculating a number to any exponent is the same as multiplying a number by itself the number of times indicated by the exponent. One multiplied by itself is always one, so one raised to the millionth power will still be one. 21. Student A should not have made the 2 negative when moving 2 to the -3 from the numerator to the denominator. Student B should not have added the exponents for (22 + 2) in the denominator. 22. 4790 m © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved.
LSN 3–3
Saxon Algebra 2
Lesson 13
3 3
23. V = Surface Area · Depth = 8.24 × 10 · 3.93 × 10 = 3.24 × 10 17m 3. Two times the volume of the Atlantic Ocean is 2(3.24 × 1017) = 6.48 × 10 17 m 3. V = Surface Area · Depth = 1.66 × 10 14 m 2 × 3.93 × 10 3 m ≈ 6.5 × 10 17m 3. 24. 9,345,600 ft 25. Length times width is an area of one side. Volume divided by this area gives the measurement of the other side, which is the height. First simplify the volume and area. 3 2 -2 4 x y x y _ _ Volume: = y
x
-3 2
x y
-2 3 -1
5
x y x y _ = Area: _ x -4 -2 2 y
x
y
height = volume ÷ area = volume × reciprocal of area 4 y x 1 _ ·_ =_ = x
y5
y
26. 8 movies at the first store will cost $35. 8 movies at the second store will cost $42. She must consider that the second store charges more for each movie rental. 27. 8 28. He multiplied the highway fuel efficiency by the city mileage. 61(15 - 4) + 50(4) = 871 miles 29. Associative Property of Multiplication; 9 · 9 is generally memorized as equaling 81, but 27 · 3 is more difficult to multiply without a calculator. 30. a. $2.24 + x b. $2.24 + $5.97 = $8.21 © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved.
LSN 3–4
Saxon Algebra 2
3
Warm Up 3 1. exponent 2. False 3. 81 Lesson Practice 3 a. 8 1 b. _ 16 1 c. -_ 4 1 d. - _ 8 1 e. - _ 16
f. x7y-5 g. x5y2 x h. _ 6 y
i. x ab-2by ab+1 j. 8 × 1017 k. 1.60 × 10 3 pounds
© 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved.
LSN 3–1
Saxon Algebra 2
Lesson
3
1 5. _ 12 2
Practice 3
16x y 1 _ 5 3 a b c
1. -24
6.
2. 31
2x2 _ 7. 10 y
3. Commutative Property
9
4y 8. _ 6 x
4. Distributive Property
9. 9π m2 10. 74°
11. Let the circumference be C, the number of girls be g, and the average height be h. Then, C = g × h = 7 -3 3 × 10 × 1.4 × 10 . The Commutative Property of Multiplication allows for these numbers to be multiplied 7 -3 in any order to give C = 10 × 10 × 3 × 1.4. The exponents of 10 can be added mentally to give C = 10 4 × 3 × 1.4. Let 1.4 = 1 + 0.4. Then, 3 × 1.4 = 3(1 + 0.4) = 3 + 1.2 = 4.2 by the Distributive 4 Property and mental math. Therefore, C = 10 × 4.2 = 4.2 × 10 4 km by the Commutative Property of Multiplication. 12. a. Think of $18 as $20 - $2. Write an expression: 0.1(20 - 2). Use the distributive property: 0.1(20) - 0.1(2). Multiply: 2 - 0.2. Subtract: 1.8. A 10% tip is $1.80. b. A 15% tip equals a 10% tip plus one-half of the 10% tip. So, a 15% tip equals $1.80 + $0.90 = $2.70. 13. The first step should be labeled “Distributive Property.” The second step should be labeled “Multiply.” © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved.
LSN 3–2
Saxon Algebra 2
Lesson
3
14. a. -5 b. The result would increase by 2y c. 1 15. 3(33) + 2(75) = 99 + 150 = 249 mg 16. The first square has one side of length 5u - u = 4u. So, 2 the area of the first square = (4u)(4u) = 16u . The second square has one side of length 4u - 2u = 2u. So, the area 2 of the second square = (2u)(2u) = 4u . The combined area = 16u 2 + 4u 2 = 20u 2. 17. (17, 14) 18. 3(-1) - 2(1) + (1)(-1)2 - 5(-1) + 4(1)(-1)2 + 6(1) = -3 - 2 + 1 + 5 + 4 + 6 = 11 2 -2g + 4f + 5fg = -2(-1) + 4(1) + 5(1)(-1)2 = 2 + 4 + 5 = 11 19. A 20. Calculating a number to any exponent is the same as multiplying a number by itself the number of times indicated by the exponent. One multiplied by itself is always one, so one raised to the millionth power will still be one. 21. Student A should not have made the 2 negative when moving 2 to the -3 from the numerator to the denominator. Student B should not have added the exponents for (22 + 2) in the denominator. 22. 4790 m © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved.
LSN 3–3
Saxon Algebra 2
Lesson 13
3 3
23. V = Surface Area · Depth = 8.24 × 10 · 3.93 × 10 = 3.24 × 10 17m 3. Two times the volume of the Atlantic Ocean is 2(3.24 × 1017) = 6.48 × 10 17 m 3. V = Surface Area · Depth = 1.66 × 10 14 m 2 × 3.93 × 10 3 m ≈ 6.5 × 10 17m 3. 24. 9,345,600 ft 25. Length times width is an area of one side. Volume divided by this area gives the measurement of the other side, which is the height. First simplify the volume and area. 3 2 -2 4 x y x y _ _ Volume: = y
x
-3 2
x y
-2 3 -1
5
x y x y _ = Area: _ x -4 -2 2 y
x
y
height = volume ÷ area = volume × reciprocal of area 4 y x 1 _ ·_ =_ = x
y5
y
26. 8 movies at the first store will cost $35. 8 movies at the second store will cost $42. She must consider that the second store charges more for each movie rental. 27. 8 28. He multiplied the highway fuel efficiency by the city mileage. 61(15 - 4) + 50(4) = 871 miles 29. Associative Property of Multiplication; 9 · 9 is generally memorized as equaling 81, but 27 · 3 is more difficult to multiply without a calculator. 30. a. $2.24 + x b. $2.24 + $5.97 = $8.21 © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved.
LSN 3–4
Saxon Algebra 2
