Download 1-8 Algebraic Expressions

1-8 Algebraic Expressions
Name
Date
Billy has 15 more than twice as many checkers as Grace. If Grace has
c checkers, write an expression for the number of checkers Billy has.
Let Grace’s checkers be represented by c
Twice means multiply by 2. More than means add.
15
2c
So the expression that represents Billy’s checkers is 2c 15.
Evaluate 5w 6vw, when v 4 and w 8.
5w 6vw
6vw means 6 • v • w.
5(8) 6(4)(8)
Substitute 4 for v and 8 for w.
40 (192)
Multiply.
40 192
Subtract by adding the opposite.
232
Add.
Remember: You can use a handheld
to check your answer.
Write each word phrase as an algebraic expression.
1. 5 more than a
2. 3 more than five times d
3. 6 times the quotient of x and y
6
5d ⴙ 3 or (3 ⴙ 5)d
aⴙ5
( xy )
Write each algebraic expression as a word phrase. Possible responses shown
4. 4x 2
5. 7w 3
Copyright © by William H. Sadlier, Inc. All rights reserved.
the product of 4 and x,
decreased by 2
6. 4(a 11)
3 less than the product
of 7 and w
7. 9(f 13)
8. 11 d 45
9. 32 g 59
45 more than the quotient
of 11 and d
the product of 9 and the
difference of f and 13
the product of 4 and the
sum of a and 11
59 more than the quotient
of 32 and g
Write an algebraic expression to represent each situation.
10. Carmen worked h hours. If she works 7 more
hours, how many hours will she have worked?
Let h be the number of hours worked
7 more means add 7.
hⴙ7
12. Max gives an equal number of cards to
5 friends. If he gives c cards, how many
does each friend get?
c ⴜ 5 or
11. Tran worked w weeks. If he works 9 more
weeks, how many weeks will he have worked?
wⴙ9
13. Olivia reads an equal number of pages for
8 days. If she reads p pages in all, how many
pages does she read each day?
c
5
p ⴜ 8 or
Lesson 1-8, pages 16–19.
p
8
Chapter 1
15
For More Practice Go To:
Evaluate each algebraic expression for the given values of the variables.
You can use your handheld to check.
14. 4a 2(7 a), when a 3
15. 5b 3(2 b), when b 4
5(4) ⴙ 3(2 ⴙ 4)
20 ⴙ 3(6)
20 ⴙ 18
38
4(3) ⴙ 2(7 ⴙ 3)
12 ⴙ 2(10)
12 ⴙ 20
32
16. 12 2v 6v, when v 1
17. –q2 3qt 1, when q 2 and t 2
12 ⴚ 2(–1) ⴙ 6(ⴚ1)
12 ⴙ 2 ⴚ 6
14 ⴚ 6
8
ⴚ(2)2 ⴚ 3(2)(ⴚ2) ⴙ 1
ⴚ4 ⴙ 12 ⴙ 1
8ⴙ1
9
8
10
19. c d , when c 11 and d 11
cd
18. h2 5hk 6, when h 3 and k 3
ⴚ(ⴚ3)2 ⴚ 5(3)(ⴚ3) ⴙ 6
ⴚ9 ⴙ 45 ⴙ 6
36 ⴙ 6
42
20.
(3x y)2
1
1
if x 4 and y 4
x2 y
2
(3( 41 ) ⴙ (ⴚ 41 ))
2
( 41 ) ⴙ (ⴚ 41 )
2
3ⴚ1
(
4
4)
ⴝ
1 ⴚ1
16 4
4
ⴚ
3
8 ⴙ
11
8 ⴚ
11
10
18
11 ⴝ 11 ⴝ 18 • ⴚ11 ⴝ ⴚ9
11
2
10
ⴚ2
11
11
( e)2
1
1
21. 2d
if d 3 and e 3
d2 2e
2
2
2
2
(
)
4
ⴝ
4
16
ⴝ
• ⴚ
16
3
3
ⴚ
16
( )
(2( 31 ) ⴙ (ⴚ 31 ))
2
( 31 ) ⴙ 2(ⴚ 31 )
( 2 ⴚ 1)
ⴝ 3 3
1ⴚ 2
9 3
ⴚ1
5
ⴝ
2
( 31 )
ⴚ5
9
( )
ⴝ 1 • ⴚ9
9
5
23. Kyle increased a number by 6, multiplied
the sum by 8, and then divided the product
by 4. If his answer is 4, what was his
starting number?
22. A length of rope is cut into 3 pieces. The
second piece is 3 more than twice as long as
the first piece, x. The third piece is 4 times as
long as the second piece. Write an algebraic
expression for the length of each piece.
Let x represent the first piece; 2x ⴙ 3
represents the second piece, and 4(2x ⴙ 3)
the third piece.
ⴚ4 • (ⴚ4) ⴝ 16; 16 ⴜ 8 ⴝ 2; 2 ⴚ 6 ⴝ ⴚ4;
Kyle started with ⴚ4.
24. The quotient of the sum of two numbers and 9 is squared and then increased
by 15. The sum is then tripled. Write an algebraic expression to represent the
situation and evaluate it when a 5 and b 14.
3
16
[(a ⴙ9 b)
2
] [(ⴚ5 ⴙ9 14)
ⴙ 15 ; 3
Chapter 1
2
]
[( 99 )
ⴙ 15 ⴝ 3
2
]
ⴙ 15 ⴝ 3(1 ⴙ 15) ⴝ 3(16) ⴝ 48
Copyright © by William H. Sadlier, Inc. All rights reserved.
Solve. Show your work.