Topic A&B
65 + ____ - 15 = 65
____ + g - g = k
a + b - _____ = a
15
k
b
Give an example of the commutative property of addition and multiplication.
a + b = b + a
a x b = b x a
Write the expression:
a) Five divided by the sum of a and b
b) The quotient of k decreased by 4 and 9
c) The quantity 4 minus m divided by the sum of n and 11
a) 5/(a + b)
b) (k-4)/9
c) (4-m) / (n+11)
Kathleen lost a tooth today. Now she has lost 4 more than her sister Clara lost.
a) write an expression to represent the number of teeth Cara has lost. Let K represent the number of teeth Kathleen lost.
b) Write an expression to represent the number of teeth Kathleen lost. Let C represent the number of teeth Cara lost.
c) If Cara lost 3 teeth, how many teeth has Kathleen lost? Show substitution with your equations!
a) K - 4
b) C + 4
c) C + 4; 3 + 4= 7; Kathleen lost 7 teeth
State when the following equations and inequalities will be true and when they will be false:
a) 5g > 45
b) 14 = 5 + k
a) true g > 9 ; false g less than or equal to 9
b) true k=9; false k doesn't equal 9
12 / 3 x ____ = 12
f x h / h = ______
_____ / r x r= p
3
f
p
a) write an expression showing the sum of 8 and a number f.
b) write an expression showing 5 less than the number k.
c) write an expression showing the sume of a number h and a number w minus 11.
a) 8 + f or f + 8
b) k - 5
c) h + w - 11
Write an expression for the text:
a) A number h is tripled and then decreased by 8.
b) Sidney brought s carrots to school and combined them with Jenan's j carrots. She then split them equally among 8 friends.
a) 3h - 8
b) (s+j) / 8
Anna charges $8.50 per hour to babysit.
a) Write an expression describing her earnings for working H hours.
b) How much will she earn if she works for 3.5 hours? show your work with the equation and substitution.
c) How long will it take Anna to earn $51.00? Show your work with the equation.
a) 8.5h
b) $29.75
c) 6 hours
Find the solution and show your work:
a) 7f = 49
b) 1 = r/12
c) 40 = 1/2p
a) 7
b) 12
c) 80
What are the equivalent expressions to these:
4 x 9
7h
j + j + j + j + j
9 + 9 + 9 +9
h + h + h + h + h + h + h
5j
Simplify:
a) 5g x 7h
b) 3 x d x e x 9 x y x z
c) (4mp)(11)
a) 35gh
b)27deyz
c) 44mp
Write an expression for the text:
a) 15 less than the quotient of e and d.
b) Marissa's hair was 10 inches long, and then she cut h inches.
a) e/d - 15
b) 10-h
Krystal Klear Cell Phone Company charges $5.00 per month for service. The company also charges $0.10 for each text message sent.
a) write an equation for when a user sends T number of messages.
b) If Suzannah's budget is $10 per month, how many text messages can she send in one month? Set it up as an equation and solve for T. Show your work!
a) 0.1T + 5
b) 0.1T + 5 = 10; she can send 50 text messages
Solve the equation using tape diagram and algebraically (show your work):
a) j + 12 = 25
b) k - 16 = 4
a) j=13
b) k=20
What is the difference between 6z and z6?
6z= z + z + z + z + z + z
z6= z x z x z x z x z x z
Write equivalent expressions:
a) 2x + 8y
b) 13ab + 15ab
c) 20g + 24h
a) 2(x + 4y)
b) ab(13 + 15)
c) 4(5g + 6h)
Write an expression for the text:
a) a number x increased by 6, and then the sum is doubled.
b) The total of h and b is split into 5 equal groups.
a) 2(x+6)
b) (h+b) / 5
Naomi's allowance is $2.00 per week. If she convinces her parents to double her allowance each week for two months....
a) what will her weekly allowance be at the end of the second month (week 8)?
b) write the expression that describes Naomi's allowance during week w in dollars.
a) $256.00
b) $2w
Solve the equations algebraically (show your work):
a) 64 = 16u
b) r/10 = 4
c)12 = x/4
d) 18z = 72
a) u=4
b) r=40
c) x=48
d) z=4
Evaluate the expressions (must show your work):
a) 12 x (3 +22)/2 - 10
b) 12 x (3+2)2 /2 - 10
a) 32
b) 140
Write equivalent expressions:
a) 2(b+c)
b) 5(7h + 3m)
c) e(f+g)
a) 2b + 2c
b) 35h + 15m
c) ef + eg
Write an expression for the text:
a) Jazmin has increased her $45 by m dollars and then spends a third of the entire amount.
b) Bill has d more than 3 times the number of baseball cards as Frank. Frank has f baseball cards.
a) 45 + m / 3 or one third (45 + m)
b) 3f + d or d + 3f
CDs cost $12 each at the Music Emporium. the company charges $4.50 for shipping and handling, regardless of how many CDs are purchased.
a) If you know how many CDs someone orders, can you determine how much money they will spend? Write the expression to show this.
b) use your expression to determine how much money will be spent when buying 8 CDs.
a) 12D + 4.5
b) 12(8) + 4.50 = 100.50
Karter has 24 T-shirts. Karter has 8 fewer pairs of shoes than pairs of pants. If the number of T-shirts Karter has is double the number of pants he has, how many pairs of shoes does Karter have? Let p represent the number of pants Karter has and s represent the number of pairs of shoes he has. Solve with tape diagram and algebraically.
Tshirt equation/Tape diagram:
2p = 24; p=12
Shoes equation/Tape diagram:
s + 8 = 12; s=4
Karter has 4 pair of shoes