Topics 6 & 7 Equations (with some vocab)
Zacarias and Paz together have $756.80. If Zacarias has $489.50, how much does Paz have?
$267.30
Tina had some money in her piggy bank. She added $7.65. She now has exactly $42.00. Use the equation m + 7.65 = 42 to find how much she started with.
$34.35
Kelly earned $27 for babysitting. She has also earned money for doing chores. Altogether she has $113. How much did she earn doing chores?
$86
associative property
(3 + 4) + 5 = 3 + (4 + 5)
Bianca sold n cookies at the bake sale on Friday for $0.75 each. She earned a total of $48. Write an equation that represents the amount of cookies Bianca sold at the bake sale?
0.75n = 48
Catherine studied 1.25 hours for her science test. This was 0.5 hours less than she studied for her algebra test. How long did she study for her algebra test?
1.75 hours
Amy is making bracelets. For one bracelet she uses 9 beads. For two bracelets she uses 18 beads. If this pattern continues, how many beads will Amy need to make 15 bracelets?
135
Peter collects old toy cars. He collects 14 cars for n weeks until he has 56 cars. Write an equation that represents the amount of weeks it took Peter to save his cars?
14n = 56
Simplify: 8 x (3^3 + 2) - 11
221
Ruth is making lemonade. For every 3 cups of water she uses 6 lemons, for 4 cups 8 lemons, etc. If this pattern continues, how many lemons will she need for 12 cups of water?
24
Trish noticed that she had taken notes on 50 pages of her notebook. 195 pages were still blank. How many total pages are in her notebook?
245
x + 29 = 54
25
Greg picked a total of 42 grapes at a farm. This is 15 more than the number of blueberries he picked. Find the number of apples Greg picked.
27
Chrissy has 50 minutes before school. She spends 34 minutes getting ready and the rest of the time eating breakfast. Write an equation that represents the amount of time Chrissy spent eating breakfast?
34 + n = 50
Tatiana has $38. She earns some more money selling newspapers in her neighborhood. She now has $84. Write an equation that represents the amount of money Tatiana earned selling newspapers?
38 + n = 84
Multiplicative Identity
4 x 1 = 4
commutative property
5 x 8 = 8 x 5
distributive propery
5(6 + 7) = 5(6) + 5(7)
Meg needs to go to the airport. It takes her 100 minutes to get there by car. This is 2 times the time it takes by train. Find how long it takes Meg to get to the airport by train.
50 minutes
Simplify: 3x + 5y + 2x + 10 - 3y - 6
5x + 2y +4
y + 4.5 = 12
7.5
There were 200 students that participated in a clean up event at a nearby lake. This is one fourth of the entire student population. How many students are at the school.
800
Additive Identity
9 + 0 = 9
Jen is putting together gift baskets for Valentine's Day. In one basket, she uses 12 chocolates. For two baskets she uses 24 chocolate. If this pattern continues, how many chocolates will she use for 8 baskets?
96 chocolates
order of operations
Rules describing what sequence should be used to evaluate expressions
The (addition/subtraction/multiplication/division) property of equality simply states...
That as long as you perform the same operation on both sides of the equal sing, the equation remains balanced.
Multiple
The result (product) of multiplying an whole number with another whole number.
ratio
a comparison of two numbers using division
exponent
a number that tells how many times the base number is multiplied by itself
term
a number, variable or the product of a number and variable
composite number
a whole number greater than zero that has more that two different factors
prime number
a whole number greater than zero with only one set of factors, 1 and itself.
What turns an expression into an equation?
an equal sign
A mathematical phrase that may have numbers, variables and operators, but no comparison symbols.
expression
quadrants
four sections of a coordinate grid separated by the x and y axes.
When solving equations, you need to...
isolate the variable.
reciprocals
numbers relate to each other in such a way that when multiplied together the product is 1
Solve for r. 48 + r = 97
r=49
quotient
the answer to a division problem
product
the answer to a multiplication problem
difference
the answer to a subtraction problem
sum
the answer to an addition problem
denominator
the bottom number of a fraction that tells how many equal parts are in the whole.
dividend
the number being divided
a coefficient is
the number part of a variable term
Divisor
the number you divide by
Multiplicative property of zero
the product of any number and zero is zero.
integers
the set of whole numbers and their opposites.
additive inverse
the sum of any number and its opposite is zero.
Numerator
the top number of a fraction that tells how many equal parts are described in the fraction.
True or false? When solving an equation, the left and right side of the equation are equal.
true
Inverse operations
undo each other.
variable
unknown value
4 + x = 7
x = 3
22 + x = 26
x = 4
x + 2 = 9
x = 7
If x + 9.8 = 14.7, what is the value of 8(x - 3.7)?
x = 9.6
8 = x + 8
x=0
x + 4 = 5
x=1
2.8 = 1.4 + n
x=1.4
5 = x - 5
x=10
x + 2 = 12
x=10
x/10 = 1
x=10
x - 11 = 0
x=11
8 = x - 4
x=12
x - 20 = 100
x=120
x - 4 = 10
x=14
x - 7 = 8
x=15
x + 18 = 34
x=16
x - 4 = 14
x=18
x/3 = 6
x=18
x + 1 = 3
x=2
x - 10 = 10
x=20
x/3 = 7
x=21
x - 9 = 14
x=23
x - 8 = 17
x=25
x - 9 = 18
x=27
x/4 = 7
x=28
15 = 5x
x=3
8x = 24
x=3
x + 8 = 11
x=3
x - 12 = 18
x=30
x/3 = 10
x=30
132 + x = 155
x=33
x/7 = 5
x=35
x/9 = 4
x=36
12/x = 3
x=4
Riley collects stickers. She has 220 stickers. Her sister has 55 stickers in her collection. How many times as many stickers does Riley have? Use the equation 55x = 220.
x=4
x - 20 = 20
x=40
x - 13 = 30
x=43
2 + x = 50
x=48
x/8 = 6
x=48
Solve for X. 32x = 160
x=5
x + 8 = 13
x=5
x - 4 = 1
x=5
x/8 = 7
x=56
24/x = 4
x=6
54 = 9x
x=6
7x = 42
x=6
x + 3 = 9
x=6
x/8 = 8
x=64
10x = 70
x=7
56 = 8x
x=7
x/9 = 8
x=72
4 + x = 12
x=8
4x = 32
x=8
x - 1 = 7
x=8
x/10 = 8
x=80
x/9 = 9
x=81
10 + x = 19
x=9
3 = x/3
x=9
6 + x = 15
x=9
72 = 8x
x=9
x - 8 = 1
x=9
Gina baked 5 batches of cookies for a total of 75 cookies. Using the equation 5y=75, how many cookies were in each batch?
y=15
