Substitution
Is the following equation true or false if j = 8?
152 ÷ j = 21
false
What is the rule for all four of the properties of equality?
Whatever you do to one side of the equation, you must do to the other side of the equation.
Addition & Subtraction
Multiplication & Division
y- ⁴⁄₉ = ⅔
y = 1 ⅑
1.8x = 40.14
x = 22.3
r = 1, 3, 6, 8
which of the given values for r, if any, is the solution to the equation?
24 ÷ r = 6
No solution is given in the set of values.
True or false?
If: 23 + x = 60
Then: 23 + x - 1 = 60 - 1
True - the same value was subtracted from each side (subtraction property of equality)
Find the value of x:
x - 40 = 3
x = 43
ˣ⁄₅ = 8
x = 40
r ÷ 5.5 = 18.2
r = 100.1
Which of the following is not a solution if a = 6
1. 8a = 48
2. 11 - a = 6
3. a + 3 = 9
4. 54 ÷ a = 9
12(x + y) = 12z
Find the value of b:
56 ÷ b = 8
b = 7
x - ⅗ = ⁷⁄₁₀
x = 1 ³⁄₁₀
k - 48.55 = 19.97
k = 68.52
Kiwi spent $5.12 on hot chocolate and a cookie. The hot chocolate cost $1.30. Use the equation c + 1.30 = 5.12 to find out what type of cookie he bought.
chocolate chip - $3.54
sugar - $3.82
peanut butter - $3.92
3.82 + 1.30 = 5.12
Which equality properties was used in the following equation?
If: 12 + 8 = 20
Then: (12 + 8) ÷ 2 = 20 ÷ 2
The Equality Property of Division
Elijah and his four Avenger pals spent an equal amount of time searching for Infinity Stones. Iron Man added their times and found that each of the 5 Avengers spent 3 hours searching. Write and solve a division equation to find the total number of hours Elijah and the Avengers spent looking.
c ÷ 5 = 3
c = 15
When solving an equation involving a mixed number, such as y + ¾ = 4 ½, what do you need to do to the mixed number?
You first need to turn the mixed number into an improper fraction.
Miss Soldano needs 67.25 grams of sugar for her chocolate chip cookies. She bakes more than one batch of cookies. If she uses a total of 201.75 grams of sugar, how many batches of cookies did she make? Write and solve an equation
201.75 ÷ b = 67.25
b = 3
OR
67.25b = 201.75
b = 3
Jeffrey says that y = 5 is the solution of the equation 7y = 45. How can you check to see whether Jeffrey is correct? Is Jeffrey correct?
You can substitute 5 for the value of y to see whether the solution of the equation is true. 7 x 5 = 35, not 45, so Jeffrey is incorrect.
Tony wrote y + 6 = 15. Then, he wrote (y + 6) ÷ 3 = 15 and said the second equation was still equal. How can Tony fix his second equation to make it so that he is correct?
Tony can divide 15 ÷ 3 like he did on the left side of the equation.
Emily typed 1,125 words in 15 minutes. Let w represent the number of words typed. If Emily typed an equal amount of words per minute, write and solve a multiplication equation to represent the problem.
15w = 1125
w = 75
Genesis needs to swim a total of 8 miles this week. So far, she swam 5 ⅜ miles. Use the equation 5⅜ + m = 8 to find out how many more miles Genesis needs to swim.
2⅝
t + 3.75 = 4.50
t = 0.75