Order of Operations
3 x 5 - 10 =
5
h + 30 = 45
h = 15
4 x f = 40
f = 10
True or false. When two numbers are multiplied together, it matters what order they are in. This is also known as the commutative property of multiplication.
Explain your thinking using an example.
False.
For example:
3 x 2 = 6 and 2 x 3 = 6
It does not matter what order you perform this in.
Lisa and Moe participated in basketball game. Together, they scored 17 points. If Lisa scored 8 points, how many points did Moe score?
Using a variable to represent the unknown variable. Write an equation, and solve it. Write a short sentence.
8 + m = 17
m = 11
Moe scored 11 points at the basket ball game.
90 ÷ 2 + 4 =
49
15 = 10 + s
s = 5
t x 41 = 82
t = 2
Are the following equations equal? Yes or No (solve each equation prove your answer).
1) 12 + 22 = 22 + 12
2) 10 ÷ 2 = 2 ÷ 10
3) 3 x 2 = 2 x 3
1) Yes
34 = 34
2) No
5 ≠ 0.2
3) Yes
6 = 6
Smith and his friends are gaming online. An hour later, 6 friends go offline. 5 friends continue playing. How many of them were gaming online initially?
Using a variable to represent the unknown variable. Write an equation, and solve it. Write a short sentence.
f - 6 = 5
f = 11
There were 11 friends playing originally.
8 + 4 x (7 - 2) =
28
3 = 11 - n
n = 8
12 = 144 ÷ d
d = 12
14 + 6 = 12 + 8
If I multiply each side of this equation by 2, will it still be equal? Show your work.
Solution:
14 + 6 x 2 = 12 + 8 x 2
14 + 12 = 12 + 16
26 = 28
No. The equation will not be equal if you multiply 2 to both sides of the equation.
How many boxes of envelopes can you buy with $12 if one box costs $3?
Using a variable to represent the unknown variable. Write an equation, and solve it. Write a short sentence.
12 ÷ 3 = e
OR
e x 3 = 12
Solution: e = 4
You can buy 4 boxes of envelopes for 12 dollars.
19 + 40 ÷ 5 − (8 + 5) =
14
200 - k = 132
k = 68
7n = 28
n = 4
Using preservation of equality, solve these problems.
Problem 1: n + 5 = 10
Problem 2: 42 = p - 8
Problem 3: f + 13 = 20
Solutions:
Problem 1: n = 5
Problem 2: p = 50
Problem 3: f = 7
Hank works as a gas attendant during the summer. Each day he makes $80. Of the $80 he sets aside $15 each day, and puts it in his savings account. How much money will Hank save after working 20 days in the summer?
Using a variable to represent the unknown variable. Write an equation, and solve it. Write a short sentence.
15 x 20 = m
m = 300
Hank will save $300 dollars over the summer.
6×(21-12-7)+24÷3 =
20
12 + 5 - n = 12
n = 5
y/5 = 5
y= 25
Using preservation of equality, solve these problems.
Problem 1: n x 10 = 30
Problem 2: j ÷ 6 = 4
Problem 3: f ÷ 4 = 3
Solutions:
Problem 1: n = 3
Problem 2: j = 24
Problem 3: f = 12
Ronaldo and 3 of his friends went out to eat. They decided to split the bill evenly. Each person paid $36. What was the total bill?
Using a variable to represent the unknown variable. Write an equation, and solve it. Write a short sentence.
36 x 4 = b
b = 144
The total bill was $144.