Vocabulary
A mathematical sentence that contains an equals sign, stating that two quantities are equal.
Equation
n + 3.5 = 6.7
n = 3.2
p – 11 = –5
p = 6
On Saturday mornings, Mandy volunteers at the hospital where her mother works. One Saturday, she answers phone calls at the information desk while the receptionist is away. Then she spends 25 minutes delivering flowers to patients' rooms. In all, Mandy volunteers at the hospital for 45 minutes that day.
Write and solve the equation.
t + 25 = 45
t = 20 minutes
2/3 =x/6
x=4
A letter that represents a unknown value
variable
–5 = m + 11
m = -16
12 = g – 56
g = 68
Pablo is building a wooden birdhouse for his mom. He finds a plank in the garage to use for the base. When he realizes it's too long, Pablo cuts 3.2 inches off the plank. Now it's the correct length of 9.25 inches.
Write an equation and solve.
t - 3.2 = 9.25
t = 6.05 inches
(1/5)b=35
A replacement value for the variable in an open sentence. A value for the variable that makes the equation true.
Solution
17 = h + 33
h = -16
x – 18 = –2
x = 16
On a sunny fall day, Ariel and her family go to an orchard to pick apples for their famous apple pies. First, they pick enough Golden Delicious apples to fill a bag. Then, they pick enough Honeycrisp apples to fill another bag. The bag of Honeycrisp apples weighs 18 pounds. In all, Ariel's family picks 22 pounds of apples.
Write and solve an equation.
x + 18 = 22
x = 4 pounds
Mrs. May is buying treats for her class. She buys c cookies for $1.25 each for a total of $23.75. How many cookies did she buy?
19
The operation that reverses (or undoes) the effect of another operation.
inverse operation
k + 9 = -1
k = -10
r - 72 = -31
r = 41
Natalie buys organic almonds priced at $77 from the grocery store. How much did she pay the cashier, if she received $23 in change?
Write and solve the equation.
x - 77 = 23
x = 100 dollars
Chelsea and three of her friends went out to eat. They decided to split the bill evenly. Each person paid $9. Write the equation and solve to see what the total bill was?
x/4=9
x=36
In Algebra, a number on its own - not attached to a variable.
constant
x + 1.6 = 0.8
x = -0.8
-121 = z - 99
z = -22
Trevor takes up a test at school and completes it in an hour. The test has two sections. If he takes 35 minutes to complete the first section, how much time does he have left to complete the second section?
Write and solve the equation.
x + 35 = 60
x = 25 minutes
A bag of candy is divided evenly among a class of 23 students. Each student got 4 pieces. How many pieces of candy were in the bag? Write an equation and solve.
x/23=4
x=92