# Algebra: Multiplication and Division - Grade 5 Math

## Algebra: Forming and Solving Simple Equations Involving Multiplication and Division

### Forming Simple Equations with One Unknown

#### Practice Example 1: Multiplication

Mary bought 7 box of apples. Each box has 6 apples. If the total number of apples bought was y. Form a simple equation that can be used to find the value of y.
Total number of boxes: 7
Number of apples in each box: 6
Total number of Apples bought: y
Equation: 7 x 6 = y

#### Practice Example 2: Division

Patricia has 40 pens. She wants to back the pens equally into 5 boxes. Once packed, each box will contain t pens. Form an equation to find the value of t.
Total Number of Pens: 40
Number of boxes packed: 5
Number of pens in each box: t
Equation: 40 ÷ 5 = t

#### Practice Example 3: Try it!

In a Grade 5 class, a teacher shared 24 books equally among the learners. Each learner got 3 books. There are a total of n learners in the class. Form a simple equation to use to find the total number of learners, n.
Total Number of books: 24
Number of books per learner: 3
Total number of Grade 5 learners: n
To create the equation, we have to determine the sign to use. Is it multiplication or division?
We use division (÷)
Equation: 24 ÷ 3 = n

### Solving Simple Equations Involving Multiplication and Division

#### Practice Example 4: Multiplication

Find the value of p in
p x 3 = 12
Note
a x b = c is the same as ab = c
Hence: p x 3 = 12 is the same as p3=12 which is the same as 3p = 12.
We divide both sides by the known value 3:
3p/3 = 12/3
p = 12/3
p = 4

#### Practice Example 5: Division

Find the value of y in
y ÷ 4 = 5
Note
a ÷ b = c is the same as a/b = c
Hence: y ÷ 4 = 5 is the same as y/4 = 5.
We multiply both sides by the known value 4:
4 x y/4 = 5 x 4
y = 5 x 4
y = 20

#### Practice Example 6: Try it!

Brian had 18 marbles. He shared them equally among 3 friends. If each friend got p marbles, how many marbles did each friend get?
Total Number of marbles: 18
Number friends: 3
Total number of marbles per student: p
To create and solve the equation, we have to determine the sign to use: multiplication or division.
The simple equation is:
3 x p = 18 which is the same as 3p = 18
We divide both sides by the known value 3:
3p/3 = 18/3
p = 18/3
p = 6