BALANCING AND SOLVING EQUATIONS WITH SHAPES

Example 2 :

Solve 

23 = 56 - ▲

Solution :

23 = 56 - ▲

Add triangle on both sides.

23 + ▲ = 56 - ▲ + ▲

23 + ▲= 56

Subtract 23 on both sides.

▲ = 56 - 23

▲ = 33

Example 3 :

Solve 

32 = 78 - ▲

Solution :

32 = 78 - ▲

Add triangle on both sides.

32 + ▲ = 78 - ▲ + ▲

32 + ▲= 78

Subtract 32 on both sides.

▲ = 78 - 32

▲ = 46

Example 4 :

Solve 

36 = 112 - ▲

Solution :

36 = 112 - ▲

Add triangle on both sides.

36 + ▲ = 112 - ▲ + ▲

36 + ▲= 112

Subtract 23 on both sides.

▲ = 112 - 36

▲ = 76

Example 5 :

Solve 

52 = 105 - ▲

Solution :

52 = 105 - ▲

Add triangle on both sides.

52 + ▲ = 105 - ▲ + ▲

52 + ▲= 105

Subtract 52 on both sides.

▲ = 105 - 52

▲ = 53

Solve the following word problems using inverse operations. The equations are partially set up. You may like to use a calculator.

Example 6 :

For my school fete I baked 3 batches of cookies, realized that wasn’t enough and so I bought a dozen more. How many were in one batch if I had 84 cookies altogether?

Solution :

Let ▲ be one batch of cookies.

3 x ▲ + 12 = 84

Subtract 12 on both sides.

3 x▲ + 12 - 12 = 84 - 12

3 x▲ = 72

Divide by 3 on both sides, we get

▲ = 72/3

▲ = 24

So, one batch will contain 24 cookies.

Example 7 :

8 same sized year 5 classes assembled in the playground for photo day. There were 11 students absent. How many students are there in each class if there were 213 there on the day?

Solution :

Let ▲number of students in year 5 class.

Number of students who were absent = 11

8 x ▲ - 11 = 213

Add 11 on both sides.

8 x ▲ - 11 + 11 = 213 + 11

8 x ▲ = 224

Dividing by 8 on both sides, we get

▲ = 224/8

▲ = 28

So, each class will contain 28 students.