BALANCING AND SOLVING EQUATIONS WITH SHAPES

Sometimes the symbol is not at the beginning so you rearrange the equation by performing an inverse operation.

This is because it is easier to solve when the symbol is on the left hand side of the equals sign.

Example 1 :

Solve

12 = 78 - ▲

Solution :

12 = 78 - ▲

12 + ▲ = 78 -▲+▲

12 + ▲= 78

Subtract 12 on both sides.

12 - 12 + ▲ = 78 - 12

▲ = 66

Example 2 :

Solve

23 = 56 -

Solution :

23 = 56 -

23 +  = 56 - ▲ + ▲

23 + ▲= 56

Subtract 23 on both sides.

▲ = 56 - 23

▲ = 33

Example 3 :

Solve

32 = 78 -

Solution :

32 = 78 -

32 +  = 78 - ▲ + ▲

32 + ▲= 78

Subtract 32 on both sides.

▲ = 78 - 32

▲ = 46

Example 4 :

Solve

36 = 112 -

Solution :

36 = 112 -

36 +  = 112 - ▲ + ▲

36 + ▲= 112

Subtract 23 on both sides.

▲ = 112 - 36

▲ = 76

Example 5 :

Solve

52 = 105 -

Solution :

52 = 105 -

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

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.

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