# Using decimal multipliers to solve percentage increase problems.

If you are carrying out a percentage increase question then you are making the amount larger by a given percentage. Here are two methods that you can use to work out a percentage increase question:

Method 1

1. Work out 1% of your number. Do this by dividing the amount by 100

2. Multiply this amount by your percentage.

3. Add this amount back onto the original amount.

Method 2

1. Add the percentage to 100.

2. Change the percentage to a decimal (by dividing by 100).

3. Multiply the amount by this decimal.

Both methods will give exactly the same answer. The second method is a quicker method and it can be applied to harder percentage questions.

Example 1

Increase 62m by 18%

Method 1

1. Work out 1% of your number. Do this by dividing the amount by 100

1% = 0.62 ( 62 ÷ 100 = 0.62)

2. Multiply this amount by your percentage.

0.62 × 18 = 11.16

3. Add this amount back onto the original amount.

62 + 11.16 = 73.16m

Method 2

1. Add the percentage to 100.

100 + 18 = 118%

2. Change the percentage to a decimal (by dividing by 100).

118% = 1.18 (divide by 100)

3. Multiply the amount by this decimal.

62 × 1.18 = 73.16

Example 2

A bank account contains £2000. If the interest rate is 3.7%, how much money will be in the account at the end of the year?

Method 1

1. Work out 1% of your number. Do this by dividing the amount by 100

1% = £20 ( 2000 ÷ 100 = 20)

2. Multiply this amount by your percentage.

20 × 3.7 = £74

3. Add this amount back onto the original amount.

2000 + 74 = £2074

Method 2

1. Add the percentage to 100.

100 + 3.7 = 103.7%

2. Change the percentage to a decimal (by dividing by 100).

103.7% = 1.037 (divide by 100)

3. Multiply the amount by this decimal.

2000 × 1.037 = £2074

So you can see that both methods give a final answer of £2074 in the bank account at the ned of the year.

Example 3

A tree is 4m tall. Over the next year it grows by 27%. How tall is the tree now?

Method 1

1. Work out 1% of your number. Do this by dividing the amount by 100

1% = 0.04 (4 ÷ 100 = 0.04)

2. Multiply this amount by your percentage.

0.04 × 27 = 1.08

3. Add this amount back onto the original amount.

4 + 1.08 = 5.08m

Method 2

1. Add the percentage to 100.

100 + 27 = 127%

2. Change the percentage to a decimal (by dividing by 100).

127% = 1.27 (divide by 100)

3. Multiply the amount by this decimal.

4 × 1.27 = 5.08m

So the tree is 5.08m tall.

Check out this link below to find some more questions but on percentage decreases.

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