Percent (Procent)

Ämne / Topic

Percent increase and decrease calculations.

Finding percentage point (procentenhet)

Inlärningsmål / Learning Goals

Understand percent

Google Slides & Videos

3. Aktiviteter / Key Activities

Introduce learners to the formulas that they will need to know how to use.

Percentage Increase

For a percentage increase, the decimal or fraction that you multiply the amount by will be greater than 1.

Example: Jane deposits £1,360 into her bank account which has an interest rate of 2.2% per year. Assuming that she does not deposit or withdraw any money, how much money will she have in a year’s time?

The new total value of Jane’s account will be equal the original total plus 2.2% of the original total. To find this total we multiply £1,360 by 1+0.022=1.022.

Therefore, the total value is, 1,360×1.022=£1,389.92

Percentage Decrease

For a percentage decrease, the decimal or fraction that you multiply the amount by will be less than 1.

Example: If Jane decides to withdraw 25% of the total £1,389.92, we find the decimal equivalent as

1−0.25=0.75

Therefore after the withdrawal, the value of the account is,

1,389.9×0.75=£1,042.44.

Percentage Change

Percentage change is used to find the change in a value as a percentage.

Percentage ‘Change’=(Original / Change) × 100

Example: Calculate the percentage change when a car goes down in value from £8,500 to £7,000.

Using the equation above we can calculate the percentage change by first calculating the difference, which is, £8,500−£7,000=£1,500. We then need to divide this difference by the original amount and multiply by 100 to get the percentage change:

Percentage Change=(£8,500 / £1,500) ×100

=17.65%

Percent formulas:

Increase and decrease in percent:

(%) increase/ decrease = new - original

original

Percent and percentage points:

% increase = difference

original

Per mille:

per mille = 1

1000

After the learners have been introduced to the different formulas that they will be using in this concept, they will practice using these formulas with the examples that the teacher will be going through.

Example 1:

Unemployment in a municipality increased from 5 195 people to 5 347 people.

What was the percentage increase?

(%) increase = new - original

original

= (5 347 - 5 195)

5 195

= 152

5 195

= 0,029 x 100 (multiply by 100, because we want the answer as a percent)

= 2,9 %

Example 2:

In August, unemployment fell from 8,2 % to 7,7 %.

How much did unemployment decrease in terms of

a. Percentage points

Percentage points = (8,2 % - 7,7 %)

= 0,5 %

b. percent

% Decrease = 0.5

8,2

= 0,0609 x 100

= 6,1 %

Example 3:

In a lottery, in a market, there are 7 500 lots. Of these, 50 are the lotteries that make a profit.

What proportion doe it correspond to? Round off to tenths of a thousand.

Share of winnings = 50

7500

= 0,0067 x 1000 (x1000 because it says round to tenths of a 1000)

=6,7%.

Example 4:

The highest mountain in the world is Mount Everest, which is 8 848 m high. Swedens highets mount is Kebnekaise, which is 2 106 m high.

a. How many percent lower is Kebnekaise than Mount Everest?

(%) increase = new - original

original

= 8 848 - 2 106

8 848

= 6 742

8 848

= 0,7619 x 100

= 76,1 %

b. How many percent higher is Mount Everest than Kebnekaise? Round to the nearest percent.

(%) increase = new - original

original

= 8 848 - 2 106

2 106

= 6 742

2 106

= 3,201 x 100

= 320 %

4. Kolla vad eleverna kan / Check for understanding / Exit ticket

Check in with each student as they work through problems. Call on students during instruction.

Question 1: Without using a calculator, work out 33% of 180

See video below

Question 2: Matteo scored 99 out 150 on an exam. What is his score as a percentage?.

See video below

Question 3: Mildred’s salary has increased from £24,600 to £25,338. By what percentage has her salary increased?

In this question the difference between the two salaries is £25,338 − £24,600 = £738

The original amount (the amount before it was increased) was £24,600, so the percentage increase can be calculated as follows:

(£738 / £24,600) × 100

= 3%

Question 4: The price of a motorbike is reduced by 10%. In a sale, the new price is reduced further by 10%. By what percentage has the original price of the scooter been reduced in this sale?

To most people, this would appear a very easy question with an answer of 20%, but this answer is, sadly, incorrect!

The easiest thing to do to solve this question is to invent a price for the motorbike. You can invent any price you want, but it would be advisable to make the price a nice, easy number and, since this question concerns percentages, giving the motorbike a price of £100 makes life extremely easy.

If the motorbike costs £100, when if it is reduced by 10%, then its new value is £90.

If the motorbike now costs £90 and is further reduced by 10%, then we need to deduct 10% from this £90 value (and not the previous £100 value).

10% of £90 = £9

So the new value of the motorbike is £81.

So the motorbike has decreased in value from £100 to £81. Since we set the motorbike’s original price as £100, the percentage decrease here should be relatively obvious. If not, remember that to calculate a percentage decrease (or increase), you need to divide the difference between the two values by the original value and multiply by 100.

The original value of the motorbike was £100, and its new value is £81, so the percentage decrease can be calculated as follows:

£100−£81 = 19

(19 / 100) × 100=19%

Therefore, the motorbike has decreased in value by 19% and not 20%.

5. Stängning / Closure / Summary of lesson

Take up difficult problems from leveled questions on the board.