Percentage (S1 - NT)
A percentage is expressed as a number our of 100.
Symbol: %
% means out of 100
25% => 25/100
% and fraction
Example: Express 20% as a fraction
Step : Change % to /100 and reduce to lowest term
20% => 20/100
= 1/5
Example: Express 1/4 as a percentage
Step: Multiply by 100 and add a percent
1/4 = 1/4 x 100
= 25%
% and Decimal
Example: Express 25% as a decimal
Step: Divide number by 100 and remove the %
25% = 25/100
= 0.25
Example: Express 0.38 as a percentage
Step : Multiply by 100 and add %
38% = 38/100
= 0.38
Percentage greater than 100%
100% = 100/100 = 1
Example:
Express 120% as (a) a decimal (b) a fraction
Step 1: Write the percent with /100
120% = 120/100
Step 2: 'Split' value with 100/100 or 1
120/100 = 1 20/100
Step 3: Compute required value
(a) 20/100 = 1/5
120% = 1 1/5
(b) 20/100 = 0.2
120% = 1.2
Finding a Percentage Part of a Whole
=> To Find a Quantity Given the Percentage
To Find the value of A% of a quantity B,
=> Changing the A% to /100
A x B
100
Example
Calculate 25% of 80
Step1: Use the formula A/100 x B
25/100 x 80
Step2: Compute the value
25/10041 x 8020
= 20
Example: What is 6% of 300?
6% of 300
= 6/100 x 300 (step 1)
= 18 (step 2)
Example: What is 110% of 50?
110% of 50 = 110/100 x 50 (Step 1)
= 55 (Step 2)
Expressing a Quantity as a percentage
Example
Cindy has $20. She spent $15 to buy a dress. What percentage of the money is spent?
She has $20 (Whole). She spent $15 (part).
Expressing A(part) as a percentage of B(whole) :
=> A x 100%
B
Step1: Use formula
= 15/20 x 100
Step 2 : Compute the value
= 3/4 x 100
= 75%
Example
Express 9g as a percent of 150g
= 9/150 x 100. (Step 1)
= 93 x 102 0 (Step 2)
1550
= 3 x 2
= 6%
Finding the Whole Given a Percentage
Example
Anna spends 10% of her money to buy 1 pencil. If the pen costs $2. How much money does she have at first (100%)?
Step1: Relate the % to the value
10% -> $2
Step2: Find 1% of the value
1% -> 2/10 = $0.2
Step3: Find the whole (100%)
100% -> 100 x 0.2
= $20
Comparing Two Quantities by Percentage
Example
Gina scored 7/10 in her first Science test, and 16/25 for her second test. Which test did she score better?
Step 1: Convert both marks to %
7/10 = 7/10 x 100 = 70%
16/25 = 17/25 x 100 = 68%
Step 2 : Compare the two percent value and Answer
She did better in her first test.
Increasing/Decreasing a Quantity by a Given Percentage
Example
Increase $500 by 20%
Step1: Find 1% of $500
1% -> 500/100 = $5
Step2: Compute required percent or Step2: total of percent increase
20% -> 20 x 5 120% -> 120 x 5 = $600
= $100
Step3: (Increase) Add to original Amount
Increase = $500 + $100 = $600
Finding Percentage Change (Increase/Decrease)
Example
John's pay increased from $2000 to $2000. How many percent has his pay increased?
Step1: Compute the increase/decrease
$2200 - $2000 = $200
Step2: Amount increased x 100. [Formula]
original amount
= 12/20 x 100 [** the denominator is the Whole(original amount0]
Step3: Compute the value
126/2010 x 100
= 60%
=> Formula : Amount Increase/Decreased x 100
Original Amount
Example
Calculate the percentage change for increasing 20 to 32
Increase = 32 – 20. (Step 1)
= 12
% change = 12/20 x 100 (Step 2)
= 126/2010 x 100 (Step 3)
= 60%
Finding the Whole Given the Percentage Increase/Decrease
Example
The price of a book was increased by $2. The increase is equal to 10% of the original price. Find the original price of the book.
10% = $2 (Step 1 : Find 1%)
1% = $0.2
100% = $0.2 x 100 (Step 2 : Find 100%)
= $20.
* When calculating percentage changes (increase or decrease), always divide by the original value.
Profit and Loss
Cost Price = The price to make/buy something to sell
Selling Price = The price to sell something
There is a profit when Selling Price > Cost Price
There is a loss when Cost Price > Selling Price
Profit = Selling Price - Cost Price
=> Selling Price = Cost Price + Profit
Loss = Cost Price - Selling Price
Example
Kathy bought a bag for $25, and sell it for $30.
(a) What is her profit?
Cost Price = $25
Selling Price = $30
Profit = $30 - $25 = $5
(b) What is her profit as a percentage of the cost price?
Profit % = Profit x 100%
Cost Price
Example
A watch is sold at a profit of 20%.
(a) Find the cost price of the bag if the profit is $40.
20% = $40
1% = $40/20 = $2 (Step 1 : Find 1%)
100% = $2 x 100 (Step 2 : Find 100% = Cost Price)
= $200
(b) What is the selling price?
Selling price = Cost price + profit
= $200 + $40 = $240.
Practice
1. Express the following percentages as fractions in the simplest form.
(a) 5% (b) 5 1/2% (c) 1.4% (d) 0.8% (e) 125%
2. Express the following percentages as decimals.
(a)10% (b) 53% (c) 180% (d) 0.75% (e) 6.5%
3. Express each of the following as a percentage
(a) 1/2
(b) 0.35
(c) 0.008
(d) 3/5
4. Find the following:
(a) 20% of $45
(b) 80% of $200
(c) 120% of 150
4. Express
(a) 21g as a percentage of 70g
(b) 15 mins as a percentage of 1 hour
(c) $25 as a percentage of $400
5. Which has a higher percentage: 40 marks out of 50 or 45 marks out of 60?
6. Calculate the increase or decrease.
(a) Increase the time of 90 minutes by 12%
(b) Decrease the selling of $64 by 25%
7. The new packaging for a packet of chips increased from 300g to 360g. Find the percentage increase.
8. The marked price of a tablet is $267.50 inclusive of GST. If the GST is 7%, find
(a) its price before GST
(b) the amount of GST levied on it.
9. The original price for a pair of shoe is $25. At a sale, it was sold for $22. Find the percent decrease in price.
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