Percentages and fractions
Adding and subtracting
Convert if needed *so they have same denominator* then add or subtract numerators Add or subtract whole numbers separately
Profit and loss
Cost price - price when it's a buy Selling price - price when it's a sell If selling price is more than cost price you make a profit If selling price is less than cost price you make a loss
increase/decrease note
If given final price just guess and check for increase and decrease only
Percentage profit
profit/cost price x 100
Examples using GST
1) Find price of a Tv if it sells for $722 (+10% GST) GST: 10% of $722 =72.20 Selling price = 72.20 + 722 =$794.20 2) Lounge sells for $2695 including GST Find selling price 100 + 10% 110% 1% = 2695/110 =$24.5
Percentages without a calculator
1/4 1/2 3/4 1/3 2/3 1/5 2/5 3/5 25% 50% 75% 33 1/3% 66 2/3% 20% 40% 60% 1/10 1/8 10% 12 1/2%
GST
10% (Goods and Services Tax)
If original price is wanted or If whole amount is wanted
=UNITARY METHOD
How to decrease
Decrease $150 by 12% 12% of $150 12/100 x 150 = $18 150 - 18 (decrease) = $132
Examples of percentages without a calculator
Find 25% of 32 kg 25% = 1/4 1/4 of 32kg =8kg
Unitary method - increase
If given FINAL PRICE and you have to... Increase - unitary method but divide price by (100 + percentage given) Example: 18% profit on cakes. She sells a cake for $330.40. What was the original cost? 100 + 18 =118% 118% = $330.40 1% = 330.40/118 =2.83 100% = 2.83 x 100 =$280
Unitary method - decrease
If given FINAL price and you have to... Decrease - unitary method but divide price by (100 - percentage given) Example: A dress is discounted by 25%. Sale price is $225, what was the original price/ 100 - 25 =75% 75% = $225 1% = 225/75 =3 100% = 3 x 100
How to increase
Increase $200 by 7% 7% of $200 =7/100 x 200 =14 +200 (increase) =214
Increasing and decreasing percentages
Increase - make bigger, GST, profit Decrease - make smaller, reduce, discount
Multiplying and dividing fractions
Multiply numerators and denominators separately then simplify *Sometimes it is easier to simplify first* Divide by a fraction, a/b, multiply its reciprocal To divide or multiply mixed numerals, convert to improper fractions first
Unitary
One unit
Percentages, fractions and decimals
Percentage is a fraction whose denominator is 100 To convert a fraction or decimal into a percentage, multiply by 100 To order a fractions, decimals and percentages, convert each to a percentage to convert a percentage into a decimal, convert to a fraction, then divide by 100
Fractions and percentage of a quantity
Percentage/100 x quantity or percentage divided by 100 x quantity
Expressing amounts as fractions and percentages
To write an amount as a fraction of a whole amount fraction = amount/whole amount To write an amount as a percentage of a whole amount percentage = amount/whole amount x 100%
Percentage loss
loss/cost price x 100