Percentages and fractions

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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


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