Fractions, Decimals & Percentages Week 04: Fractions, Decimals & Percentages Calculate fraction and percentage parts Perform +, -, x and ÷ with fractions Order fractions, percentages and decimals by size Use fractions and percentages to calculate increases and decreases Calculate reverse percentages and express one number as a percentage of another Convert between fractions, decimals and percentages Calculate and use equivalent fractions, decimals and percentages

What did we do last week?

Which integer values satisfy these inequalities?

Key Terminology anrctifo rceeepntag cedmali nuatorrme danmintoore queivantel fyimplis cireasen cereased allccuate Fraction Percentage Decimal Numerator Denominator Equivalent Simplify Increase Decrease Calculate

Converting Fractions, Decimals & Percentages Fraction to Decimal: numerator ÷ denominator Decimal to Percentage: x 100 Percentage to Fraction: percentage becomes numerator, denominator is 100. Simplify. Fraction Percentage Decimal

Complete these FDP conversions…

¼ Fractions Denominator: The total number of parts Numerator: The number of parts we are interested in

Divide by the bottom number, multiply by the top Finding a fraction Calculate ¾ of 500. Divide by the denominator (bottom number) to get the value of ¼: 500  4 = 125 Multiply by the numerator (top number) to get the answer: 125 x 3 = 375 Divide by the bottom number, multiply by the top

Finding a fraction 3/8 of 32 ½ of 24 2/5 of 20 6/7 of 14

Exam question A TV programme lasting an hour has ⅖ of it dedicated to adverts. The rest of the programme is split equally between current affairs and sport. How long is spent on Sport ? ⅖ of 60 = 60 ÷ 5 = 12, 12 x 2 = 24 minutes of advertising 60 – 24 = 36 minutes remaining 36 ÷ 2 = 18 minutes for each of current affairs and sport.

Exam question A £45 pair of jeans have 1/3 off the price in a sale. What is the sale price? Original Price: £45 1/3: 45 ÷ 3 = £15 New Price: £45 - £15 = £30 The sale price of the jeans is £30.

Simplify the fractions… Customers have paid the following amounts to begin to pay off their overdraft. Simplify the fractions below: £300 paid of £450 £50 paid of £600 £400 paid of £1000 £60 paid of £120 £30 paid of £40 £45 paid of £90 £110 paid of £450

Equivalent fractions        

Equivalent fractions

Ordering fractions We use equivalent fractions when ordering fractions: We find the common denominator and use it to place the fractions in order from smallest to largest.

Making fractions Fractions are sometimes hidden in words instead of numbers: 60 learners were questioned in a recent survey and 15 were found to be smokers. Where’s the fraction? The total number = 60, the amount that were smokers = 15 = 15/60 Can the fraction be simplified? Yes! ¼ The survey found a quarter of learners smoked.

Making fractions Santander recently conducted a survey on their customers: 200 are 0 - 18 years old 400 are 19 - 24 years old 700 are 25 - 39 years old 900 are 40 - 64 years old 300 are 65+ years old What is the fraction of people between 19 and 39? 1100/2500 What is this fraction when simplified? 11/25

Adding and Subtracting Fractions To add or subtract fractions, a common denominator is needed (use the “kiss & smile” method): 1 2 + 2 5 =

Multiplying Fractions Multiply across numerators, then across denominators: 3 7 x 4 9 =

Dividing Fractions Flip the second fraction, then multiply: 5 8 ÷ 2 3 =

Percentage of an amount (Calculator) Use the percentage button on your calculator! What is 20% of 500? Type in 500 x 20% = You should get the answer 100. Alternative: Percent means ‘out of 100’, so divide by 100 then multiply by the percentage you are looking for: ÷ 100 = 5 5 x 20 = 100.

Percentage of an amount (Calculator)

Percentage of an amount (Non-Calculator) You can work out any percentage without a calculator using the following: 50% = ÷ 2 25% = ÷ 2 again 75% ? 10% = ÷ 10 20% ? 5% ? 15% ? 1% = ÷ 100

Percentage of an amount (Non-Calculator) 20% of 400 = 15% of 60 = 90% of 180 = 60% of 600 = 5% of 350 = 25% of 550 = 40% of 800 = 35% of 350 =

One number as a percentage of another Write as a fraction, calculate decimal value, then multiply by 100 to get a percentage: Freddie scored 25 out of 40 on his Maths test. What percentage did he get right? 25/40 25 ÷ 40 = 0.625 0.625 x 100 = 62.5% Freddie scored 62.5% on the Maths test.

One number as a percentage of another A Blu-Ray contains a movie and some bonus features. The movie is 120 minutes long and the bonus features are 30 minutes long. What percentage of the disc is: a) The movie? 120/150 = 0.8 or 80% b) The bonus features? 30/150 = 0.2 or 20%

One number as a percentage of another

Percentage increase and decrease Work out the percentages as before. Increase means ‘add on to’ and decrease means ‘take away from’: Account Holder 2016 Balance % Change 2017 Balance H. Solo £5, 102 10% increase K. Broflovski £80, 980 30% decrease S. Smith £32, 654 5% increase J. T. Kirk £200, 902 10% decrease £5, 612.20 £56, 686 £34, 286.70 £180, 811.80

Match the percentage to the equivalent fraction 35% 1/50 120% 7/20 24% 4/5 2% 6/5 80% 6/25

Percentage Profit/Loss When a value has increased or decreased, it can be useful to know this as a percentage: Change in amount x 100 original amount

Percentage Profit/Loss

Reverse percentages There is a 20% sale on in Topshop. The bag I want is now £60. What was the original cost? 20% off = still paying 80% £60 = 80% 60 ÷ 80 = 0.75 (1%) 0.75 x 100 = £75 The bag originally cost £75

Reverse percentages In a sale, everything is reduced by 30%. If an armchair costs £175 in the sale, how much did it cost before the sale? 30% off = still paying 70% £175 = 70% 175 ÷ 70 = 2.5 (1%) 2.5 x 100 = £250 The armchair originally cost £250.

Reverse percentages A mouse increases its body weight by 15%. If it now weighs 368g, what was the mouse’s original weight? 368g = 115% 368 ÷ 115 = 3.2 (1%) 3.2 x 100 = 320g The mouse originally weighed 320g.

Formula to calculate compound interest: Total = Original Amount x (100 + interest rate/100)no. interest payments

£2000 earning Compound Interest at 5% per year for 3 years Total = Original Amount x (100 + interest rate/100)no. interest payments Original Amount = £2,000 100 + interest rate = 105 ÷ 100 = 1.05 Number of interest payments = 3 (1 a year for 3 years) £2000 x 1.053 = £2,315.25

Compound Interest 1. £10,000 earning Compound Interest at 1% per year for 3 years 2. £8,650 earning Compound Interest at 2% per year for 5 years 3. £5,000 earning Compound Interest at 0.5% per year for 4 years 4. £10,000 earning Compound Interest at 1.5% per year for 6 years 5. £8,000 earning Compound Interest at 3% per year for 7 years