www.academicowl.co.uk (+)44 07534 819 661 QTS REVISION 2013 1. Equivalent fractions

so 5/8 has the same value as 25/x, meaning that whole fraction was times by the same number . In this case , looking at 7 and 35, the fraction was times by 5=> if we times the 8 by 5 we’ll find X

How many ? How many litres are 7 gallons? How many km are 45 miles? How many miles are in 64 km?

2. Simplify fractions A number can be divided by 2 if it ends in 0; 2; 4; 6; 8; ex: 34; 46; 50; A number can be divided by 3 if the sum of figures divides by 3 ex: 123=1+2+3=6 342= 3+4+2= 9 996= 9+9+6= 18+6=24=2+4=6 A number can be divided by 5 if it ends in 0 or 5 Ex: 435; 285; 450; 210 A number can be divided by 10 if it ends in 0 ex: 10; 3400; 2400;

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Practice:

3. Decimals to fractions Write the number without the decimal point and on the denominator put a 1 and as many 0s as many decimals you have: Ex: 0.2= 1.25 =

0.37=

two decimals = two zeroes

3.26=

Practice: 0.73 =

1.2 =

0.7=

12.6=

0.94 =

2.70=

Fractions to decimals To turn a fraction into a decimal you need to get To have the denominator (bottom of the fraction) 10, 100 or 1000. One zero = one decimal

Practice = = =

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4. Percentages To turn a fraction into a percentage you need to have the denominator 100 = 15% Pairs of numbers that give 100 are: 2 and 50; 5 and 20; 4 and 25

Write the following fractions as percentages:

5. How to Multiply decimals 0.24 x 5 = 24 x 5 = 120 now you put the decimal point back => 1. 2 The number of decimals needs to be constant, so if you have 2 decimals before the multiplications then you have 2 decimals after Practice 1.5 x 6= 0.25 x 0.3 = 2.6 x 4= 5.2 x 5 = 1.2 x 2.3 = 0.4 x 0.7 = 200 x 2.6= 30 x 1.5 x 20=

Calculating a percentage out of a fraction: 30% of 210 = 0.3 x 210= 63 45% of 300 = 0.45 x 3000= 1350 27% of 140 = 0.27 x 14 = 37.8 roxana@academicowl.co.uk 3

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Practice: 24% of 310 = 36% of 270= 44% of 200= 60% of 340= 54% of 250= 6. Fast division 1324/5= 2 ← 5 goes into 13 two times (13-10), the remainder (3) needs to be written on top of 13 (1335) So the amount remaining is 35, 5 goes into 35 7 times , so the answer is 27 More Practice 368 /8= 105/5= 225/5= 213/3= 231/3= 175/7= 336/3= 7. Ratio A school calculated that it had given merits to boys and girls in the ratio of 2:3 . There were a total of 225 merits given. How many merits did the girls get? What about the boys?

When working with ratios you need to add up the two ratios and divide the total by it. In this case the sum of ratios is 2+3=5 , so we need to divide the total number of merits by 5 225:5= 45 groups (with 2 boys and 3 girls each) to find out the number of merits for boys times by 2 and for girls times by 3 as follows: 3x45= 135 merits for girls 2x45= 90 merits for boys =

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Practice: 1:4 Boys : Girls 125 in total girls=? 1:5 Girls : Boys 132 in total boys=? 2:3 Boys : Girls 250 in total Girls=?

8. Proportions There are 30 pupils in a class, 20 of them are boys. What is the proportion of girls? The number of girls is 30 - 20= 10 the proportion of girls is

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Practice: 50 pupils 24 girls 40 pupils 15 boys 750 pupils 25 girls 530 pupils 100 girls

proportion of boys= proportion of boys= proportion of boys= proportion of girls=

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