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Fraction Revision

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**Things you need to know about fractions...**

Finding Fractions of Amounts Equivalent Fractions and cancelling down Top Heavy Fractions and Mixed Numbers These are REALLY important Adding and Subtracting Fractions Multiplying Fractions Dividing Fractions Fractions and Decimals Fractions and Percentages Ordering Fractions Click this to get back here Things you should know

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**Finding Fractions of Amounts**

3 5 If you are asked for of an amount 1 5 3 5 Find by dividing by 5 and then find by multiplying by 3. 3 5 To find of 60: 60 ÷ 5 = 12 12 x 3 = 36 3 5 of 60 is 36

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**Finding Fractions of Amounts**

2 7 If you are asked for of an amount 1 7 2 7 Find by dividing by 7 and then find by multiplying by 2. 2 7 To find of 35: 35 ÷ 7 = 5 5 x 2 = 10 2 7 of 35 is 10

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**Finding Fractions of Amounts**

5 9 If you are asked for of an amount 1 9 5 9 Find by dividing by 9 and then find by multiplying by 5. 5 9 To find of 63: 63 ÷ 9 = 7 5 x 7 = 35 5 9 of 63 is 35

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**Finding Fractions of Amounts**

A quick way to remember what to do is: “Divide by the bottom, times by the top”

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Fractions of Amounts 10 multiple choice questions, work out your answer then click to see if you were right

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What is.. 1 of 60 2 15 6 A) B) 30 40 C) D)

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What is.. 1 of 60 4 20 15 A) B) 4 12 C) D)

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What is.. 1 of 36 3 6 9 A) B) 8 12 C) D)

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What is.. 1 of 56 4 14 16 A) B) 12 18 C) D)

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What is.. 3 of 66 6 13 11 A) B) 21 33 C) D)

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What is.. 3 of 100 4 75 A) B) 80 25 C) D)

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What is.. 3 of 100 5 20 60 A) B) 35 15 C) D)

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What is.. 1 of 200 8 45 50 A) B) 80 25 C) D)

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What is.. 20 Of 280 40 80 100 A) B) 140 120 C) D)

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What is.. 7 of 90 9 70 49 A) B) 81 74 C) D)

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**Multiplying Fractions**

To multiply simply times the numbers at the top, then times the numbers at the bottom, you may have to simplify 3 4 5 8 15 32 x = 2 7 5 6 10 42 5 21 x = = 3 5 7 9 21 45 7 15 x = =

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**Simplify before multiplying**

1 6 7 5 6 1x5 7x1 5 7 x = This will help with division too, do it after the keep, change flip bit = 1 1 4 5 3 8 1x3 5x2 3 10 x = = 2 2 4 9 6 7 4x2 3x7 8 21 x = = 3

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**Dividing Fractions 4 7 3 4 4 7 4 3 16 21 ÷ = x = 1 2 7 8 1 2 8 7 8 14**

To divide remember KEEP, CHANGE, FLIP KEEP the first fraction CHANGE the multiply sign to divide FLIP the second fraction 4 7 3 4 4 7 4 3 16 21 ÷ = x = 1 2 7 8 1 2 8 7 8 14 4 7 ÷ = x = = 3 4 5 8 3 4 8 5 24 20 ÷ 1 5 = x = =1 4 20 1 or

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Equivalent Fractions

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**Three friends each have 12 sweets**

2/4, ½ and 3/6 look different but these fractions are all the same, they are EQUIVALENT They all eat 6 sweets Three friends each have 12 sweets Abbie puts hers into 4 piles and eats 2 of them Libby puts hers into 2 piles and eats 1 of them Chrissy puts hers into 6 piles and eats 3 of them Chrissy has had 3/6 Abbie has had 2/4 Libby has had 1/2

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**Are these fractions EQUIVALENT?**

Simplify the fractions 8 1 ÷8 24 3 Look for the biggest number that goes into the top and bottom of the fractions Divide by the number 12 1 ÷12 These fractions are equivalent 36 3

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**Are these fractions EQUIVALENT?**

Simplify the fractions 8 4 ÷2 10 5 Look for the biggest number that goes into the top and bottom of the fractions 12 Divide by the number 3 ÷4 These fractions are NOT equivalent 16 4

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**Are these fractions EQUIVALENT?**

Simplify the fractions 9 3 ÷3 Look for the biggest number that goes into the top and bottom of the fractions 12 4 Divide by the number 21 3 ÷7 These fractions are equivalent 28 4

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What number goes here? 15 3 ÷5 20 4 32 4 ÷8 40 5

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What number goes here? 2 8 X8 3 24 1 9 X9 5 45

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Equivalent Fractions 10 multiple choice questions. Work out your answer then click to see if you were right

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**Which fraction is equivalent to....**

12 39 28 A) B) 48 4 10 C) D)

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**Which fraction is equivalent to....**

13 39 4 12 A) B) 48 5 20 C) D)

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**Which fraction is equivalent to....**

14 5 16 7 21 A) B) 3 10 4 16 C) D)

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**Which fraction is equivalent to....**

1 10 3 30 4 44 A) B) 4 44 4 44 C) D)

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**Which fraction is equivalent to....**

34 12 20 18 20 A) B) 16 20 15 20 C) D)

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**Which fraction is equivalent to....**

25 6 25 6 15 A) B) 8 22 12 35 C) D)

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**Which fraction is equivalent to....**

56 15 24 30 36 A) B) 35 36 10 18 C) D)

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**Which fraction is equivalent to....**

49 12 54 16 81 A) B) 8 27 1636 C) D)

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**Which fraction is equivalent to....**

57 10 21 35 35 A) B) 3042 15 28 C) D)

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**Which fraction is equivalent to....**

9 11 6377 27 22 A) B) 63 88 45 44 C) D)

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**Cancelling fractions down**

It is often best to have the numbers possible when we write fractions 12 20 3 5 Instead of we would have We have cancelled the fractions down, by dividing top and bottom numbers by the same number (in this case 4)

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15 35 3 7 = Divide by 5 24 36 2 3 = Divide by 12 55 66 5 6 = Divide by 11

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**Cancelling fractions down**

If we pick the biggest number possible to divide by we only have to cancel down once. We must always check that there are no more numbers which go into the top and bottom number When there are no more numbers which go into the top and bottom of the fraction, the fraction is FULLY SIMPLIFIED or CANCELLED DOWN FULLY

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**10 multiple choice questions**

Cancelling Fractions 10 multiple choice questions

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Cancel completely 1215 3 5 3 4 A) B) 2 5 45 C) D)

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Cancel completely 48 13 28 A) B) 12 1 4 C) D)

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Cancel completely 7 21 1 3 37 A) B) 18 1 7 C) D)

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Cancel completely 1525 3 4 4 5 A) B) 5 6 3 5 C) D)

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Cancel completely 28 32 7 8 7 14 A) B) 14 16 4 6 C) D)

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Cancel completely 2736 5 7 3 5 A) B) 6 8 3 4 C) D)

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Cancel completely 2460 3 8 2 5 A) B) 2 7 1 5 C) D)

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Cancel completely 5566 8 9 5 6 A) B) 6 7 4 6 C) D)

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Cancel completely 48 64 34 4 6 A) B) 3 5 2 3 C) D)

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Cancel completely 5672 1 2 2 5 A) B) 79 6 7 C) D)

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**Mixed numbers and top heavy fractions**

When you see a fraction with a large number in front of it, this is a MIXED NUMBER. 2 2 3 This mean, 2 and 2 thirds When we have a fraction where the number at the top (NUMERATOR) is bigger than the number at the bottom (DENOMINATOR) we have a TOP HEAVY FRACTION 5 3 8 4 9 2

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**Mixed numbers and top heavy fractions**

You need to be able to: turn MIXED NUMBERS into TOP HEAVY FRACTIONS turn TOP HEAVY FRACTIONS into MIXED NUMBERS

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**Top heavy fractions to mixed numbers**

14 3 How many 3’s go into 14? 4 What is the remainder? 2 So we can make 4 wholes and we have 2 thirds left over: 14 3 = 4 2 3

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**Top heavy fractions to mixed numbers**

19 5 How many 5’s go into 19? 3 What is the remainder? 4 So we can make 3 wholes and we have 4 fifths left over: 19 5 = 3 4 5

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**Top heavy fractions to mixed numbers**

31 10 How many 10’s go into 31? 3 What is the remainder? 1 So we can make 3 wholes and we have 1 tenth left over: 31 10 = 3 1 10

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**Mixed Numbers to Top heavy fractions**

To turn the mixed numbers into top heavy fractions: 3 1 10 31 10 = Multiply these numbers together= 30 Add on the number at the top= 31 (this will be the top number) The number at the bottom will stay the same

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**Mixed Numbers to Top heavy fractions**

To turn the mixed numbers into top heavy fractions: 5 3 4 23 4 = Multiply these numbers together= 20 Add on the number at the top= 23 (this will be the top number) The number at the bottom will stay the same

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**Mixed Numbers to Top heavy fractions**

To turn the mixed numbers into top heavy fractions: 6 2 5 32 10 = Multiply these numbers together= 30 Add on the number at the top= 32 (this will be the top number) The number at the bottom will stay the same

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**10 multiple choice questions**

Top heavy fractions 10 multiple choice questions

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2 = 2 3 22 3 4 3 A) B) 8 3 7 3 C) D)

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3 = 4 5 17 5 19 5 A) B) 34 5 12 5 C) D)

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4 = 1 2 8 2 4 2 A) B) 12 2 9 2 C) D)

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10 = 3 5 53 5 13 4 A) B) 35 5 50 5 C) D)

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6 = 1 3 18 3 9 3 A) B) 6 3 19 3 C) D)

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= 10 3 1 3 A) 9 3 B) 1 3 2 9 1 3 C) 1 3 D)

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= 57 8 8 6 A) 1 8 B) 2 8 7 9 3 8 C) 1 8 D)

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= 15 4 4 3 A) 3 4 B) 1 4 3 4 1 4 C) 3 4 D)

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= 21 10 2 1 A) 1 10 B) 11 10 10 2 11 20 C) 1 2 D)

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= 26 5 4 5 A) 1 5 B) 6 5 6 5 1 5 C) 1 5 D)

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**Fractions and Percentages**

Think of percentages as fractions with 100 as the denominator so, 17 100 17 % = 32 100 32 % = 88 100 88 % =

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**Fractions and Percentages**

Some fractions can be simplified 25 100 1 4 25 % = = 55 100 11 20 55 % = = 30 100 3 10 30 % = =

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**Fractions and Percentages**

To turn a fraction into a percentage you need to use what you know about equivalent fractions. Turn your fraction into an equivalent fraction over 100. 12 60 x5 20 100 60%

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**Fractions and Percentages**

To turn a fraction into a percentage you need to use what you know about equivalent fractions. Turn your fraction into an equivalent fraction over 100. 7 70 x10 10 100 70%

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**Fractions and Percentages**

Sometimes you need to simplify the fraction first. 40 14 2 x20 = 100 35 5 40%

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**Fractions and Percentages**

Sometimes you need to simplify the fraction first. 65 26 13 x5 = 100 40 20 65%

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**Practise Questions, click to show answers**

60% 70% 8% 27% 80% 1 4 33 100 51 100 4 5 1 5

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**Fractions to Percentages**

10 multiple choice questions, work out your answer then click to see if you were right

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**Convert this fraction to a percentage**

12 20% 100% A) B) 50% 40% C) D)

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**Convert this fraction to a percentage**

14 40% 25% A) B) 4% 2% C) D)

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**Convert this fraction to a percentage**

1 10 10% 100% A) B) 1% 20% C) D)

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**Convert this fraction to a percentage**

15 2% 15% A) B) 5% 20% C) D)

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**Convert this fraction to a percentage**

34 80% 12% A) B) 45% 75% C) D)

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**21 100 A) B) C) D) Convert this fraction to a percentage 0.21% 2.1%**

210% 21% C) D)

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**Convert this fraction to a percentage**

4 10 4% 40% A) B) 44% 10% C) D)

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**Convert this fraction to a percentage**

35 6% 15% A) B) 60% 80% C) D)

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**1 100 A) B) C) D) Convert this fraction to a percentage 100% 1% 0.1%**

0.110% C) D)

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**13 A) B) C) D) Convert this fraction to a percentage 33.333333.. % 13%**

11% C) D)

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**Adding and Subtracting Fractions**

Two rulers add three rulers is: 5 rulers 9 pens Four pens add five pens is: Two pens add Five rulers is: 7 Pieces of equipment We can’t so this until we have a name that describes both groups When we add fractions we need them to have the same name

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**Adding and Subtracting Fractions**

= 5 7 2 7 + 3 7 = 6 9 2 9 + 4 9 = 4 11 1 11 + 3 11

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**Adding and Subtracting Fractions**

= 5 7 2 7 + 3 7 = 6 9 2 9 + 4 9 = 2 11 5 11 - 3 11

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**Adding and Subtracting Fractions**

We need to make sure the denominator of both fractions is the same before we add or subtract We need a number in the 5 and 10 times table to use as our bottom number- 10? = 2 5 + 3 10 4 10 + 3 10 = 7 10

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**Adding and Subtracting Fractions**

We need to make sure the denominator of both fractions is the same before we add or subtract We need a number in the 3 and 12 times table to use as our bottom number- 12? = 1 3 + 5 12 4 12 + 5 12 = 9 12

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**Adding and Subtracting Fractions**

We need to make sure the denominator of both fractions is the same before we add or subtract We need a number in the 5 and 6 times table to use as our bottom number- 30? = 2 5 + 3 6 12 15 30 + 30 27 30 =

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**Adding and Subtracting Fractions**

We need to make sure the denominator of both fractions is the same before we add or subtract We need a number in the 8 and 3 times table to use as our bottom number- 24? = 7 8 - 2 3 21 16 24 - 24 = 5 24

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**Adding and Subtracting Fractions**

7/8 8/12 7/9 7/10 2/3 11/12 8/15 16/12 or 1 ¼ 11/24 1 7/12 1 5/56 29/30 29/52 1 1/10 5/8 5/12 1/3 2/5 1/2 7/20 8/21 23/36 9/22 71/126 Adding and Subtracting Fractions Click for answers Home

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**Fractions and Decimals**

To turn fractions into decimals and decimals into fractions we need to remember column names Thousandths Hundreds Tens Units Tenths Hundredths

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**0.03 0.5 Decimals to Fractions is 3 hundredths is 5 tenths 3 100 5 10**

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**0.12 0.01 Decimals to Fractions is 1 hundredth 12 is 12 hundredths 100**

Tenths 0.12 12 100 is 12 hundredths Tenths Hundredths 0.01 is 1 hundredth 1 100

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**Don’t forget you may have to simplify**

Decimals to Fractions Don’t forget you may have to simplify Hundredths Tenths Thousandths 0.032 32 1000 is 32 thousandths Hundredths Tenths Thousandths 0.154 154 1000 is 154 thousandths

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**000.000 Fractions to Decimals 7 10 = 0.7 64 100 = 0.64 3 100 = 0.03 =**

Hundreds Tens Units Tenths Hundredths Thousandths Fractions to Decimals 7 10 = 0.7 64 100 = 0.64 3 100 = 0.03 = 0.053 = 0.152 53 1000 = 0.002 152 1000 2 1000

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Fractions to Decimals You can also turn fractions into decimals by dividing the top number by the bottom number either with a calculator or any other method you may know

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**To order fractions you need to know all about equivalent fractions**

Ordering Fractions To order fractions you need to know all about equivalent fractions

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**It’s difficult to order fractions when they have different denominators**

1 2 1 4 3 5 3 10 11 20 What number is in the 2,4,5,10 and 20 times table, we need a common multiple 20?

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**Make all fractions have 20 as a denominator**

1 2 1 4 3 5 3 10 11 20 10 20 5 20 15 20 6 20 11 20 Now order them 15 20 11 20 6 20 10 20 5 20

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**What denominator do we need now?**

1 3 4 6 2 5 5 12 5 6 20 60 40 60 24 60 25 60 50 60 Now order them 50 60 40 60 24 60 25 60 20 60

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**Ordering Fractions- click for answers**

1/4 3/8 ½ and 4/8 3/4 2/5 ½ 3/5 and 6/10 2/29 1/3 5/12 1/1 4/6 3/4 1/4 1/2 2/3 5/6 7/8 1/4 2/5 1/2 6/10 3/4 1/3 4/9 1/2 2/3 5/6 2/6 1/4 5/12 2/3 7/9 2/7 2/4 5/8 11/14 3/2

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**The top number of a fraction is the NUMERATOR**

Things you should know The top number of a fraction is the NUMERATOR The bottom number of a fraction is the DENOMINATOR Fraction Percentage Decimal 1/2 50% 0.5 1/4 25% 0.25 3/4 75% 0.75 1/5 20% 0.2 1/10 10% 0.1 1/100 1% 0.01

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Additional Examples 1A: Solving Equations with Decimals

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