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KS3 Mathematics N5 Using Fractions 1 of 49 © Boardworks Ltd 2004 Contents N5 Using fractions N5.1 Fractions of shapes N5.2 Equivalent fractions N5.3 One number as a fraction of another N5.4 Fractions and decimals N5.5 Ordering fractions 2 of 49 © Boardworks Ltd 2004 Quarter or not? 3 of 49 © Boardworks Ltd 2004 Quarters 4 of 49 © Boardworks Ltd 2004 Dividing shapes into given fractions 5 of 49 © Boardworks Ltd 2004 Fractions of shapes Remember, one quarter is written: one thing 1 divided into four equal parts 6 of 49 4 © Boardworks Ltd 2004 Fractions of shapes What fraction of this diagram is shaded? 7 of 49 © Boardworks Ltd 2004 Fractions of shapes Two fifths is written as: two parts 2 numerator 5 denominator out of five parts altogether 8 of 49 © Boardworks Ltd 2004 Fractions of shapes activity 9 of 49 © Boardworks Ltd 2004 Contents N5 Using fractions N5.1 Fractions of shapes N5.2 Equivalent fractions N5.3 One number as a fraction of another N5.4 Fractions and decimals N5.5 Ordering fractions 10 of 49 © Boardworks Ltd 2004 Equivalent fractions 11 of 49 © Boardworks Ltd 2004 Equivalent fractions What does equivalent mean? 12 of 49 © Boardworks Ltd 2004 Equivalent fractions Look at this diagram: ×2 3 4 = ×2 13 of 49 ×3 6 8 = 18 24 ×3 © Boardworks Ltd 2004 Equivalent fractions Look at this diagram: ×3 2 3 = ×3 14 of 49 ×4 6 9 = 24 36 ×4 © Boardworks Ltd 2004 Equivalent fractions Look at this diagram: ÷3 18 30 = ÷3 15 of 49 ÷2 6 10 = 3 5 ÷2 © Boardworks Ltd 2004 Equivalent fractions 16 of 49 © Boardworks Ltd 2004 Cancelling fractions to their lowest terms A fraction is said to be expressed in its lowest terms if the numerator and the denominator have no common factors. Which of these fractions are expressed in their lowest terms? 14 16 7 8 20 27 3 13 15 21 5 7 14 35 2 5 32 15 Fractions which are not shown in their lowest terms can be simplified by cancelling. 17 of 49 © Boardworks Ltd 2004 Drag and drop equivalent fractions 18 of 49 © Boardworks Ltd 2004 Mixed numbers and improper fractions When the numerator of a fraction is larger than the denominator it is called an improper fraction. For example, 15 is an improper fraction. 4 We can write improper fractions as mixed numbers. 15 4 can be shown as 15 = 4 19 of 49 3 3 4 © Boardworks Ltd 2004 Improper fraction to mixed numbers 37 Convert to a mixed number. 8 37 8 8 8 8 + + + = 8 8 8 8 8 + 1+1+1+1+ 5 = 4 8 = 37 ÷ 8 = 4 remainder 5 5 8 5 8 37 = 8 This number is the remainder. 4 5 8 This is the number of times 8 divides into 37. 20 of 49 © Boardworks Ltd 2004 Mixed numbers to improper fractions 2 to a mixed number. 7 3 2 37 =1 + 1 + 1 + Convert 2 7 7 7 7 2 = + + + 7 7 7 7 23 = 7 To do this in one step, … and add this number … 3 2 23 = 7 7 … to get the numerator. Multiply these numbers together … 21 of 49 © Boardworks Ltd 2004 Find the missing number 22 of 49 © Boardworks Ltd 2004 Contents N5 Using fractions N5.1 Fractions of shapes N5.2 Equivalent fractions N5.3 One number as a fraction of another N5.4 Fractions and decimals N5.5 Ordering fractions 23 of 49 © Boardworks Ltd 2004 Writing one amount as a fraction of another Sometimes we need to know one amount as a fraction of another. What fraction of one week is three days? Monday Tuesday Wednesday 3 Thursday Friday Saturday Sunday three days out of 7 24 of 49 seven days altogether © Boardworks Ltd 2004 Writing a number as a fraction of another We can describe one number as a fraction of another. What fraction of 72 is 45? ÷9 45 5 We write = 72 8 ÷9 We can say 45 is 5/8 of 72. 25 of 49 © Boardworks Ltd 2004 Writing a number as a fraction of another What fraction of 2.5 metres is 75 centimetres? First, convert 2.5 metres to 250 centimetres. ÷25 75 3 We write = 250 10 ÷25 We can say 75 centimetres is 3/10 of 5 metres. 26 of 49 © Boardworks Ltd 2004 Writing a number as a fraction of another We can also write a larger number as a fraction of a smaller one. What fraction of 25 is 35? ÷5 35 7 We write = 25 5 ÷5 We can say 35 is 7/5 of 25 or 12/5 of 25. 27 of 49 © Boardworks Ltd 2004 Writing one amount as a fraction of another 28 of 49 © Boardworks Ltd 2004 Fractions of distances 29 of 49 © Boardworks Ltd 2004 Fractions on a clock face 30 of 49 © Boardworks Ltd 2004 Contents N5 Using fractions N5.1 Fractions of shapes N5.2 Equivalent fractions N5.3 One number as a fraction of another N5.4 Fractions and decimals N5.5 Ordering fractions 31 of 49 © Boardworks Ltd 2004 Pelmanism – Fractions and decimals 32 of 49 © Boardworks Ltd 2004 Comparing decimals and fractions 33 of 49 © Boardworks Ltd 2004 Converting decimals to fractions 34 of 49 © Boardworks Ltd 2004 Using equivalent fractions over 10, 100, or 1000 We can convert some fractions to decimals by converting them to an equivalent fraction over 10, 100 or 1000. For example, ×5 13 65 = 20 100 ×5 65 = 0.65 100 35 of 49 © Boardworks Ltd 2004 Converting fractions to decimals 36 of 49 © Boardworks Ltd 2004 Fractions and division A fraction can be thought of as the result of dividing one whole number by another. For example, 30 30 ÷ 8 = = 8 3 6 = 8 3 3 4 We can also write this answer as a decimal: 3 37 of 49 3 = 4 3.75 © Boardworks Ltd 2004 Converting fractions to decimals There are many ways to convert a fraction to a decimal. The quickest way is to use a calculator. For example, 5 = 5 ÷ 16 = 0.3125 16 This is a terminating decimal. 6 = 6 ÷ 11 = 0.545454… This is a recurring decimal. 11 All recurring and terminating decimals can be written as exact fractions. 38 of 49 © Boardworks Ltd 2004 Recurring decimals . 1 = 1 ÷ 3 = 0.33333… = 0.3 3 . 1 = 1 ÷ 6 = 0.16666… = 0.16 6 .. 2 = 2 ÷ 11 = 0.18181… = 1.18 11 . . 3 = 3 ÷ 7 = 0.42857142857142… = 0.428571 7 3 We can also write = 0.43 (to 2 decimal places). 7 39 of 49 © Boardworks Ltd 2004 Using short division We can also convert fractions to decimals using short division. For example, 5 =5÷7 7 0 .7 1 4 2 8 5 7 . . . 5 1 3 2 6 4 5 7 5.0 0 0 0 0 0 0 . . 5 = 0.714285 7 40 of 49 © Boardworks Ltd 2004 Contents N5 Using fractions N5.1 Fractions of shapes N5.2 Equivalent fractions N5.3 One number as a fraction of another N5.4 Fractions and decimals N5.5 Ordering fractions 41 of 49 © Boardworks Ltd 2004 Using diagrams to compare fractions 42 of 49 © Boardworks Ltd 2004 Using decimals to compare fractions 3 7 Which is bigger or ? 8 20 We can compare two fractions by converting them to decimals. 3 8 = 3 ÷ 8 = 0.375 7 = 7 ÷ 20 = 0.35 20 0.375 > 0.35 so 43 of 49 3 8 > 7 20 © Boardworks Ltd 2004 Using equivalent fractions 3 5 Which is bigger or ? 8 12 Another way to compare two fractions is to convert them to equivalent fractions. First we need to find the lowest common multiple of 8 and 12. The lowest common multiple of 8 and 12 is 24. 3 5 Now, write and as equivalent fractions over 24. 8 12 ×3 3 8 9 = 24 ×3 44 of 49 ×2 and 5 10 = 12 24 so, 3 8 < 5 12 ×2 © Boardworks Ltd 2004 Using a graph to compare fractions 45 of 49 © Boardworks Ltd 2004 Ordering fractions 46 of 49 © Boardworks Ltd 2004 Fractions on a number line 47 of 49 © Boardworks Ltd 2004 Mid-points 48 of 49 © Boardworks Ltd 2004 Connect three fractions 49 of 49 © Boardworks Ltd 2004