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Transcript
Mathematics Fractions Re-cap1 Equivalent fractions spider diagram 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. 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 3 3 4 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. Mixed numbers to improper fractions 2 to an improper fraction. 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 Multiply these numbers together … … to get the numerator. Find the missing number Finding a fraction of an amount 2 What is of £18? 3 We can see this in a diagram: 2 of £18 = £18 ÷ 3 × 2 = £12 3 Finding a fraction of an amount What is 2 of 3.5m? 5 1 To find 1 25 of an amount we need to add 1 times the amount to two fifths of the amount. 1 × 3.5 m = 3.5 m so, 1 and 2 of 3.5 m = 1.4 m 5 2 of 3.5 m = 3.5 m + 1.4 m = 4.9 m 5 7 We could also multiply by 5 MathsBlox Using equivalent fractions 3 5 Which is bigger or ? 8 12 To compare two fractions 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 ×2 and 5 10 = 12 24 ×2 so, 3 8 < 5 12 Ordering fractions