1. Working with fractions

2. Look at this diagram: 3 4 = 6 8 ×2×2 ×2×2 = 18 24 ×3×3 ×3×3 Equivalent fractions

3. Look at this diagram: 18 30 = 6 10 ÷3 = 3 5 ÷2 Equivalent fractions

4. 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 20 27 3 13 15 21 14 35 32 15 Fractions which are not shown in their lowest terms can be simplified by cancelling. 7 8 5 7 2 5

5. 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 4 is an improper fraction. We can write improper fractions as mixed numbers. 15 4 can be shown as 15 4 = 3 3 4

6. Improper fractions to mixed numbers Convert to a mixed number. 37 8 8 = 8 8 +++ 8 8 8 8 8 8 + 5 8 5 8 1 + 1 + 1 += 1 + = 4 5 8 4 37 ÷ 8 = 4 remainder 5 37 8 = 4 5 8 4 This is the number of times 8 divides into 37. 4 This number is the remainder. 5

7. 2 7 3 Mixed numbers to improper fractions 2 7 3 = 2 7 1 + 1 + 1 + = 7 7 +++ 7 7 7 7 2 7 = 23 7 To do this in one step, = Multiply these numbers together … … and add this number … … to get the numerator. 23 7

8. Writing one amount as a fraction of another Sometimes we need to know one amount as a fraction of another. 3 7 three days out of seven days altogether What fraction of one week is three days? MondayTuesdayWednesdayThursdayFridaySaturdaySundayMondayTuesdayWednesday

9. Now try these: Write the first amount as a fraction of the second amount (in simplest form/lowest terms): 1. 12 as a fraction 0f 15.2. seven as a fraction of nine3. 16 out of 20 4. January, February and March as a fraction of one year.5. 60p as a fraction of £1. 6. 18 as a fraction of 24.7. Three as a mixed number of two.8. 33 out of 99.

10. Answers: