S 1 Fractions Parent Class Fractions Two fifths

S 1 Fractions Parent Class

Fractions Two fifths is written as: two parts 2 Numerator 5 Denominator out of five parts altogether 2 of 46

Fraction of an amount When we work out a fraction of an amount we divide by the denominator and multiply by the numerator Examples, 2 of 18 litres 3 = 18 ÷ 3 × 2 =6× 2 = 12 litres 3 of 46 5 of £ 24 6 = 24 ÷ 6 × 5 = 4× 5 = £ 20

Question Time (Question 1) 4 of 46

Simplifying fractions 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. 5 of 46

Question Time (Question 2) 6 of 46

Mixed and Improper Fractions When the numerator of a fraction is larger than the denominator it is called an improper fraction. 15 is an improper fraction or top heavy. 4 We can write improper fractions as mixed numbers. 15 can be visually shown as 4 15 ÷ 4 = 3 remainder 3 7 of 46 15 = 4 3 3 4

Improper fractions to mixed numbers 37 Convert to a mixed number. 8 37 8 8 + + + = 8 8 8 + 1+1+ 5 = 4 8 = 5 8 This number is the remainder. 37 ÷ 8 = 4 remainder 5 37 = 8 4 5 8 This is the number of times 8 divides into 37. 8 of 46

Mixed numbers to improper fractions Convert 3 2 = 7 3 2 to an improper fraction. 7 2 7 1+1+1+ 7 7 7 2 = + + + 7 7 23 = 7 To do this in one step, … and add this number … 3 2 23 = 7 7 Multiply these numbers together … 9 of 46 … to get the numerator.

Question Time (Question 3 & 4) 10 of 46

Multiplying Fractions 3 2 What is × ? 8 5 To multiply two fractions together, multiply the numerators together and multiply the denominators together: 3 3 12 4 = × 8 40 10 5 3 = 10 11 of 46

Multiplying Fractions What is 5 5 12 × ? 6 25 Start by writing the calculation with any mixed numbers as improper fractions. To make the calculation easier, cancel any numerators with any denominators. 35 7 12 2 14 × = 5 6 25 5 1 = 12 of 46 2 4 5

Question Time (Question 6) 13 of 46

Adding & Subtracting Fractions When fractions have the same denominator it is quite easy to add them together and to subtract them. For example, 3 5 + 1 5 = 3+1 = 5 4 5 We can show this calculation in a diagram: + 14 of 46 =

Adding & Subtracting Fractions 7 8 – 3 8 = 7– 3 8 = 4 1 8 2 = 1 2 Fractions should always be cancelled down to their lowest terms. We can show this calculation in a diagram: – 15 of 46 =

Adding & Subtracting Fractions 1 7 4 + + = 9 9 9 12 9 = 1 3 9 1 3 = 1 1 3 Top-heavy or improper fractions should be written as mixed numbers. 16 of 46

Adding & Subtracting Fractions 1 45 + 3 2 5 = 75 3 Add your whole numbers together and then your fractions. 17 of 46

Question Time (Question 5) 18 of 46

Fractions with different denominators are more difficult to add and subtract. For example, 1 1 What is + ? 2 3 We can show this sum using diagrams: + 3 6 19 of 46 + = 2 6 = 3+2 = 6 5 6

What is 3 1 + 4 3 1. Write each fraction over the lowest common denominator. × 3 3 1 × 4 + × 3 4 3 × 4 9 4 = + 12 12 2) Add the fractions together. 13 = 12 1 20 of 46

What is 2 3 + 5 4 1 3 1) Write each fraction over the lowest common denominator. 1 × 5 3 × 3 + 3 × 5 5 × 3 5 9 = + 15 15 2) Add the fractions together. 9 5 = + 15 15 14 = 15 2 2 6 6 21 of 46 4 4

What is 5 2 3 2 1 7 1) Write each fraction over the lowest common denominator. 5 = 5 2 × 7 3 × 7 1 × 3 7 × 3 2 21 14 21 2) Subtract the fractions together. 14 3 = 21 21 11 = 21 3 3 22 of 46

A problem with subtractions What about 23 of 46 9 1 5 - 2 3 4

Question Time (Question 7) 24 of 46