Chapter 7 Fractions

Learning Objectives Work out fractions of a shaded shape Find equivalent fractions Simplifying fractions Writing fractions of 2 quantities Change improper fractions into mixed numbers Change mixed numbers into improper fractions Add/ subtract fractions Multiply fractions Divide fractions Problems involving fractions Fractions on a calculator Convert recurring decimals into fractions Convert fractions to recurring decimals

Equivalent Fractions You must multiply top (numerator) and bottom (denominator) by the same multiply Examples Write 3 equivalent fractions to ¾

Simplifying Fractions Divide both top (numerator) and bottom (denominator) by the same number Examples Simplify the following (a) 25/60 (b) 52/90 (c) Write 42 as a fraction of 80

Top-Heavy Fractions – Mixed Numbers A top heavy fraction has the top bigger than the bottom To convert a top heavy fraction into a mixed number divide the top by the bottom The answer is the whole number bit The remainder is the new top The bottom stays the same

Examples Top-Heavy – Mixed Numbers Change the following into mixed numbers (a) 13/2 (b) 50/3 (c) 100/7 (d) 32/5

Mixed Numbers - Top-Heavy Fractions A top heavy fraction has the top bigger than the bottom To convert a mixed number into an improper fraction New top = whole number × bottom + top The bottom stays the same

Examples Mixed Numbers – Top-Heavy Fractions Change the following into improper fractions (a) 41/2 (b) 36/11 (c) 21/7 (d) 83/5

Finding Fractions of Quantities Divide by the bottom and multiply by the top Examples 2/5 of 60 2/3 of 12 1/5 of 30 8/12 of 24

Adding/ Subtracting Fractions Make all fractions top-heavy (if possible) Make all bottoms the same by multiply Add the tops Do not change the bottoms Make all answers mixed numbers (if possible) EXAMPLES ½ + ¾ ½ + 1/9 3/8 + ¾

More Examples 33/10 – 15/8 ¾ + 2/3 11/10 – 5/6 34/7 – 25/8 33/16 – 25/24

Multiplying Fractions Make all fractions top heavy if possible Cancel (divide by the same number) any top and bottom When no more cancelling can be done multiply the tops and multiply the bottoms EXAMPLES 1. 2/5 × 12/21 2. 23/4 ×12/5 3. 25/8 × 31/3 4. 5/6 of 42/7

Dividing Fractions Make all fractions top-heavy if possible Turn the fraction after the dividing sign up-side-down and multiply EXAMPLES 13/5 ÷ 4/9 2/3 ÷ 5 22/15 ÷ 13/5 52/5 ÷ 12/3

Problems Involving Fractions Jenny spends 3/5 of her money. If she has £1.40 left how much money did she have to start with? In an experiment a weight is added to a spring. The spring increases by 2/5. It’s new length is 21 cm, what was it’s length before the weight was added?

Decimals to Fractions If 1 decimal place put it over 10 If 2 decimal places put it over 100 EXAMPLES Change the following into fractions 0.45 0.5 0.81

Fractions into Decimals Divide the top by the bottom EXAMPLES Change the following into decimals ¼ 4/5 108/200

Recurring Decimals Use dots to show recurring EXAMPLES Change the following into decimals 1/3 1/6 6/13