Transcript Fractions
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 1. Write 3 equivalent fractions to ¾ Simplifying Fractions • Divide both top (numerator) and bottom (denominator) by the same number Examples 1. 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 1. 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 – TopHeavy Fractions 1. 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 1. 2/5 of 60 2. 2/3 of 12 3. 1/5 of 30 4. 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 1. ½ + ¾ 2. ½ + 1/9 3. 3/8 + ¾ More Examples 1. 2. 3. 4. 5. 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-sidedown and multiply EXAMPLES 1. 13/5 ÷ 4/9 2. 2/3 ÷ 5 3. 22/15 ÷ 13/5 4. 52/5 ÷ 12/3 Problems Involving Fractions 1. Jenny spends 3/5 of her money. If she has £1.40 left how much money did she have to start with? 2. 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 1. 0.45 2. 0.5 3. 0.81 Fractions into Decimals • Divide the top by the bottom EXAMPLES Change the following into decimals 1. ¼ 2. 4/5 3. 108/200 Recurring Decimals • Use dots to show recurring EXAMPLES Change the following into decimals 1. 1/3 2. 1/6 3. 6/13