Adding and Subtracting Fractions Learning Objective To add

Adding and Subtracting Fractions

Learning Objective • To add and subtract fractions. Success Criteria • To add and subtract fractions with the same denominator. • To add and subtract fractions with different denominators. • To add and subtract mixed number fractions.

Starter: Lowest Common Multiple Find the lowest common multiple for each pair of numbers. 1 3 and 4 12 2 5 and 6 30 3 3 and 6 6 4 4 and 8 8 5 5 and 10 10 Extension Find the missing numbers for each fraction. ? 1. – 25 = — 20 5 ? 2. – 8 = — 40 25 3. – 65 = — ?

Starter: Lowest Common Multiple Find the lowest common multiple for each pair of numbers. 1 3 and 4 12 2 5 and 6 30 3 3 and 6 6 4 4 and 8 8 5 5 and 10 10 Extension Find the missing numbers for each fraction. 8 1. – 25 = — 20 5 25 2. – 8 = — 40 25 3. – 65 = — 30

Adding and Subtracting Fractions with the Same Denominator To add fractions which have the same denominator, you must add only the numerators together. 2 5 7 — + — = — 10 10 10 Practice Question Prove that – 2 + – 2 is – 32 6 6 =

Adding and Subtracting Fractions with Different Denominators 2 chairs + 3 chairs = 5 chairs 7 rulers – 5 rulers = 2 rulers What would 2 chairs + 7 rulers be? We can’t add them together because they aren’t the same object. We can only add them together when they are the same. This is the same for fractions.

Adding and Subtracting Fractions with Different Denominators 2 5 3 10 –+— At the moment you can’t add these fractions together because they have different denominators. Remember, they must have the same denominator before you can add the fractions together. What could we do to the fractions so we can add them? Discuss this with the person next to you.

Adding and Subtracting Fractions with Different Denominators 3 10 – 2 + — 5 1 We need to find the lowest common multiple for 5 and 10. 10 2 This needs to be the denominator for both fractions. 3 2 – +— 5 ? — 10 3 +— 10 Now write the equivalent fraction for – 52 2 4 – =— 10 5 4 Now that the denominators are the same, perform the addition. 3 7 4 — +— =— 10 10 10

Adding and Subtracting Fractions with Different Denominators 1 4 – 5 - – 8 1 We need to find the lowest common multiple for 8 and 4. 8 2 This needs to be the denominator for both fractions. — 5 - — 1 8 5 — 8 3 - 4 ? — 8 Now write the equivalent fraction for – 41 1 2 – =— 8 4 4 Now that the denominators are the same, perform the subtraction. 2 3 5 — -— =— 8 8 8

Adding and Subtracting Fractions with Different Denominators – 1 + – 2 4 1 7 We need to find the lowest common multiple for 4 and 7. 28 2 This needs to be the denominator for both fractions. —? + —? — 1 + — 2 4 3 7 28 Now write the equivalent fraction for – 41 — 7 + — 8 — 1 + — 2 4 4 28 7 28 28 Now that the denominators are the same, perform the subtraction. 8 1 7 — +— =— 5 28 28 28

Adding and Subtracting Fractions with Different Denominators – 3 - – 2 4 1 5 We need to find the lowest common multiple for 4 and 5. 20 2 This needs to be the denominator for both fractions. —? - —? — 3 - — 2 4 3 5 20 Now write the equivalent fractions. 8 — 3 - — 2 4 4 20 15 - — — 20 5 20 Now that the denominators are the same, perform the subtraction. 8 7 1 — -— =— 5 20 20 20

Adding and Subtracting Fractions with Different Denominators Activity Sheets

Adding and Subtracting Mixed Number Fractions How could we calculate the following? Discuss with the person next to you. 1 2 – 1 + 3 – 4 3

Adding and Subtracting Mixed Number Fractions 1 Convert your mixed number fractions to improper fractions. 1 3 1 4 2—+3— 9 10 4 3 –+— 2 Find the lowest common multiple for 4 and 3. 12 3 This needs to be the denominator for both fractions. 9 10 4 3 –+— ? ? 12 12 —+—

Adding and Subtracting Mixed Number Fractions 4 Write the equivalent fractions. 9 10 4 3 27 12 12 –+— 40 —+— 5 Now that the denominators are the same, perform the addition. 40 67 27 — +— =— 12 12 12 6 Don’t forget to write your answer as a mixed number fraction, if appropriate. 67 12 —=5 —

Adding and Subtracting Mixed Number Fractions 1 Convert your mixed number fractions to improper fractions. 2 - — 1 — 3 2 5 — 1 7 5 2 4 - — 9 4 Find the lowest common multiple for 5 and 4. 20 3 This needs to be the denominator for both fractions. — 1 - — 9 7 5 4 ? — - —? 20 20

Adding and Subtracting Mixed Number Fractions 4 Write the equivalent fractions. — 1 - — 9 7 4 5 68 - — 45 — 20 5 20 Now that the denominators are the same, perform the subtraction. 68 - — 45= — 23 — 20 6 20 20 Don’t forget to write your answer as a mixed number fraction, if appropriate. 23 = 1 — 3 — 20 20

Adding and Subtracting Mixed Number Fractions Activity Sheet

Challenge: Write a 5 -step guide on how to add and subtract fractions.