Fractions Dividing Fractions Learning Objective To divide fractions
Fractions Dividing Fractions
Learning Objective • To divide fractions. Success Criteria • To divide fractions by applying ‘K. C. F’. • To divide a fraction and write the answer in its simplest form. • To divide mixed number fractions.
Starter: Equal to 1 What do you have to multiply each of these numbers by to obtain the answer 1? 1. – 1 × 2 or 2– 2 1 1 2. 10 × — 10 2 – × 4 or 8 – 3. 8 2 1 4. 5 × – 5 2 – 5. 3 × 1 – 1 or 3– 2 2 Extension: Explain, in your own words, any patterns that you notice.
Reciprocals 1 • Looking at the first question, if you multiply – by 2, you get the 2 answer 1. • We call this number a reciprocal. • The product of a number and its reciprocal must be 1. • Or, equivalently, the reciprocal of a number is 1 divided by that number. • The reciprocal of a fraction is the fraction turned upside down. 1 • For example, the reciprocal of 12 is —. This is because 12 is the same as 12 12 —; and — upside down is —. 12 1 1
Dividing Fractions Dividing fractions isn’t as tricky as it might seem; we can use a short-cut. We can use something called K. C. F. K = Keep C = Change F = Flip
Dividing Fractions 3 – 4 1. We keep the first fraction as it is. 3 – 4 ÷ 1 – 2 2. We change the ÷ sign to a × sign. 3. We flip the last fraction to give its reciprocal. × 2 – 1 Now, we can follow our steps for multiplying fractions. 3 x 2 4 x 1 6 — 4 1 So our answer is 1 – 23 = 1 – 21
3 4 1 2 –÷– Dividing Fractions 3 1. We can rewrite this fraction as the super fraction: – 4 1 3 1 — 2. We are going to simplify – ÷ – by making the 2 4 2 denominator of the super fraction equal to 1. 1 3. To do this we must multiply by the reciprocal of – , which is 2 –. 2 1 4. Remember, the new super fraction must still be equivalent so we 2 multiply both the numerator and denominator by –. 1 5. We can therefore rewrite our super fraction: 2 3– – 2 3 – × – 4 1 4 × 1 which is equivalent to – 3 × 2 – — —= 4 1 1 – – 1 × 2 1 2
5 – 8 ÷ 2 – 3 Dividing Fractions 1. Apply ‘Keep, Change, Flip’. 5 – ÷ 2– 8 3 5 – × 3– 8 2 2. Multiply the numerators together. 5 × 3 = 15 3. Multiply the denominators together. 8 × 2 = 16 15 4. —. This can’t be simplified so it is our final answer. 16
1 – 1 ÷ 1 – 1 2 Dividing Fractions 3 1. Turn your mixed number fractions into improper fractions. 3 – ÷ 4– 2 3 2. Apply ‘Keep, Change, Flip’. 3 – × 3– 2 4 3. Multiply the numerators together. 3× 3=9 4. Multiply the denominators together. 2× 4=8 5. Write your answer as a mixed number fraction. 9 – = 1 1– 8 8
Dividing Fractions 2 1 2 6–÷ 2–=3– 2 4 8 Is she correct? Be prepared to explain and prove your answer.
Plenary: and That’s a Rap Write a rap to help you remember ‘Keep, Change, Flip’ when dividing fractions.
- Slides: 12