Discover Mathematics P5: Term 2, Unit 7, Lessons 1–3
GoalUse fraction strips to see how fractions with different denominators fit together and to add and subtract them.
New words
fraction strip · a bar cut into equal parts to show a fractionunlike denominators · different denominators, such as 2 and 3simplify · to write a fraction with the smallest possible numbers, such as 4/6 = 2/3
Explanation
Strips of the same length are cut into halves, thirds, sixths and so on. When you line them up, you can see that 1/2 covers the same length as 3/6 and 1/3 covers 2/6. To add 1/2 + 1/3, replace both by sixths: 3/6 + 2/6 = 5/6. To subtract, take away parts of the same size: 3/4 − 2/3 uses twelfths, because 3/4 = 9/12 and 2/3 = 8/12, so the difference is 1/12. Add or subtract only the numerators when the parts have the same size, and keep the denominator. If the answer can be written with smaller numbers, simplify it.
Worked examples
Add 1/2 + 1/3 with strips. One half is 3 sixths and one third is 2 sixths. Together 5 sixths: 1/2 + 1/3 = 5/6.
Fraction
In twelfths
3/4
9/12
2/3
8/12
Difference
1/12
Subtract 3/4 − 2/3. In twelfths: 3/4 = 9/12 and 2/3 = 8/12. 9/12 − 8/12 = 1/12.
Add 2/5 + 1/2. Use tenths: 2/5 = 4/10 and 1/2 = 5/10. The sum is 9/10.
Class activity
Paper strips. Cut three strips of paper of the same length. Fold one into halves, one into thirds and one into sixths and label every part. Lay them one under the other. Use them to show 1/2 + 1/6, 5/6 − 1/2 and 2/3 − 1/6, and write each answer.
