1
Pieces taken from a whole
Discover Mathematics P4: Term 2, Unit 9, Lessons 5–7
GoalTake a fraction away from one whole and subtract fractions with the same denominator.
New words
whole · all the equal parts together, written as 1 or as 8/8, 4/4 and so onsubtract · to take away; the denominator stays the samedifference · the answer of a subtraction
Explanation
A whole can be written as a fraction with the same top and bottom: 1 = 8/8 = 4/4 = 10/10. To take a fraction away from 1, write the whole with the same denominator and subtract the numerators. For 1 − 3/8, write 1 = 8/8, then 8/8 − 3/8 = 5/8. We took 3 pieces from 8 pieces and 5 pieces are left. The size of the pieces (the denominator) does not change when we subtract, only the number of pieces changes. The same works for any fractions with the same denominator: 7/10 − 4/10 = 3/10. Check by adding back: 3/8 + 5/8 = 8/8 = 1.
Worked examples
A bed of 8 equal rows is in the school garden and 3 rows are planted with mint. 1 − 3/8 = 8/8 − 3/8 = 5/8 of the bed is still empty.
A bottle holds 1 litre. Mina pours out 2/5 litre. 1 − 2/5 = 5/5 − 2/5 = 3/5 litre is left in the bottle. Check: 2/5 + 3/5 = 5/5 = 1.
Subtract fractions with the same denominator: 7/10 − 4/10. Subtract the numerators and keep the denominator: 7 − 4 = 3, so the difference is 3/10.
Class activity
Paper strips. Cut a paper strip into 8 equal parts. Cover 3 parts and read the fraction that is covered and the fraction that is not covered. Write both as a subtraction from 1.
Practice
1
Find 1 − 2/6.
6/6 − 2/6 = 4/6.
2
Find 1 − 7/12.
12/12 − 7/12 = 5/12.
3
Find 9/10 − 4/10.
9 − 4 = 5, so 5/10.
4
Karim has a ribbon 1 metre long and uses 3/4 metre. How much ribbon is left?
1 − 3/4 = 4/4 − 3/4 = 1/4 metre.
5
Nour says 1 − 3/8 = 7/8 because 8 − 1 = 7. What is wrong? What is the right answer?
She changed the denominator. The pieces are still eighths. 8/8 − 3/8 = 5/8.