13
Adding and subtracting fractions with different denominators
Textbook, pp. 47–50
GoalKnow and apply the rule for adding and subtracting fractions with different denominators.
New words
addition · qo‘shishsubtraction · ayirishsum · yig‘indidifference · ayirma
Explanation
To add or subtract fractions with different denominators, first bring them to a common denominator. Then add or subtract the numerators and keep the denominator unchanged. If the result can be reduced, reduce it; if it is an improper fraction, separate the whole part. For example 1/4 + 1/6 = 3/12 + 2/12 = 5/12. We never add the denominators: 1/2 + 1/3 is 5/6, not 2/5.
Worked examples
5/6 − 3/8: LCM(6, 8) = 24, so 20/24 − 9/24 = 11/24.
7/10 + 1/6: LCM = 30, 21/30 + 5/30 = 26/30 = 13/15 (reduced by 2).
Class activity
“Fraction shop”: groups play shop: one product weighs 1/3 kg, another 1/4 kg. A customer buys both: how many kilograms in all? The group writes the sum in a ledger and another group checks it.
Practice
1
Compute 2/3 + 1/4.
11/12
2
Compute 7/8 − 1/6.
17/24
3
Aziza spent 1/3 of her money on a book and 1/4 on notebooks. What part of her money did she spend?
7/12
4
Why is 1/2 + 1/3 = 2/5 wrong?
The parts have different sizes, so we must first make them equal: 3/6 + 2/6 = 5/6. Also, 2/5 is even less than 1/2, but a sum must be bigger than each of its addends.