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Review: divisibility and fractions with different denominators

Lessons 52–53 · 2 lessons · M.A. Mirzaahmedov, A.A. Rahimqoriyev, Sh.N. Ismailov, M.A. To‘xtaxodjayeva. Mathematics Grade 6, 2nd edition. O‘qituvchi NMIU, Tashkent, 2017
53

Final review: adding and subtracting fractions with different denominators

Textbook, p. 227
GoalReview adding, subtracting and comparing fractions with different denominators and mixed numbers.
New words
common denominator · umumiy maxrajmixed number · aralash sonirreducible fraction · qisqarmas kasrcomparing · taqqoslash
Explanation

Before adding or subtracting fractions with different denominators we bring them to a common denominator using the LCM. Then we operate on the numerators, reduce the answer and separate the whole part if it is an improper fraction. When adding mixed numbers, add the whole and fractional parts separately; when subtracting, if needed, take one unit from the whole part and add it to the fractional part. To compare, bring the fractions to a common denominator and compare numerators.

Worked examples
5/6 − 3/8: LCM(6, 8) = 24, 20/24 − 9/24 = 11/24.
3 1/4 + 2 5/6 = 5 + 3/12 + 10/12 = 5 13/12 = 6 1/12.
Class activity

“Fraction relay”: team members come to the board in turn and perform the next operation in a chain: (1/2 + 1/3) − 1/4 + ... The last pupil writes the total and the team checks every step.

Practice
1
Compute 7/12 + 5/18.
2
Compute 4 1/6 − 1 3/4.
3
2/5 of a road was paved on Monday and 3/10 on Tuesday. What part of the road is left?
4
Which is greater, 7/9 or 11/14? How did you decide?