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Fraction problems; Chapter V review

Lessons 49–50 · 2 lessons · B.Q. Khaydarov. Mathematics Grade 5, Parts 1–2. Revised and expanded third edition. Tashkent, 2020
50

Chapter V review problems

Textbook: Part 2, lesson 50, pp. 52–55
GoalReview of Chapter V on common fractions: fractions, comparing, operations, mixed numbers, problems.
New words
common fraction · oddiy kasrmixed number · aralash sonimproper fraction · noto‘g‘ri kasrequal fractions · teng kasrlar
Explanation

A common fraction is written a/b: b is the number of shares in the whole, a is the number of shares taken. When fractions with the same denominator are added or subtracted, the operation is done on the numerators only. The whole part is taken out of an improper fraction, and a mixed number is turned into an improper fraction. Mixed numbers are added and subtracted by whole and fractional parts; a whole is broken up if needed. The quotient of natural numbers is written as a fraction: a : b = a/b. Problems use the methods for a part of a number and for finding the whole from its part.

Worked examples
Calculate: 4 2/7 + 3 6/7 = 7 8/7 = 8 1/7. Subtraction: 8 − 3 2/7 = 7 7/7 − 3 2/7 = 4 5/7.
Compare: 9/11 < 12/11, because the denominators are equal and 9 < 12. Also 12/11 > 1 while 9/11 < 1.
Class activity

“Fraction relay”: one pupil writes a fraction, the next turns it into a mixed number and the third adds 1 5/8 to it. Check that the answers agree.

Practice
1
Calculate 18/25 − 7/25 + 9/25.
2
Solve the equation: x + 3 2/9 = 8.
3
7/10 of a 50 m path was paved. How many metres?
4
Why can mixed numbers help explain that 14/5 > 2?