☰ Contents · Mathematics

Shares and common fractions

Lessons 41–42 · 2 lessons · B.Q. Khaydarov. Mathematics Grade 5, Parts 1–2. Revised and expanded third edition. Tashkent, 2020
41

Shares and common fractions

Textbook: Part 2, lesson 41, pp. 18–23
GoalThe idea of a share and a common fraction; numerator and denominator; finding a part of a number.
New words
share · ulushcommon fraction · oddiy kasrnumerator · suratdenominator · maxraj
Explanation

All points of a circle are the same distance from its centre; the part of the plane bounded by a circle is called a disc, and its diameter is 2 times its radius. If a whole thing is divided into equal pieces, each piece is called a share. For example, if a cake is cut into 8 equal pieces, each piece is «one eighth». If 3 of the 8 shares are taken, we get «three eighths», written 3/8. Such a notation is a common fraction: the number below the fraction line is the denominator (into how many shares the whole was divided), the number above is the numerator (how many shares were taken). A half is 1/2, a quarter is 1/4, an eighth is 1/8. To find a part of a number, divide the number by the denominator and multiply by the numerator.

Worked examples
Find 5/9 of a 36 m rope: 36 : 9 = 4 (m) is one share, 4 · 5 = 20 (m).
3 km of a 14 km road have been covered. The number 3 is 3/14 of 14, because the whole has 14 shares and 3 are taken.
Class activity

“Paper folding”: fold a long paper strip into 8 equal parts, colour 5 of them and write the fraction (5/8). If scissors are needed, ask an adult for help.

Practice
1
A pizza was cut into 6 equal slices and 4 were eaten. Which fraction shows the eaten part?
2
How many apples are 3/8 of 48?
3
Of 30 pupils in a class, 23 are girls. What part of the class are the girls?
4
Why can the denominator of a fraction not be zero?