45
Division and fractions
Textbook: Part 2, lesson 45, pp. 35–37
GoalWrite a quotient as a fraction; write a natural number as a fraction; divide a sum by a number.
New words
quotient · bo‘linmafraction line · kasr chizig‘iremainder · qoldiqdividing a sum · yig‘indini bo‘lish
Explanation
The fraction line acts as a division sign: a : b = a/b. For example, if 3 loaves are shared equally by 4 children, each gets 3 : 4 = 3/4 of a loaf. If the division has no remainder, the quotient is a natural number (20 : 5 = 20/5 = 4); if there is a remainder, the quotient is a fraction. Any natural number can be written as a fraction with any denominator: put the product of the number and the denominator in the numerator, for example 3 = 15/5. To divide a sum by a number, divide each addend separately and add the quotients: (a + b) : c = a : c + b : c.
Worked examples
Share 5 pens among 8 pupils equally: 5 : 8 = 5/8 of a pen each. Cutting a 6 m ribbon into 7 equal pieces gives pieces of 6/7 m each.
(48 + 36) : 12 = 48 : 12 + 36 : 12 = 4 + 3 = 7. Second way: 84 : 12 = 7. Both ways give the same answer.
Class activity
“Fair sharing”: share 3 identical paper strips equally among 4 people. Fold each strip into 4 parts, count the shares each person gets and check that 3 : 4 = 3/4.
Practice
1
Write 9 : 13 as a common fraction.
9/13
2
Write 7 as a fraction with denominator 4: 7 = ?/4
28/4
3
Calculate (63 + 45 + 27) : 9 by dividing each addend.
15
4
Why can 2 : 5 = 2/5 be explained with loaves?
Sharing 2 loaves among 5 people, we cut each loaf into 5 parts and give everyone 2 parts, that is 2/5.