85
Comparing fractions (practice)
Textbook: Part 3, lesson 85, pp. 43–45
GoalComparing fractions with the same numerator: the smaller denominator gives the greater fraction; comparing a fraction with 1.
New words
same numerator · bir xil suratsize of a share · ulush o‘lchamismaller denominator · kichik maxrajcomparison · taqqoslash
Explanation
Two fractions with the same numerator have the same number of shares, but the shares are different sizes. The larger the denominator, the more parts the whole is cut into and the smaller each share is. So of fractions with equal numerators, the one with the smaller denominator is greater: 1/3 > 1/5. A proper fraction is less than 1; an improper fraction is greater than or equal to 1.
Worked examples
3/5 > 3/8 because 5 < 8: a fifth is bigger than an eighth.
7/8 < 1 (proper), 9/8 > 1 (improper).
Class activity
“Pieces of bread”: take identical paper circles (loaves). Fold one into 4 equal pieces and another into 8. Children lay a 1/4 piece on a 1/8 piece, see which is bigger and explain why.
Practice
1
Compare 3/8 and 3/5.
3/8 < 3/5
2
Compare 5/6 and 5/9.
5/6 > 5/9
3
Write in decreasing order: 2/3, 2/9, 2/5, 2/7.
2/3, 2/5, 2/7, 2/9
4
The same loaf is shared equally by 4 people or by 8 people. In which case is each piece bigger? Write the piece as a fraction.
among 4, 1/4
5
Find the smallest of 4/11, 4/13, 4/7, 4/9.
4/13