12
Comparing fractions with different denominators
Textbook, pp. 43–46
GoalLearn to compare fractions with different denominators.
New words
comparing · taqqoslashgreater · kattasmaller · kichikorder / sequence · ketma-ketlik
Explanation
To compare fractions with different denominators, first bring them to a common denominator, then compare the numerators: the fraction with the bigger numerator is greater. With equal denominators the one with the bigger numerator is greater. With equal numerators the one with the smaller denominator is greater, because its parts are bigger. A proper fraction is less than 1, an improper fraction is at least 1. These facts speed up comparing.
Worked examples
5/6 and 7/9: LCM(6, 9) = 18. 5/6 = 15/18 and 7/9 = 14/18. Since 15 > 14, 5/6 > 7/9.
3/8 and 3/5: equal numerators, and 5 < 8, so 3/5 > 3/8.
Class activity
“Fraction staircase”: each pupil gets a fraction card. They line up in increasing order. The class checks the order by bringing the fractions to a common denominator.
Practice
1
Compare 3/4 and 5/7 (>, <).
>
2
Write 1/2, 2/3, 3/5 in increasing order.
1/2, 3/5, 2/3
3
Ali read 3/5 of a book and Bobur read 4/7. Who read more?
Ali: 3/5 = 21/35 and 4/7 = 20/35, and 21/35 > 20/35.
4
Why is 3/8 < 3/5 even though 8 > 5?
A bigger denominator means the whole is cut into more parts, each part smaller; in both cases we take 3 parts.