Comparing Proper Fractions
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Students learn to compare fractions with the same denominator, which are called like fractions, by comparing the numerators. For example, to compare 7/9 and 4/9, note that 7 > 4, so 7/9 > 4/9. Students also learn to compare fractions with the different denominators, which are called unlike fractions, by first finding a common denominator, then comparing the numerators. For example, to compare 1/2 and 1/3, first find a common denominator, or the Least Common Multiple of 2 and 3, which is 6. To get 6 in the denominator of 1/2, multiply the numerator and denominator by 3, to get 3/6. To get 6 in the denominator of 1/3, multiply the numerator and denominator by 2, to get 2/6. Next, compare 3/6 and 2/6. Note that 3 > 2, so 3/6 > 2/6, which means that 1/2 > 1/3.