Compare fractions

You know that one half and two quarters are equivalent fractions. We multiply the numerator and the denominator by 2. Today, we will compare and order unlike fractions, which have different denominators. Mei eats three quarters of a mooncake. Kavin eats five eighths of an identical mooncake. Who eats more? Here is Mei's mooncake. Here is Kavin's mooncake, the same size. Mei's mooncake has 4 equal parts. She eats 3 parts, so she eats three quarters. Kavin's mooncake has 8 equal parts. He eats 5 parts, so he eats five eighths. Kavin eats 5 parts and Mei eats 3, but the parts are not the same size. One of Mei's parts is the same size as 2 of Kavin's parts. To compare, we need parts of the same size. Cut each of Mei's 4 parts into 2 equal parts. 4 times 2 is 8. Each shaded part now has 2 small parts. 3 times 2 is 6. Now both have 8 equal parts. Mei has 6 parts shaded. Six eighths is more than five eighths. Mei's shaded part is longer. So Mei eats more. A bigger denominator does not always mean a bigger fraction.

Which fraction is greater, three fifths or seven tenths? Try it first. Pause if you like. Here are two strips of the same size. The first strip has 5 equal parts, with 3 shaded. The second strip has 10 equal parts, with 7 shaded. We make both strips have 10 equal parts. Cut each of the 5 parts into 2 equal parts. 5 times 2 is 10, and 3 times 2 is 6. Seven tenths is more than six tenths. So seven tenths is the greater fraction.

Arrange two thirds, five sixths and seven twelfths from smallest to greatest. Try it first. Pause if you like. Here are three strips of the same size. The first strip has 3 equal parts, with 2 shaded. The second strip has 6 equal parts, with 5 shaded. The third strip has 12 equal parts, with 7 shaded. We make every strip have 12 equal parts. Cut each of the 3 parts into 4 equal parts. 3 times 4 is 12, and 2 times 4 is 8. Cut each of the 6 parts into 2 equal parts. 6 times 2 is 12, and 5 times 2 is 10. Seven twelfths is less than eight twelfths, and eight twelfths is less than ten twelfths. Eight twelfths is two thirds, and ten twelfths is five sixths. From smallest to greatest, the order is seven twelfths, two thirds, five sixths. To compare fractions, first make the parts the same size. Then compare the numerators.