Fraction Comparisons and Relationships

Three friends each had a piece of cake. Emily ate 5/9 of her cake. David ate1/3 of his cake. Fiona ate 3/7 of her cake. The fractions are shown.

5/9, 1/3, 3/7

Which expression correctly lists the amounts of cake each of the friends ate in order from least to greatest?

• a. 1/3 <3/7<5/9

• b. 3/7 < 1/3 < 5/9

• c. 1/3 < 5/9 < 3/7

• d. 3/7 < 5/9 < 1/3

Determine if the sum or difference is closer to the benchmark fractions. Justify your reasoning.

Part A: 3/4 - 1/3

greater than 1 or less than 1?

Determine if the sum or difference is closer to 0 or 1. Justify your reasoning.

Part B: 3/7 + 2/9

closer to 0 or closer to 1

Arrange the following fractions from least to greatest. 7/4, 2/3, 9/10, 3/3

Emily finished 2/5 of her project in the morning and 1/3 in the afternoon. How much of her project did she complete in total?

• 11/15

• 7/15

• 1/2

• 13/15

James is making a cake. The recipe calls for 2/4 cups of chocolate chips and 3/8 cups of sprinkles. How many cups of chocolate chips and sprinkles are needed for the recipe? Justify your answer with a model or equation.

Ms. Lee had 5/6 of a liter of juice. She poured 1/4 of a liter into a glass. How much juice does Ms. Lee have left?

• 1/3

• 7/12

• 1/2

• 2/3

Michael claims that 3/4 + 1/3 = 4/7. Do you agree with Michael’s answer? Explain why he is correct or incorrect.

For a science project, Alex recorded the amount of sugar he consumed at breakfast over 10 days. He displayed the data in a line plot.

• 3/4

• 5/8

• 1/2

• 7/8

Linda recorded the rainfall in inches for the last 10 rainy days. She represented the data on a line plot. What is the total rainfall in inches for the 2 days with the least amount of rain?