Comparing Fractions
Sarah and Jake are running a race. Sarah has completed 3/5 of the race, while Jake has completed 4/6. Who has run farther? Explain.
Jake has run farther. 4/6 = 2/3, and 2/3 > 3/5.
Tasha shaded 3/6 of a rectangle. Which fractions also describe the shaded area? (Select all that apply: 1/2, 3/6, 2/4, 4/8)
Correct answers: 1/2, 3/6, 2/4.
What fraction is equivalent to 2/4?
1/2
Arrange these fractions in order from least to greatest: 1/4, 2/3, 3/8.
1/4, 3/8, 2/3.
Chase and Abigail both walked to school. In 10 minutes, Chase walked 2/5 of the way, and Abigail walked 3/7 of the way. Who walked farther?
Chase walked farther because 2/5 less then 3/7.
Emma says that 7/10 is greater than 3/5 because 7 is bigger than 3. Is she correct? If not, explain her mistake and write the correct comparison.
Emma is incorrect. She compared numerators without considering denominators. 3/5 = 6/10, so 6/10 > 7/10 is false. The correct comparison is 7/10 > 3/5.
Which fraction names the unshaded part of a model where 5/9 of it is shaded? Explain.
The unshaded part is 4/9, because 1 - 5/9 = 4/9.
Write two fractions that are equivalent to 3/9.
Possible answers: 1/3, 2/6, 4/12.
Use a number line to order 1/6, 2/5, and 1/2 from least to greatest.
1/6, 2/5, 1/2.
Erika spent 3/8 of her money on a toy. What fraction of her money did she not spend?
Erika did not spend 5/8 of her money.
Use a number line to compare 5/8 and 3/4. Which fraction represents a greater distance?
3/4 is greater than 5/8 because when converted to a common denominator (8), 3/4 = 6/8, which is greater than 5/8.
A fruit basket is divided into 5 equal parts. What fraction represents the entire basket?
The entire basket is 5/5 = 1.
Complete the pattern: 1/2 = 2/4 = 3/?
3/6
Compare 5/12 and 3/8 using >, <, or =.
5/12 < 3/8
A recipe calls for 3/4 of a cup of sugar. If Ava only has a 1/2 cup measuring spoon, how many scoops does she need?
1 1/2 scoops (or three 1/2 cups).
A pizza is cut into 12 equal slices. Another pizza is cut into 8 equal slices. Who gets the bigger piece: someone eating 1 slice of the first pizza or someone eating 1 slice of the second? Explain.
The pizza with 8 slices has larger pieces, so one slice of the second pizza is bigger.
Draw a model to represent 2/3. Then write an equivalent fraction for it.
A model showing 2 out of 3 sections shaded. An equivalent fraction is 4/6, 6/9, etc.
Explain why 5/10 and 1/2 are equivalent. Use a visual model.
Both fractions 5/10 and 1/2 represent the same amount when simplified. A visual model would show half of a whole being divided differently.
Olivia used ribbon in a craft project. She used 5/6 yard of red, 2/3 yard of blue, and 3/4 yard of yellow. Order them from shortest to longest.
2/3 < 3/4 < 5/6.
Gary, Barry, and Larry baked identical cakes. At a party, guests ate 2/5 of Gary’s cake, 1/2 of Barry’s cake, and 3/8 of Larry’s cake. Which cake was eaten the most?
Barry’s cake was eaten the most because 1/2 > 3/8 > 2/5.
Jackson and Mateo each have the same number of marbles. 4/7 of Jackson’s marbles are blue, while 5/9 of Mateo’s are blue. Who has a greater fraction of blue marbles? Explain.
Jackson’s bracelet has a fraction closer to 0, because 4/7 is closer to 1/2 than 5/9. However, 5/9 of Mateo’s bracelet means he has more red beads.
A school cafeteria made a large cake and cut it into 16 equal pieces. What fraction represents the entire cake? What fraction represents half of the cake?
The entire cake is 16/16 = 1, and half of the cake is 8/16 = 1/2.
True or false: 7/8 and 14/16 are equivalent fractions. If true, explain why. If false, correct the mistake.
True because 7/8 = 14/16 when multiplying both numerator and denominator by 2.
A class is divided into 9 equal groups. One group has 2/9 of the students, another has 1/3, and another has 4/9. Order the fractions from least to greatest.
1/3 < 2/9 < 4/9.
Noah is measuring two pieces of wood. One is 5/6 yard long, and the other is 4/5 yard long. Use a number line to compare the lengths. Which is longer?
5/6 > 4/5