Question

Oleg and Anya drew these models to help them find the difference of Three-fourths and One-half.

Oleg's work. Top: Three-fourths. A fraction bar divided into 4 parts. 3 are shaded. Bottom: One-third. A fraction bar divided into 3 parts. 1 is shaded. Anya's work. Top: Three-fourths. A fraction bar divided into 8 parts. 6 are shaded. Bottom: One-third. A fraction bar divided into 8 parts. 4 are shaded.
Which best describes which models can be used to find the difference?

Anya is correct because the product of 2 and 4 is 8, so each model must have 8 pieces.
Anya is correct because dividing the bars into 8 pieces results in bars with 6 of 8 pieces shaded and 4 of 8 pieces shaded.
Oleg is correct because 4 is the smallest multiple of 2 and 4, so each model must have 4 pieces.
Oleg is correct because dividing each bar into 2 pieces results in a bar with 1 of 4 pieces shaded.

Answer 1

Answer: "Anya is correct because dividing the bars into 8 pieces results in bars with 6 of 8 pieces shaded and 4 of 8 pieces shaded."

Reason: Anya’s bars show 3/4 = 6/8 and 1/2 = 4/8, so you can subtract (6/8 − 4/8 = 2/8 = 1/4). Oleg’s models use different-sized pieces (the bars aren’t partitioned the same), so they can’t be directly compared. (Note: you could also use 4 pieces as a common partition since 1/2 = 2/4, but Oleg’s shown partitions must match to work.)