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Amari had \( 2 \frac{2}{3} \) yards each of pink ribbon and blue ribbon. She cut the pink ribbon into \( \frac{1}{6} \) yard pieces. She cut the blue ribbon into \( \frac{1}{9} \) yard pieces. What is true about the number of pieces of ribbon Amari cut?

A. She cut the same number of pieces from each ribbon.
B. She cut more pieces from the pink ribbon than the blue ribbon.
C. She cut more pieces from the blue ribbon than the pink ribbon.
D. She cut an equal number of pieces from the pink and blue ribbons combined.

Answer :

Final answer:

Amari had 2 2/3 yards of both pink and blue ribbon. She cut the pink ribbon into 16 pieces of 1/6 yard each, and the blue ribbon into 24 pieces of 1/9 yard each, meaning c) she cut more pieces from the blue ribbon than the pink ribbon.

Explanation:

Amari had a total of 2 2/3 yards of both pink and blue ribbon. To find the number of pieces each color of ribbon is cut into, we need to divide the total length of each ribbon by the length of one piece.

For the pink ribbon, which is cut into 1/6 yard pieces, we calculate the number of pieces by dividing 2 2/3 yards by 1/6. Using the formula for dividing fractions, which is to multiply by the reciprocal, we have:

(2 2/3) / (1/6) = (8/3) * (6/1) = 48/3 = 16 pieces.

For the blue ribbon, which is cut into 1/9 yard pieces, we perform a similar calculation:

(2 2/3) / (1/9) = (8/3) * (9/1) = 72/3 = 24 pieces.

Thus, we can conclude that the correct answer is: (c) She cut more pieces from the blue ribbon than the pink ribbon.

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