Lynne bought a bag of grapefruit, $1 \frac{5}{8}$ $1 5/8$ pounds of apples, and $2 \frac{3}{16}$ $2 3/16$ pounds of bananas. The total weight of her purchases was $7 \frac{1}{2}$ $7 1/2$ pounds. How much did the bag of grapefruit weigh?

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Lynne bought a bag of grapefruit, $1 \frac{5}{8}$ $1 5/8$ pounds of apples, and $2 \frac{3}{16}$ $2 3/16$ pounds of bananas. The total weight of her purchases was $7 \frac{1}{2}$ $7 1/2$ pounds. How much did the bag of grapefruit weigh?

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Answer 1 · 2018-06-22T15:49:50

The bag weighed $3 \frac{11}{16}$ $3 11/16$ pounds.

Explanation:

First, we need to get all three of our fractions under a common denominator. To do this, let's first change our mixed numbers into improper fractions:

$1 \frac{5}{8} = \frac{13}{8}$ $1 5/8=13/8$

$2 \frac{3}{16} = \frac{35}{16}$ $2 3/16=35/16$

$7 \frac{1}{2} = \frac{15}{2}$ $7 1/2=15/2$

Next, let's put each fraction under a common denominator using the LCM, or least common multiple. 16, in our case, is the LCM.

$\frac{13}{8} \cdot \frac{2}{2} = \frac{26}{16}$ $13/8*2/2=26/16$

$\frac{35}{16}$ $35/16$

$\frac{15}{2} \cdot \frac{8}{8} = \frac{120}{16}$ $15/2*8/8=120/16$

Finally, let's do some subtraction to get our answer:

$\frac{120}{16} - \frac{26}{16} - \frac{35}{16} = \frac{120 - 26 - 35}{16} = \frac{59}{16} = 3 \frac{11}{16}$ $120/16-26/16-35/16=(120-26-35)/16=59/16=3 11/16$

Hope this helps!

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Lynne bought a bag of grapefruit, $1 \frac{5}{8}$ $1 5/8$ pounds of apples, and $2 \frac{3}{16}$ $2 3/16$ pounds of bananas. The total weight of her purchases was $7 \frac{1}{2}$ $7 1/2$ pounds. How much did the bag of grapefruit weigh?

1 Answer

Explanation:

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Lynne bought a bag of grapefruit, $1 \frac{5}{8}$ $1 5/8$ pounds of apples, and $2 \frac{3}{16}$ $2 3/16$ pounds of bananas. The total weight of her purchases was $7 \frac{1}{2}$ $7 1/2$ pounds. How much did the bag of grapefruit weigh?