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

Firstly, let's convert our mixed numbers into improper fractions in order to bring all three of our fractions under a common denominator:

Next, let's use the least common multiple (LCM)—16 in our example—to bring each fraction under a common denominator.

Finally, to find our answer, let's subtract a little bit:

I hope this is useful.

To find the weight of the bag of grapefruit, subtract the combined weight of the apples and bananas from the total weight of all purchases.

Total weight of purchases = Weight of grapefruit + Weight of apples + Weight of bananas 7 1/2 pounds = Weight of grapefruit + 1 5/8 pounds + 2 3/16 pounds

To subtract the combined weight of the apples and bananas from the total weight of all purchases, you need to convert the weights to fractions with the same denominator.

1 5/8 pounds = 13/8 pounds 2 3/16 pounds = 7/16 pounds

Now, subtract the combined weight of the apples and bananas from the total weight of all purchases.

Total weight of purchases - Weight of apples - Weight of bananas = Weight of grapefruit 7 1/2 pounds - (13/8 pounds + 7/16 pounds) = Weight of grapefruit 7 1/2 pounds - (13/8 pounds + 7/16 pounds) = Weight of grapefruit 7 1/2 pounds - (26/16 pounds + 7/16 pounds) = Weight of grapefruit 7 1/2 pounds - 33/16 pounds = Weight of grapefruit 7 1/2 pounds - 33/16 pounds = Weight of grapefruit 15/2 pounds - 33/16 pounds = Weight of grapefruit (120/16 pounds) - (33/16 pounds) = Weight of grapefruit (120 - 33)/16 pounds = Weight of grapefruit 87/16 pounds = Weight of grapefruit

Now, simplify the fraction.

87/16 pounds = 5 7/16 pounds

So, the bag of grapefruit weighed 5 7/16 pounds.