Under very specific instructions, a jeweller made one ring for the queen and one ring for the princess. The gem on the queen's ring weighed 3 3/4 carats and the stone on the princess's ring weighed 1/8 of a carat. How much heavier was the stone on the queen's ring than the stone on the princess's?Write your answer as a fraction or as a whole or mixed number.
Question
Under very specific instructions, a jeweller made one ring for the queen and one ring for the princess. The gem on the queen's ring weighed 3 3/4 carats and the stone on the princess's ring weighed 1/8 of a carat. How much heavier was the stone on the queen's ring than the stone on the princess's?Write your answer as a fraction or as a whole or mixed number.
Solution
To find out how much heavier the stone on the queen's ring was than the stone on the princess's, we need to subtract the weight of the princess's stone from the weight of the queen's stone.
First, we need to convert the mixed number 3 3/4 to an improper fraction. To do this, we multiply the whole number by the denominator and add the numerator. This gives us 15/4 carats for the queen's stone.
The princess's stone weighed 1/8 of a carat.
Now we subtract the weight of the princess's stone from the weight of the queen's stone:
15/4 - 1/8 = 60/16 - 2/16 = 58/16
To simplify this fraction, we divide both the numerator and the denominator by their greatest common divisor, which is 2:
58/16 = 29/8
So, the stone on the queen's ring was 29/8 carats heavier than the stone on the princess's ring.
To express this as a mixed number, we divide the numerator by the denominator:
29 ÷ 8 = 3 remainder 5
So, the stone on the queen's ring was 3 5/8 carats heavier than the stone on the princess's ring.
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