Question

Jill is making a long cape she needs 4 1/3 yards of blue fabric for the outside of the key she needs 3 2/3 yards of purple fabric for the lining the Cape

Answer 1

A) Notice that the two mixed fractions are equivalent to

`\begin{gathered} 4(1)/(3)=4+(1)/(3) \\ \text{and} \\ 3(2)/(3)=3+(2)/(3) \end{gathered}`

Jill transformed 4 into 12/3 and 3 into 9/3, and then she subtracted the second quantity from the first one. She forgot about the 1/3 and 2/3.

B) The correct calculation is

`\begin{gathered} 4(1)/(3)-3(2)/(3)=(4+(1)/(3))-(3+(2)/(3))=4+(1)/(3)-3-(2)/(3)=(4-3)+((1)/(3)-(2)/(3))=1+(-(1)/(3))=(2)/(3) \\ \Rightarrow4(1)/(3)-3(2)/(3)=(2)/(3) \end{gathered}`

The answer to part B) is 2/3