Amanda has put in [tex]\frac{53}{63}[/tex] extra cups
Solution:
Given that, recipe for cupcakes calls for [tex]4\frac{4}{9}[/tex] cups of flour
Amanda accidentally put in [tex]5\frac{2}{7}[/tex] cups
To find: Number of extra cups put in
Let us first convert the mixed fraction to improper fraction
Multiply the whole number part by the fraction's denominator.
Add that to the numerator.
Then write the result on top of the denominator.
[tex]\rightarrow 4\frac{4}{9} = \frac{9 \times 4+4}{9} = \frac{40}{9}\\\\\rightarrow 5\frac{2}{7} = \frac{7 \times 5 + 2}{7} = \frac{37}{7}[/tex]
Number of extra cups put in can be found by finding the difference between accidentally put cups and original cups
[tex]\text{ Number of extra cups put in } = \frac{37}{7} - \frac{40}{9}\\\\\text{ Number of extra cups put in } = \frac{37 \times 9}{7 \times 9} - \frac{40 \times 7}{9 \times 7}\\\\\text{ Number of extra cups put in } = \frac{333}{63}-\frac{280}{63}\\\\\text{ Number of extra cups put in } = \frac{333-280}{63} = \frac{53}{63}[/tex]
Thus she has put in [tex]\frac{53}{63}[/tex] extra cups
