Question

Mia bought 10 1/9 lb of flour. She used 2 3/4 lb of flour to bake a banana cake and some to bake a chocolate cake. After baking two cakes, she had 3 5/6 lb of flour left. How much flour did she use to bake the chocolate cake?

Answer 1

We know that she started with 10 1/9 pounds and after the two cakes she was left with 3 5/6. So if we subtract what she started with minus what she is left with we will get what she used.

This is easiest done by converting the mixed numbers into improper fractions, finding a common denominator and subtracting (subtract the numerators and keep the denominator) as follows:

$10 \frac{1}{9}-3 \frac{5}{6}= \frac{91}{9}- \frac{23}{6} =\frac{182}{18}- \frac{69}{18}= \frac{113}{18}$

That's how much flour she spent on both cakes. If we subtract from this what she spent on the banana cake 2 3/4 we will be left with what she used for the chocolate cake.

This is found as follows: $\frac{113}{18} -2 \frac{3}{4} = \frac{113}{18} - \frac{11}{4} = \frac{226}{36} - \frac{99}{36} = \frac{127}{36}=3 \frac{19}{36}$

She used $3 \frac{19}{36}$ pounds of flour on the chocolate cake.

Answer 2

Mia used $3\frac{19}{36}$ lb of flour to bake the chocolate cake.

Further Explanation

Given:

Total flour $10\frac{1}{9}$ lbs

She used:

$2\frac{3}{4}$ for banana cake

x lbs for chocolate cake

Flour left $3\frac{5}{6}$ lbs

How much flour did she use to bake the chocolate cake?

so the flour that Mia use for banana cake is total flour subtract the flour that she used plus the left over.

x =Total flour - flour for banana cake - left over

$\boxed {= 10\frac{1}{9} - 2\frac{3}{4} - 3\frac{5}{6} }$

I am going to put this into improper fraction

$\boxed { = \frac{91}{9} - \frac{11}{4} - \frac{23}{6} }$

because the denominator is different, we are going to find the common denominator for 9, 4 and 6 which is 36

$\boxed {= \frac{364-99-138}{36} }\\ \boxed {= \frac{127}{36} }\\\boxed {= 3\frac{19}{36} }$

So the flour that she use to bake the chocolate cake is $3\frac{19}{36}$ lbs

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Keyword: mixed fraction, subtraction, improper fraction, part to whole relationship