Sweet Surprise Bake Shop sold slices of cake at the arts festival last weekend. Each cake was cut into eight slices. They sold 2 1/4

Question

chocolate cakes, 2 1/2
red velvet cakes, 3/4
of a carrot cake and 3 1/2
sugar cream cakes. What is the total number of cakes sold?

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(1 point)
Responses

9 cakes
9 cakes

8 1/2
cakes
8 and 1 half cakes

7 1/2
cakes
7 and 1 half cakes

7 6/7
cakes
7 and 6 sevenths cakes
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Answer 1

To calculate the total number of cakes sold, we first need to convert all the mixed fractions into improper fractions and then sum them all up.

1. Chocolate cakes: \[ 2 \frac{1}{4} = 2 + \frac{1}{4} = \frac{8}{4} + \frac{1}{4} = \frac{9}{4} \]

2. Red velvet cakes: \[ 2 \frac{1}{2} = 2 + \frac{1}{2} = \frac{4}{2} + \frac{1}{2} = \frac{5}{2} \]

3. Carrot cake: \[ \frac{3}{4} \]

4. Sugar cream cakes: \[ 3 \frac{1}{2} = 3 + \frac{1}{2} = \frac{6}{2} + \frac{1}{2} = \frac{7}{2} \]

Now we sum all the cakes sold:

\[ \frac{9}{4} + \frac{5}{2} + \frac{3}{4} + \frac{7}{2} \]

To add these fractions, we should convert the fractions to a common denominator. The least common multiple of the denominators (4 and 2) is 4. We convert each fraction:

• \(\frac{5}{2} = \frac{5 \times 2}{2 \times 2} = \frac{10}{4}\)
• \(\frac{7}{2} = \frac{7 \times 2}{2 \times 2} = \frac{14}{4}\)

Now we can sum them all up:

\[ \frac{9}{4} + \frac{10}{4} + \frac{3}{4} + \frac{14}{4} = \frac{9 + 10 + 3 + 14}{4} = \frac{36}{4} = 9 \]

So the total number of cakes sold is 9 cakes.

Answer 2

are you sure

Answer 3

Let's go through the calculations again step by step to confirm the total number of cakes sold.

1. Chocolate cakes:
   \[ 2 \frac{1}{4} = 2 + \frac{1}{4} = \frac{8}{4} + \frac{1}{4} = \frac{9}{4} \]

2. Red velvet cakes:
   \[ 2 \frac{1}{2} = 2 + \frac{1}{2} = \frac{4}{2} + \frac{1}{2} = \frac{5}{2} \]

3. Carrot cake:
   \[ \frac{3}{4} \]

4. Sugar cream cakes:
   \[ 3 \frac{1}{2} = 3 + \frac{1}{2} = \frac{6}{2} + \frac{1}{2} = \frac{7}{2} \]

Now, we will add these fractions together. To do this, we need a common denominator. The least common multiple of 4 and 2 is 4.

• Convert red velvet and sugar cream cakes to have the same denominator of 4:
  • \(\frac{5}{2} = \frac{10}{4}\)
  • \(\frac{7}{2} = \frac{14}{4}\)

Now we can rewrite the total:

\[ \frac{9}{4} + \frac{10}{4} + \frac{3}{4} + \frac{14}{4} \]

Next, we combine the numerators:

\[ \frac{9 + 10 + 3 + 14}{4} = \frac{36}{4} = 9 \]

So the total number of cakes sold is indeed 9 cakes.