Question

ray had 5 yards of ribbon. he used \\(\frac{2}{3}\\) of it. how many yards of ribbon did he use?\
a \\(\frac{10}{15}\\)\
b. \\(\frac{5}{3}\\)\
c. \\(\frac{7}{3}\\)\
d. \\(\frac{10}{3}\\)\

1. christine is making cookies. each recipe requires \\(\frac{3}{4}\\) teaspoon of ground cinnamon. if christine makes 3 batches of cookies, how many teaspoons of ground cinnamon will she use?\

a \\(\frac{9}{4}\\)\
b. \\(\frac{6}{4}\\)\
c. \\(\frac{9}{12}\\)\
d. \\(\frac{3}{12}\\)\

1. george owns a muffin shop. he bakes a total of 50 muffins on monday. a total of \\(\frac{4}{5}\\) of the muffins are blueberry, and \\(\frac{2}{5}\\) of the blueberry muffins have nuts. how many of the muffins are blueberry without nuts?\

a 16\
b. 20\
c. 24\
d. 30

Explanation:

Question 10 (Ray's Ribbon)

Step1: Identify the operation

To find the amount of ribbon used, we multiply the total length of the ribbon by the fraction used. The total length is 5 yards, and the fraction used is $\frac{2}{3}$. So the operation is $5\times\frac{2}{3}$.

Step2: Perform the multiplication

When multiplying a whole number by a fraction, we multiply the whole number with the numerator of the fraction. So $5\times\frac{2}{3}=\frac{5\times2}{3}=\frac{10}{3}$? Wait, no, wait. Wait, 5 is a whole number, so $5\times\frac{2}{3}=\frac{5\times2}{3}=\frac{10}{3}$? But wait, let's check the options. Wait, no, maybe I made a mistake. Wait, 5 yards, used $\frac{2}{3}$ of it. So $5\times\frac{2}{3}=\frac{10}{3}$? But option B is $\frac{5}{3}$, option D is $\frac{10}{3}$. Wait, no, wait, 5 times 2 is 10, over 3. So $\frac{10}{3}$ is option D? Wait, no, wait, maybe I misread the question. Wait, Ray had 5 yards, used $\frac{2}{3}$ of it. So the calculation is $5\times\frac{2}{3}=\frac{10}{3}$? But let's check the options. Option B is $\frac{5}{3}$, option D is $\frac{10}{3}$. Wait, maybe I made a mistake. Wait, 5 times $\frac{2}{3}$ is $\frac{10}{3}$, which is option D? Wait, no, wait, the options are A: $\frac{10}{15}$, B: $\frac{5}{3}$, C: $\frac{7}{3}$, D: $\frac{10}{3}$. Wait, $\frac{10}{3}$ is approximately 3.33, and $\frac{5}{3}$ is approximately 1.66. Wait, 5 yards, using $\frac{2}{3}$ of it. So 5 times $\frac{2}{3}$ is $\frac{10}{3}$, so the answer should be D? Wait, no, wait, maybe the question is "he used $\frac{2}{3}$ of it", so 5 times $\frac{2}{3}$ is $\frac{10}{3}$, so option D. But let's recheck.

Wait, maybe I made a mistake. Wait, 5 yards, $\frac{2}{3}$ of it. So $5\times\frac{2}{3}=\frac{10}{3}$, which is option D. So the answer is D? Wait, no, wait, the options: A is $\frac{10}{15}$ (which simplifies to $\frac{2}{3}$), B is $\frac{5}{3}$, C is $\frac{7}{3}$, D is $\frac{10}{3}$. So yes, $\frac{10}{3}$ is option D.

Question 11 (Christine's Cinnamon)

Step1: Identify the operation

To find the total cinnamon used, we multiply the amount per batch ($\frac{3}{4}$ teaspoon) by the number of batches (3). So the operation is $3\times\frac{3}{4}$.

Step2: Perform the multiplication

Multiplying 3 (a whole number) by $\frac{3}{4}$, we get $3\times\frac{3}{4}=\frac{3\times3}{4}=\frac{9}{4}$. So the answer is option A.

Question 12 (George's Muffins)

Step1: Find the number of blueberry muffins

First, find the number of blueberry muffins. Total muffins are 50, and $\frac{4}{5}$ of them are blueberry. So number of blueberry muffins is $50\times\frac{4}{5}$.

Step2: Calculate blueberry muffins

$50\times\frac{4}{5}=\frac{50\times4}{5}=40$ (since 50 divided by 5 is 10, 10 times 4 is 40). So there are 40 blueberry muffins.

Step3: Find blueberry muffins without nuts

$\frac{2}{5}$ of the blueberry muffins have nuts, so the fraction without nuts is $1 - \frac{2}{5}=\frac{3}{5}$. So number of blueberry muffins without nuts is $40\times\frac{3}{5}$.

Step4: Calculate the number

$40\times\frac{3}{5}=\frac{40\times3}{5}=24$ (since 40 divided by 5 is 8, 8 times 3 is 24). So the answer is option C.

Answer:

s:

1. D. $\frac{10}{3}$
2. A. $\frac{9}{4}$
3. C. 24