Question

a teacher has \\(\frac{7}{8}\\) of a roll of tape. the teacher cuts the tape into pieces that are each the length of \\(\frac{3}{10}\\) of the roll. how many pieces of tape does the teacher cut?\
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a. \\(\frac{21}{80}\\)\
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b. \\(2\frac{11}{12}\\)\
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c. \\(\frac{12}{35}\\)\
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d. \\(3\frac{17}{21}\\)

Explanation:

Step1: Understand the problem

We need to find how many pieces of length $\frac{3}{10}$ of a roll are in $\frac{7}{8}$ of a roll. This is a division problem, so we divide $\frac{7}{8}$ by $\frac{3}{10}$.

Step2: Divide the fractions

To divide fractions, we multiply the first fraction by the reciprocal of the second fraction. The reciprocal of $\frac{3}{10}$ is $\frac{10}{3}$. So we have:
$$\frac{7}{8} \div \frac{3}{10} = \frac{7}{8} \times \frac{10}{3}$$

Step3: Multiply the numerators and denominators

Multiply the numerators: $7 \times 10 = 70$. Multiply the denominators: $8 \times 3 = 24$. So we get $\frac{70}{24}$.

Step4: Simplify the fraction

Simplify $\frac{70}{24}$ by dividing numerator and denominator by their greatest common divisor, which is 2. $\frac{70 \div 2}{24 \div 2} = \frac{35}{12}$.

Step5: Convert to mixed number

Convert $\frac{35}{12}$ to a mixed number. $35 \div 12 = 2$ with a remainder of $11$, so $\frac{35}{12} = 2\frac{11}{12}$.

Answer:

B. $2\frac{11}{12}$