Question

What is the result of this calculation?

1/2x4/3+5/6/7/8




A.



B.



C.



D.

Answer 1

To solve the expression \( \frac{1}{2} \times \frac{4}{3} + \frac{5}{6} \div \frac{7}{8} \), we will follow the order of operations.

1. Calculate \( \frac{1}{2} \times \frac{4}{3} \):

\[
\frac{1}{2} \times \frac{4}{3} = \frac{1 \times 4}{2 \times 3} = \frac{4}{6} = \frac{2}{3} \quad (\text{after simplifying})
\]

2. Calculate \( \frac{5}{6} \div \frac{7}{8} \):

Dividing by a fraction is the same as multiplying by its reciprocal:

\[
\frac{5}{6} \div \frac{7}{8} = \frac{5}{6} \times \frac{8}{7} = \frac{5 \times 8}{6 \times 7} = \frac{40}{42} = \frac{20}{21} \quad (\text{after simplifying})
\]

3. Now we add the two results together:

\[
\frac{2}{3} + \frac{20}{21}
\]

To add these fractions, we need a common denominator. The least common denominator of \( 3 \) and \( 21 \) is \( 21 \).

Convert \( \frac{2}{3} \) to have a denominator of \( 21 \):

\[
\frac{2}{3} = \frac{2 \times 7}{3 \times 7} = \frac{14}{21}
\]

Now we add:

\[
\frac{14}{21} + \frac{20}{21} = \frac{14 + 20}{21} = \frac{34}{21}
\]

Thus, the final result is:

\[
\frac{34}{21}
\]

If we want to present this as a mixed number, it would be:

\[
1\frac{13}{21}
\]

So the result of the calculation \( \frac{1}{2} \times \frac{4}{3} + \frac{5}{6} \div \frac{7}{8} \) is \( \frac{34}{21} \) or \( 1\frac{13}{21} \).