Question

before you can add or subtract, the fractions should have the same bottom number - a common denominator.
multiply the bottom numbers and multiply the top numbers.
then simplify the fraction by cancelling by 3
turn the second fraction upside down and multiply. 21 and 24 have a common factor of 3, so divide top and bottom by 3.

workings
\\( \frac { 4 } { 3 } + \frac { 2 } { 7 } \\)
\\( = \frac { 2 ( 3 ) } { 7 ( 3 ) } + \frac { 4 ( 7 ) } { 3 ( 7 ) } \\)
\\( = \frac { 3 4 } { 2 1 } \\)
\\( \frac { 3 } { 6 } \times \frac { 5 } { 4 } \\)
\\( = \frac { 3 \times 5 } { 6 \times 4 } \\)
\\( = \frac { 1 5 } { 2 4 } \\)
\\( = \frac { 5 } { 8 } \\)
\\( \frac { 7 } { 3 } \div \frac { 2 } { 1 2 } \\)
\\( = \frac { 7 } { 3 } \times \frac { 1 2 } { 2 } \\)
\\( = \frac { 7 \times 3 } { 1 2 \times 2 } \\)
\\( = \frac { 2 1 } { 2 4 } \\)
\\( \frac { 3 } { 8 } = \frac { 1 4 } { 2 4 } - \frac { 9 } { 2 4 } \\)
\\( = \frac { 5 } { 2 4 } \\)

answer

Explanation:

Step1: Find common denominator

For \(\frac{2}{7}+\frac{4}{3}\), the common denominator of \(7\) and \(3\) is \(21\).
\(\frac{2\times3}{7\times3}+\frac{4\times7}{3\times7}\)

Step2: Add fractions

\(\frac{6}{21}+\frac{28}{21}=\frac{6 + 28}{21}\)

Step3: Calculate numerator

\(6+28 = 34\)
So \(\frac{34}{21}\)

For \(\frac{4}{6}\times\frac{3}{5}\), simplify \(\frac{4}{6}\) to \(\frac{2}{3}\) first.
\(\frac{2}{3}\times\frac{3}{5}=\frac{2\times3}{3\times5}\)
Cancel out the common factor \(3\), get \(\frac{2}{5}\)

For \(\frac{7}{12}\div\frac{2}{3}\), turn the second fraction upside - down and multiply.
\(\frac{7}{12}\times\frac{3}{2}=\frac{7\times3}{12\times2}=\frac{21}{24}\), simplify by dividing numerator and denominator by \(3\), get \(\frac{7}{8}\)

For \(\frac{7}{12}-\frac{3}{8}\), the common denominator of \(12\) and \(8\) is \(24\).
\(\frac{7\times2}{12\times2}-\frac{3\times3}{8\times3}=\frac{14}{24}-\frac{9}{24}=\frac{14 - 9}{24}=\frac{5}{24}\)

Answer:

\(\frac{2}{7}+\frac{4}{3}=\frac{34}{21}\), \(\frac{4}{6}\times\frac{3}{5}=\frac{2}{5}\), \(\frac{7}{12}\div\frac{2}{3}=\frac{7}{8}\), \(\frac{7}{12}-\frac{3}{8}=\frac{5}{24}\)