Sure, let's go through this step by step.
1. Subtract the Fractions:
We need to subtract [tex]\(\frac{4}{15}\)[/tex] from [tex]\(\frac{7}{10}\)[/tex].
To subtract [tex]\(\frac{4}{15}\)[/tex] from [tex]\(\frac{7}{10}\)[/tex], we need a common denominator. The least common multiple of 10 and 15 is 30.
Convert [tex]\(\frac{7}{10}\)[/tex] and [tex]\(\frac{4}{15}\)[/tex] to have a common denominator of 30:
[tex]\[
\frac{7}{10} = \frac{7 \times 3}{10 \times 3} = \frac{21}{30}
\][/tex]
[tex]\[
\frac{4}{15} = \frac{4 \times 2}{15 \times 2} = \frac{8}{30}
\][/tex]
Now subtract the two fractions:
[tex]\[
\frac{21}{30} - \frac{8}{30} = \frac{21 - 8}{30} = \frac{13}{30}
\][/tex]
2. Divide by [tex]\(\frac{2}{3}\)[/tex]:
The next step involves dividing the result, [tex]\(\frac{13}{30}\)[/tex], by [tex]\(\frac{2}{3}\)[/tex].
Dividing by a fraction is equivalent to multiplying by its reciprocal. The reciprocal of [tex]\(\frac{2}{3}\)[/tex] is [tex]\(\frac{3}{2}\)[/tex].
So, we calculate:
[tex]\[
\frac{13}{30} \div \frac{2}{3} = \frac{13}{30} \times \frac{3}{2} = \frac{13 \times 3}{30 \times 2} = \frac{39}{60}
\][/tex]
3. Simplify the Result:
Simplify [tex]\(\frac{39}{60}\)[/tex] by finding the greatest common divisor (GCD) of 39 and 60. The GCD is 3.
Divide the numerator and the denominator by their GCD:
[tex]\[
\frac{39 \div 3}{60 \div 3} = \frac{13}{20}
\][/tex]
So, [tex]\(
\left(\frac{7}{10}-\frac{4}{15}\right) \div \frac{2}{3}= \frac{13}{20}
\)[/tex]
The simplified result as a fraction is [tex]\(\frac{13}{20}\)[/tex].
