Answer :

To find the difference between [tex]\(\frac{7}{10}\)[/tex] and [tex]\(\frac{14}{15}\)[/tex], we follow these steps:

1. Find a Common Denominator: The denominators we have are 10 and 15. To subtract the fractions, we need a common denominator. The least common multiple (LCM) of 10 and 15 is 30.

2. Convert Each Fraction:
- For [tex]\(\frac{7}{10}\)[/tex], we convert it to a fraction with a denominator of 30 by multiplying both the numerator and denominator by 3:
[tex]\[
\frac{7}{10} = \frac{7 \times 3}{10 \times 3} = \frac{21}{30}
\][/tex]

- For [tex]\(\frac{14}{15}\)[/tex], we convert it to a fraction with a denominator of 30 by multiplying both the numerator and denominator by 2:
[tex]\[
\frac{14}{15} = \frac{14 \times 2}{15 \times 2} = \frac{28}{30}
\][/tex]

3. Subtract the Fractions: Now that the fractions have a common denominator, subtract the numerators:
[tex]\[
\frac{21}{30} - \frac{28}{30} = \frac{21 - 28}{30} = \frac{-7}{30}
\][/tex]

4. Convert to Decimal Form: To express [tex]\(\frac{-7}{30}\)[/tex] as a decimal, perform the division:
[tex]\[
\frac{-7}{30} \approx -0.2333
\][/tex]

So, the difference between [tex]\(\frac{7}{10}\)[/tex] and [tex]\(\frac{14}{15}\)[/tex] is approximately [tex]\(-0.2333\)[/tex].

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Rewritten by : Barada