To subtract the fractions [tex]\(\frac{3}{4}\)[/tex] and [tex]\(\frac{7}{10}\)[/tex], we need to follow these detailed steps:
1. Find a common denominator:
The denominators of the given fractions are 4 and 10. To find a common denominator, we determine the least common multiple (LCM) of these two numbers.
- Multiples of 4: 4, 8, 12, 16, 20, ...
- Multiples of 10: 10, 20, 30, ...
The smallest common multiple is 20. Therefore, the common denominator for both fractions will be 20.
2. Convert each fraction to equivalent fractions with the common denominator:
[tex]\[
\frac{3}{4} = \frac{3 \times 5}{4 \times 5} = \frac{15}{20}
\][/tex]
[tex]\[
\frac{7}{10} = \frac{7 \times 2}{10 \times 2} = \frac{14}{20}
\][/tex]
Now the fractions are [tex]\(\frac{15}{20}\)[/tex] and [tex]\(\frac{14}{20}\)[/tex].
3. Subtract the fractions:
Since the fractions now have a common denominator, we simply subtract the numerators:
[tex]\[
\frac{15}{20} - \frac{14}{20} = \frac{15 - 14}{20} = \frac{1}{20}
\][/tex]
4. Simplify the fraction if possible:
The fraction [tex]\(\frac{1}{20}\)[/tex] is already in its simplest form since the numerator and denominator have no common factors other than 1.
Therefore, the result of [tex]\(\frac{3}{4} - \frac{7}{10}\)[/tex] is:
[tex]\[
\frac{1}{20}
\][/tex]
