Answer :

Sure! Let's estimate the difference of the fractions [tex]\(\frac{18}{20}\)[/tex] and [tex]\(\frac{5}{8}\)[/tex] step by step.

1. Simplify the Fractions:
- First, simplify [tex]\(\frac{18}{20}\)[/tex]. By dividing both the numerator and the denominator by the greatest common factor, which is 2, we get [tex]\(\frac{9}{10}\)[/tex].
- The fraction [tex]\(\frac{5}{8}\)[/tex] is already in its simplest form.

2. Find a Common Denominator:
- To subtract the fractions, we need to have a common denominator. The denominators we have are 10 and 8.
- The least common multiple (LCM) of 10 and 8 is 40.

3. Convert Fractions to Have the Common Denominator:
- Convert [tex]\(\frac{9}{10}\)[/tex] to a fraction with a denominator of 40:
[tex]\[
\frac{9}{10} = \frac{9 \times 4}{10 \times 4} = \frac{36}{40}
\][/tex]
- Convert [tex]\(\frac{5}{8}\)[/tex] to a fraction with a denominator of 40:
[tex]\[
\frac{5}{8} = \frac{5 \times 5}{8 \times 5} = \frac{25}{40}
\][/tex]

4. Subtract the Fractions:
- Now that both fractions have a denominator of 40, subtract the numerators:
[tex]\[
\frac{36}{40} - \frac{25}{40} = \frac{36 - 25}{40} = \frac{11}{40}
\][/tex]

5. Estimate the Difference:
- Divide the numerator by the denominator to find the estimated difference:
[tex]\[
\frac{11}{40} = 0.275
\][/tex]

Thus, the estimated difference of [tex]\(\frac{18}{20} - \frac{5}{8}\)[/tex] is approximately 0.275.

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