Question

①$(\frac{7}{8}-\frac{1}{4})+\frac{1}{2}$ ②$\frac{19}{20}-(\frac{1}{2}-\frac{3}{10})$ ③$\frac{1}{10}+\frac{1}{100}+\frac{1}{1000}$

Explanation:

Step1: Find common - denominator for first two terms in (M)

The common denominator of 8 and 4 is 8.

Step2: Subtract fractions in (M)

\(\frac{7}{8}-\frac{2}{8}=\frac{5}{8}\)

Step3: Add remaining fraction in (M)

\(\frac{5}{8}+\frac{4}{8}=\frac{9}{8}\)

Step4: Find common - denominator for terms in parentheses in (N)

The common denominator of 2 and 10 is 10.

Step5: Subtract fractions in parentheses in (N)

\(\frac{5}{10}-\frac{3}{10}=\frac{2}{10}\)

Step6: Rewrite fraction and subtract in (N)

Rewrite \(\frac{1}{5}\) as \(\frac{4}{20}\), then \(\frac{19}{20}-\frac{4}{20}=\frac{15}{20}\)

Step7: Find common - denominator for all terms in (O)

The common denominator of 10, 100, 1000 is 1000.

Step8: Rewrite fractions in (O)

Rewrite \(\frac{1}{10}\) as \(\frac{100}{1000}\), \(\frac{1}{100}\) as \(\frac{10}{1000}\)

Step9: Add fractions in (O)

\(\frac{100}{1000}+\frac{10}{1000}+\frac{1}{1000}=\frac{111}{1000}\)

Answer:

1. For \((\frac{7}{8}-\frac{1}{4})+\frac{1}{2}\):

• First, find a common - denominator for \(\frac{7}{8}\) and \(\frac{1}{4}\). The common denominator of 8 and 4 is 8.
• Rewrite \(\frac{1}{4}\) as \(\frac{2}{8}\). Then \(\frac{7}{8}-\frac{1}{4}=\frac{7}{8}-\frac{2}{8}=\frac{7 - 2}{8}=\frac{5}{8}\).
• Now, add \(\frac{1}{2}\) (rewritten as \(\frac{4}{8}\)) to \(\frac{5}{8}\), so \(\frac{5}{8}+\frac{4}{8}=\frac{5 + 4}{8}=\frac{9}{8}=1\frac{1}{8}\).

1. For \(\frac{19}{20}-(\frac{1}{2}-\frac{3}{10})\):

• First, find a common - denominator for \(\frac{1}{2}\) and \(\frac{3}{10}\). The common denominator of 2 and 10 is 10.
• Rewrite \(\frac{1}{2}\) as \(\frac{5}{10}\). Then \(\frac{1}{2}-\frac{3}{10}=\frac{5}{10}-\frac{3}{10}=\frac{5 - 3}{10}=\frac{2}{10}=\frac{1}{5}\).
• Rewrite \(\frac{1}{5}\) as \(\frac{4}{20}\). Then \(\frac{19}{20}-\frac{4}{20}=\frac{19 - 4}{20}=\frac{15}{20}=\frac{3}{4}\).

1. For \(\frac{1}{10}+\frac{1}{100}+\frac{1}{1000}\):

• First, find a common - denominator. The common denominator of 10, 100, and 1000 is 1000.
• Rewrite \(\frac{1}{10}\) as \(\frac{100}{1000}\), \(\frac{1}{100}\) as \(\frac{10}{1000}\).
• Then \(\frac{100}{1000}+\frac{10}{1000}+\frac{1}{1000}=\frac{100 + 10+1}{1000}=\frac{111}{1000}\).

So the answers are \(1\frac{1}{8}\), \(\frac{3}{4}\), \(\frac{111}{1000}\) respectively.