Question

3 (2\frac{1}{8} - \frac{3}{4})

Explanation:

Step1: Convert mixed number to improper fraction

First, convert \(2\frac{1}{8}\) to an improper fraction. The formula for converting a mixed number \(a\frac{b}{c}\) to an improper fraction is \(\frac{a\times c + b}{c}\). So for \(2\frac{1}{8}\), we have \(a = 2\), \(b = 1\), \(c = 8\). Then \(2\frac{1}{8}=\frac{2\times8 + 1}{8}=\frac{16 + 1}{8}=\frac{17}{8}\).

Step2: Find a common denominator

The second fraction is \(\frac{3}{4}\). To subtract these two fractions, we need a common denominator. The least common denominator of 8 and 4 is 8. So we convert \(\frac{3}{4}\) to a fraction with denominator 8. We multiply the numerator and denominator by 2: \(\frac{3\times2}{4\times2}=\frac{6}{8}\).

Step3: Subtract the fractions

Now we subtract the two fractions: \(\frac{17}{8}-\frac{6}{8}=\frac{17 - 6}{8}=\frac{11}{8}\).

Step4: Convert back to mixed number (optional)

We can convert \(\frac{11}{8}\) back to a mixed number. Dividing 11 by 8, we get 1 with a remainder of 3, so \(\frac{11}{8}=1\frac{3}{8}\)? Wait, no, wait. Wait, \(2\frac{1}{8}\) is 2 + \(\frac{1}{8}\), and we are subtracting \(\frac{3}{4}\). Alternatively, we can do it as a mixed number subtraction. Let's re - do step 1 - 3 with mixed numbers.

\(2\frac{1}{8}-\frac{3}{4}=2+\frac{1}{8}-\frac{3}{4}\). Convert \(\frac{3}{4}\) to eighths: \(\frac{3}{4}=\frac{6}{8}\). Then \(2+\frac{1}{8}-\frac{6}{8}=2+(\frac{1}{8}-\frac{6}{8})\). But \(\frac{1}{8}-\frac{6}{8}\) is negative, so we borrow 1 from the whole number part. \(2 = 1+1=1+\frac{8}{8}\). So \(1+\frac{8}{8}+\frac{1}{8}-\frac{6}{8}=1+(\frac{8 + 1-6}{8})=1+\frac{3}{8}=1\frac{3}{8}\)? Wait, no, wait, earlier when we did improper fractions, \(\frac{17}{8}-\frac{6}{8}=\frac{11}{8}=1\frac{3}{8}\)? Wait, no, \(17-6 = 11\), \(\frac{11}{8}=1\frac{3}{8}\)? Wait, no, 8*1 = 8, 11 - 8=3, so yes, \(1\frac{3}{8}\)? Wait, but \(2\frac{1}{8}\) is 2.125 and \(\frac{3}{4}=0.75\), 2.125 - 0.75 = 1.375, and \(1\frac{3}{8}=1.375\). Wait, but earlier when we converted \(2\frac{1}{8}\) to improper fraction we got \(\frac{17}{8}\), \(\frac{17}{8}-\frac{6}{8}=\frac{11}{8}=1\frac{3}{8}\). But wait, is there a mistake? Wait, \(2\frac{1}{8}\) is 2 + \(\frac{1}{8}\), and we are subtracting \(\frac{3}{4}\). Let's check the first method again.

Wait, \(2\frac{1}{8}=\frac{17}{8}\), \(\frac{3}{4}=\frac{6}{8}\), \(\frac{17}{8}-\frac{6}{8}=\frac{11}{8}=1\frac{3}{8}\). Yes, that's correct.

Answer:

\(1\frac{3}{8}\) (or \(\frac{11}{8}\))