Question

a. $3\frac{1}{10} + 1\frac{3}{4} \approx \underline{\quad}$

Explanation:

Step1: Convert mixed numbers to improper fractions

First, convert \(3\frac{1}{10}\) 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 \(3\frac{1}{10}\), we have \(a = 3\), \(b = 1\), \(c = 10\). Then \(3\frac{1}{10}=\frac{3\times10 + 1}{10}=\frac{31}{10}\).

Next, convert \(1\frac{3}{4}\) to an improper fraction. Here, \(a = 1\), \(b = 3\), \(c = 4\). So \(1\frac{3}{4}=\frac{1\times4+3}{4}=\frac{7}{4}\).

Step2: Find a common denominator and add the fractions

The denominators are 10 and 4. The least common multiple of 10 and 4 is 20.

Convert \(\frac{31}{10}\) to a fraction with denominator 20: \(\frac{31}{10}=\frac{31\times2}{10\times2}=\frac{62}{20}\).

Convert \(\frac{7}{4}\) to a fraction with denominator 20: \(\frac{7}{4}=\frac{7\times5}{4\times5}=\frac{35}{20}\).

Now add the two fractions: \(\frac{62}{20}+\frac{35}{20}=\frac{62 + 35}{20}=\frac{97}{20}\).

Step3: Convert the improper fraction back to a mixed number (or decimal)

Convert \(\frac{97}{20}\) to a mixed number. Divide 97 by 20: \(97\div20 = 4\) with a remainder of 17. So \(\frac{97}{20}=4\frac{17}{20}\). If we want a decimal, \(\frac{97}{20}=4.85\). Since the problem has a "≈" sign, maybe we can also estimate. \(3\frac{1}{10}\approx3.1\) and \(1\frac{3}{4}=1.75\), then \(3.1 + 1.75 = 4.85\), which is equal to \(4\frac{17}{20}\).

Answer:

\(4\frac{17}{20}\) (or \(4.85\))