To solve the problem [tex]\(\frac{7}{20} + 4 \frac{3}{10}\)[/tex], let's break down the steps involved.
1. Convert the mixed number:
Start by converting the mixed number [tex]\(4 \frac{3}{10}\)[/tex] into an improper fraction. We do this by multiplying the whole number part by the denominator and then adding the numerator.
[tex]\[
4 \frac{3}{10} = 4 + \frac{3}{10} = \frac{4 \times 10}{10} + \frac{3}{10} = \frac{40}{10} + \frac{3}{10} = \frac{43}{10}
\][/tex]
2. Identify fractions:
Now we have the fractions:
[tex]\[
\frac{7}{20} \quad \text{and} \quad \frac{43}{10}
\][/tex]
3. Find a common denominator:
To sum two fractions, we need a common denominator. The denominators here are 20 and 10. The least common multiple (LCM) of 20 and 10 is 20.
4. Convert both fractions to have this common denominator:
[tex]\[
\frac{7}{20} \text{ already has the denominator of 20.}
\][/tex]
Convert [tex]\(\frac{43}{10}\)[/tex] to a fraction with a denominator of 20:
[tex]\[
\frac{43}{10} = \frac{43 \times 2}{10 \times 2} = \frac{86}{20}
\][/tex]
Now we have:
[tex]\[
\frac{7}{20} \text{ and } \frac{86}{20}
\][/tex]
5. Add the fractions:
Since both fractions now have the same denominator, we can add their numerators directly:
[tex]\[
\frac{7}{20} + \frac{86}{20} = \frac{7 + 86}{20} = \frac{93}{20}
\][/tex]
Thus, the solution to [tex]\(\frac{7}{20} + 4 \frac{3}{10}\)[/tex] is:
[tex]\[
\frac{93}{20}
\][/tex]
