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------------------------------------------------ Add [tex]4 \frac{3}{100}[/tex] and [tex]5 \frac{13}{15}[/tex].

Certainly! To add the mixed numbers [tex]$4 \frac{3}{100}$[/tex] and [tex]$5 \frac{13}{15}$[/tex], follow these steps:

1. Convert the mixed numbers to improper fractions:

For [tex]$4 \frac{3}{100}$[/tex]:
[tex]\[
4 \frac{3}{100} = 4 + \frac{3}{100}
\][/tex]
Converting to an improper fraction:
[tex]\[
4 \frac{3}{100} = \frac{4 \cdot 100 + 3}{100} = \frac{400 + 3}{100} = \frac{403}{100}
\][/tex]

For [tex]$5 \frac{13}{15}$[/tex]:
[tex]\[
5 \frac{13}{15} = 5 + \frac{13}{15}
\][/tex]
Converting to an improper fraction:
[tex]\[
5 \frac{13}{15} = \frac{5 \cdot 15 + 13}{15} = \frac{75 + 13}{15} = \frac{88}{15}
\][/tex]

2. Find a common denominator to add the fractions:

The denominators are 100 and 15. The least common multiple (LCM) of 100 and 15 is 300. Convert both fractions to have this common denominator.

Convert [tex]$\frac{403}{100}$[/tex] to a denominator of 300:
[tex]\[
\frac{403}{100} = \frac{403 \times 3}{100 \times 3} = \frac{1209}{300}
\][/tex]

Convert [tex]$\frac{88}{15}$[/tex] to a denominator of 300:
[tex]\[
\frac{88}{15} = \frac{88 \times 20}{15 \times 20} = \frac{1760}{300}
\][/tex]

3. Add the fractions:

Now add the fractions:
[tex]\[
\frac{1209}{300} + \frac{1760}{300} = \frac{1209 + 1760}{300} = \frac{2969}{300}
\][/tex]

4. Simplify the fraction (if possible) and convert back to a mixed number:

Divide [tex]$2969$[/tex] by [tex]$300$[/tex]:
[tex]\[
2969 \div 300 \approx 9.896666666666668
\][/tex]

So, the sum of [tex]$4 \frac{3}{100}$[/tex] and [tex]$5 \frac{13}{15}$[/tex] is approximately [tex]$9.897$[/tex].

Thus, [tex]$4 \frac{3}{100} + 5 \frac{13}{15} = 9.896666666666668$[/tex].