Sure, let's solve these math problems step by step.
### Problem 1: Addition of Fractions
We need to add the fractions [tex]\(\frac{4}{12}\)[/tex] and [tex]\(\frac{3}{12}\)[/tex].
1. Since both fractions have the same denominator, we can directly add the numerators:
[tex]\[
\frac{4}{12} + \frac{3}{12} = \frac{4 + 3}{12} = \frac{7}{12}
\][/tex]
So, [tex]\(\frac{4}{12} + \frac{3}{12} = \frac{7}{12}\)[/tex].
### Problem 1a: Subtraction of Fractions
Next, we need to subtract [tex]\(\frac{2}{10}\)[/tex] from [tex]\(\frac{7}{10}\)[/tex].
1. Since both fractions have the same denominator, we can directly subtract the numerators:
[tex]\[
\frac{7}{10} - \frac{2}{10} = \frac{7 - 2}{10} = \frac{5}{10}
\][/tex]
2. Next, we simplify the fraction [tex]\(\frac{5}{10}\)[/tex]:
[tex]\[
\frac{5}{10} = \frac{5 \div 5}{10 \div 5} = \frac{1}{2}
\][/tex]
So, [tex]\(\frac{7}{10} - \frac{2}{10} = \frac{1}{2}\)[/tex].
### Problem 2: Fraction Multiplication and Addition
Finally, we solve [tex]\(3 \cdot \frac{8}{15} + \frac{7}{15}\)[/tex].
1. First, multiply the whole number 3 by the fraction [tex]\(\frac{8}{15}\)[/tex]:
[tex]\[
3 \cdot \frac{8}{15} = \frac{3 \cdot 8}{15} = \frac{24}{15}
\][/tex]
2. Next, add this result to [tex]\(\frac{7}{15}\)[/tex]:
[tex]\[
\frac{24}{15} + \frac{7}{15} = \frac{24 + 7}{15} = \frac{31}{15}
\][/tex]
So, [tex]\(3 \cdot \frac{8}{15} + \frac{7}{15} = \frac{31}{15}\)[/tex].
### Summary
Here are the final results for each problem:
1. [tex]\(\frac{4}{12} + \frac{3}{12} = \frac{7}{12}\)[/tex]
2. [tex]\(\frac{7}{10} - \frac{2}{10} = \frac{1}{2}\)[/tex]
3. [tex]\(3 \cdot \frac{8}{15} + \frac{7}{15} = \frac{31}{15}\)[/tex]
