Certainly! Let's break down the addition of two fractions, [tex]\( \frac{1}{10} \)[/tex] and [tex]\( \frac{3}{5} \)[/tex], step by step:
1. Identify the fractions: The fractions given are [tex]\( \frac{1}{10} \)[/tex] and [tex]\( \frac{3}{5} \)[/tex].
2. Rewrite the fractions with a common denominator:
- The common denominator for 10 and 5 is 10, since 10 is the least common multiple of 10 and 5.
3. Express [tex]\( \frac{3}{5} \)[/tex] with the common denominator:
- Convert [tex]\( \frac{3}{5} \)[/tex] to a fraction with a denominator of 10.
- Multiply both the numerator and the denominator of [tex]\( \frac{3}{5} \)[/tex] by 2 to get [tex]\( \frac{6}{10} \)[/tex].
4. Add the fractions:
- Now that the fractions have the same denominator, you can add them directly.
- [tex]\( \frac{1}{10} + \frac{6}{10} = \frac{1 + 6}{10} = \frac{7}{10} \)[/tex].
5. Write the result as a decimal:
- [tex]\( \frac{7}{10} \)[/tex] can be written as 0.7.
So, [tex]\( \frac{1}{10} + \frac{3}{5} = 0.7 \)[/tex]. The fractions [tex]\( \frac{1}{10} \)[/tex] and [tex]\( \frac{3}{5} \)[/tex] add up to 0.7.
