Sure, let's add the two fractions [tex]\(\frac{y}{a}\)[/tex] and [tex]\(\frac{7}{4}\)[/tex] step by step.
1. Identify the fractions to be added:
We have two fractions: [tex]\(\frac{y}{a}\)[/tex] and [tex]\(\frac{7}{4}\)[/tex].
2. Find a common denominator:
The denominators of our fractions are [tex]\(a\)[/tex] and [tex]\(4\)[/tex]. To add the fractions, we need to find a common denominator. The simplest way is to multiply the two denominators together:
[tex]\[
\text{Common denominator} = a \cdot 4 = 4a
\][/tex]
3. Rewrite each fraction with the common denominator:
We need to rewrite each fraction so that they both have the common denominator [tex]\(4a\)[/tex].
- For the fraction [tex]\(\frac{y}{a}\)[/tex]:
[tex]\[
\frac{y}{a} = \frac{y \cdot 4}{a \cdot 4} = \frac{4y}{4a}
\][/tex]
- For the fraction [tex]\(\frac{7}{4}\)[/tex]:
[tex]\[
\frac{7}{4} = \frac{7 \cdot a}{4 \cdot a} = \frac{7a}{4a}
\][/tex]
4. Add the rewritten fractions:
Since both fractions now have the common denominator [tex]\(4a\)[/tex], we can add them directly:
[tex]\[
\frac{4y}{4a} + \frac{7a}{4a} = \frac{4y + 7a}{4a}
\][/tex]
5. Simplify the result:
There is no further simplification needed, as the numerator and the denominator do not share any common factors beyond 1. Hence, the result of adding the fractions [tex]\(\frac{y}{a}\)[/tex] and [tex]\(\frac{7}{4}\)[/tex] is:
[tex]\[
\frac{4y + 7a}{4a}
\][/tex]
So, the final answer to [tex]\(\frac{y}{a} + \frac{7}{4}\)[/tex] is:
[tex]\[
\frac{7}{4} + \frac{y}{a}
\][/tex]
