Problem 59 For exercises $23-74$, evaluat... [FREE SOLUTION]

91影视

Elementary Algebra

Laura Bracken, Ed Miller

$Math Studyset 91影视 Explanations$ Math

1 Edition

Chapter 0: Problem 59

For exercises $23-74$, evaluate. $$ \frac{1}{9}+\frac{4}{9} $$

Short Answer

Expert verified

The result is $\frac{5}{9}$.

Step by step solution

- Identify the fractions

The fractions given are $\frac{1}{9}$ and $\frac{4}{9}$. Both fractions have the same denominator.

- Add the numerators

Since the denominators are the same, you can add the numerators directly: $1 + 4$.

- Write the result

Place the sum of the numerators over the common denominator: $\frac{1 + 4}{9} = \frac{5}{9}$.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

common denominator

Adding fractions can seem tricky at first, but it's easy once you get the hang of it. One of the key steps is finding a common denominator. The denominator is the bottom number of the fraction. It's important because fractions must have the same denominator before you can add them together. For instance, in the exercise, the fractions $\frac{1}{9}$ and $\frac{4}{9}$ already share a common denominator of 9. This makes adding them straightforward. If the denominators are different, you would need to find the least common multiple (LCM) of the denominators first to make them the same.

numerator addition

Once the fractions have a common denominator, the next step is to add the numerators. The numerator is the top number of the fraction. In our exercise, the fractions $\frac{1}{9}$ and $\frac{4}{9} $ already have the same denominator. So, you just add their numerators directly. Here, 1 + 4 equals 5. Therefore, the new fraction becomes $\frac{5}{9}$. Notice that the denominator remains the same while only the numerators are added.

fraction simplification

After adding the fractions, it's important to check if the result can be simplified. Simplification means reducing the fraction to its simplest form. This involves dividing the numerator and the denominator by their greatest common divisor (GCD). In our example, the fraction $\frac{5}{9}$ is already in its simplest form because 5 and 9 have no common divisors other than 1. If they did share a common divisor, you would divide both the numerator and the denominator by that number to simplify the fraction. Simplifying fractions makes them easier to understand and work with in future calculations.

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91影视

For exercises \(23-74\), evaluate. $$ \frac{1}{9}+\frac{4}{9} $$

Short Answer

Step by step solution

- Identify the fractions

- Add the numerators

- Write the result

Key Concepts

common denominator

numerator addition

fraction simplification

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