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Chapter 1: Problem 426

Add. $$ \frac{4}{15}+\frac{7}{15} $$

Short Answer

Expert verified
\frac{11}{15}

Step by step solution

01

Identify the Fractions

The given fractions are \(\frac{4}{15}\) and \(\frac{7}{15}\).
02

Check the Denominators

Both fractions have the same denominator, which is 15.
03

Add the Numerators

Since the denominators are the same, add the numerators: \(4 + 7\).
04

Write the Result

Place the sum of the numerators over the common denominator: \(\frac{4+7}{15} = \frac{11}{15}\).

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Key Concepts

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

Common Denominator
To add fractions, they must have the same denominator. The denominator is the bottom number of a fraction. A common denominator means the denominators of the fractions you are adding or subtracting are the same. For example, in the fractions \( \frac{4}{15} \) and \( \frac{7}{15} \), both denominators are 15. When fractions share a common denominator, you can simply add or subtract the numerators. This makes it much easier to combine the fractions.
Numerators
The numerators are the top numbers of fractions. They tell us how many parts of the whole we have. In the fractions \( \frac{4}{15} \) and \( \frac{7}{15} \), the numerators are 4 and 7. When adding fractions with the same denominator, such as \( \frac{4}{15} + \frac{7}{15} \), you keep the denominator the same (15) and simply add the numerators: 4 + 7. This gives you \( \frac{11}{15} \).
Simplifying Fractions
Simplifying fractions means making the fraction as simple as possible. A fraction is simplified when there are no common factors (other than 1) between the numerator and the denominator. For example, \( \frac{11}{15} \) is already simplified since 11 and 15 have no common factors other than 1. If a fraction is not in its simplest form, you would need to divide both the numerator and the denominator by their greatest common factor (GCF). Simplifying fractions helps us to see and understand the size of the fractions more clearly.

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