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Chapter 4: Problem 690

In the following exercises, simplify. $$ \frac{2}{d}+\frac{9}{d} $$

Short Answer

Expert verified
\[ \frac{11}{d} \]

Step by step solution

01

- Identify the Common Denominator

Notice that both terms in the expression \( \frac{2}{d}+\frac{9}{d} \) have the same denominator, which is \( d \).
02

- Combine the Numerators

Since the denominators are the same, add the numerators of the fractions directly. This gives us \( 2 + 9 \).
03

- Simplify the Numerator

Simplify the expression obtained by combining the numerators: \( 2 + 9 = 11 \).
04

- Write the Final Expression

Now, put the simplified numerator over the common denominator \( d \): \[ \frac{11}{d} \]

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Key Concepts

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

common denominator
When simplifying fractions like those in \( \frac{2}{d}+\frac{9}{d} \), identifying a common denominator is key. A common denominator is a shared multiple of the denominators in the fractions involved. This means both fractions already have the same bottom number. Here, both fractions have 'd' as their denominator.
Since the denominators are the same, you don't need to do any work to make them match. The fractions are ready to be simplified.
combining numerators
Once you've identified a common denominator, you can move on to combining the numerators. Numerators are the top numbers in fractions. In our example, the numerators are 2 and 9.
Because the denominators are the same, you add the numerators directly: \( 2 + 9 = 11 \). This step is straightforward since it's just basic addition. Remember that combining numerators is only possible when the denominators are identical.
simplifying expressions
The final step focuses on simplifying the expression. Here, you take the combined numerator and place it over the common denominator.
For the example \( \frac{2}{d} + \frac{9}{d} = \frac{11}{d} \). This fraction cannot be simplified further because 11 and d have no common factors.
Simplifying expressions helps make your work clear and concise. Always check if the fraction can be simplified further by looking for common factors in the numerator and denominator.

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Most popular questions from this chapter

In the following exercises, simplify. $$ -\frac{3}{4} \div \frac{x}{3} $$

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