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Chapter 4: Problem 625

In the following exercises, add. $$\frac{x}{10}+\frac{7}{10}$$

Short Answer

Expert verified
\( \frac{x + 7}{10} \)

Step by step solution

01

Identify the common denominator

Both fractions have the same denominator which is 10.
02

Add the numerators

Since the denominators are the same, add the numerators: \( x + 7 \).
03

Write the new fraction

Place the sum of the numerators over the common denominator: \( \frac{x + 7}{10} \).

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Key Concepts

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

common denominator
When adding fractions, it's important to first identify a common denominator. The denominator is the bottom part of the fraction that tells us how many equal parts the whole is divided into.

If the fractions already have the same denominator, like in the exercise \(\frac{x}{10} \) + \(\frac{7}{10} \), you can move to the next step right away. If the denominators are different, you need to find a common denominator first. This is usually done by finding the least common multiple (LCM) of the denominators. For example, if you are adding \(\frac{2}{3} \) and \(\frac{5}{4} \), you need to adjust them to a common denominator before proceeding.
add numerators
Once you have a common denominator, the next step is to add the numerators, which are the top parts of the fractions. When denominators are the same, you simply add the numerators together.

In our example \(\frac{x}{10} \) + \(\frac{7}{10} \), since the denominator (10) is common, we just need to add the numerators: \( x + 7 \). This step involves straightforward arithmetic, making it quite simple.
simplify fractions
After adding the numerators, you write the sum over the common denominator to form a new fraction. Sometimes this fraction can be simplified further.

Simplifying a fraction means making the numerator and denominator as small as possible while keeping the same value. This is done by dividing both by their greatest common divisor (GCD). For example, if your fraction is \(\frac{8}{12}\), you can simplify it to \( \frac{2}{3} \) by dividing the numerator and denominator by 4, the GCD of 8 and 12.

However, in the case of our exercise \(\frac{x+7}{10} \), there is no need for further simplification since \(x+7 \) and 10 don鈥檛 share any common factors.

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Most popular questions from this chapter

In the following exercises, perform the indicated operations and simplify. $$\frac{11}{12}-\frac{2}{3}$$

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