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Chapter 1: Problem 427

Add. $$ \frac{x}{4}+\frac{3}{4} $$

Short Answer

Expert verified
\(\frac{x + 3}{4}\)

Step by step solution

01

Identify the common denominator

Both fractions, \(\frac{x}{4}\) and \(\frac{3}{4}\), have the same denominator, which is 4.
02

Add the numerators

Since the denominators are the same, add the numerators directly. This gives \(\frac{x + 3}{4}\).
03

Simplify the fraction (if possible)

In this case, \(\frac{x + 3}{4}\) is already in its simplest form. No further simplification is needed.

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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, having a **common denominator** is crucial. The **denominator** is the number at the bottom of the fraction, which tells you how many equal parts the whole is divided into. If the fractions you're adding have the same denominator, it simplifies the process significantly. You only need to add the numerators directly. In the original exercise, both fractions, \( \frac{x}{4} \) and \(\frac{3}{4}\), have the common denominator of 4. This means we can proceed to add the numerators without any extra steps. If the fractions had different denominators, we would need to find the least common denominator first.
Numerators
The **numerator** is the number at the top of the fraction, indicating how many parts of the whole are being considered. In the process of adding fractions, the numerators are what you add together. For the given exercise, the numerators are x and 3 from \( \frac{x}{4}\) and \( \frac{3}{4}\) respectively. Since the denominators are the same, we simply add the numerators to get \( x + 3\). This is how we get \( \frac{x+3}{4}\). Always remember: when the denominators are the same, only the numerators are added together. This keeps the fractions' value properly represented.
Simplifying Fractions
After adding fractions, look at the resulting fraction to see if it needs simplification. **Simplifying fractions** involves reducing the fraction to its simplest form. This means dividing both the numerator and the denominator by their greatest common divisor. However, in our example with \( \frac{x+3}{4}\), there are no common factors between \( x+3 \) and 4 other than 1. Hence, the fraction is already in its simplest form. Simplifying makes fractions easier to understand and work with in further calculations.

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Most popular questions from this chapter

Insurance copayment Carrie had to have 5 fillings done. Each filling cost $$\$ 80\(. Her dental insurance required her to pay \)20 \%\( of the cost as a copay. Calculate Carrie's copay: (a) First, by multiplying 0.20 by 80 to find her copay for each filling and then multiplying your answer by 5 to find her total copay for 5 fillings. (b) Next, by multiplying \)[5(0.20)](80)\( (c) Which of the properties of real numbers says that your answers to parts (a), where you multiplied \)5[(0.20)(80)]\( and \)(b),\( where you multiplied \)[5(0.20)](80),$$ should be equal?

Convert the units. Crista will serve 20 cups of juice at her son's party. Convert the volume to gallons.

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