/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 2 Add and simplify. $$ \frac{2... [FREE SOLUTION] | 91影视

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Chapter 3: Problem 2

Add and simplify. $$ \frac{2}{5}+\frac{3}{5} $$

Short Answer

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1

Step by step solution

01

Identify the Fractions

The given fractions are \(\frac{2}{5}\) and \(\frac{3}{5}\).
02

Check the Denominators

Notice that both fractions have the same denominator, which is 5.
03

Add the Numerators

Since the denominators are the same, add the numerators: \(2 + 3 = 5\).
04

Combine the Fractions

Place the sum of the numerators over the common denominator: \(\frac{5}{5}\).
05

Simplify the Fraction

Simplify \(\frac{5}{5}\) to get 1.

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Key Concepts

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

Common Denominators
When adding fractions, the first thing you need to check is if the denominators (the bottom numbers) are the same. Denominators represent the total number of equal parts the whole is divided into. For example, in the fractions \(\frac{2}{5} \) and \( \frac{3}{5} \), the denominator is 5 in both fractions. This makes it easy to combine them as you don't need to adjust anything. If the denominators were different, you would need to find a common denominator. This common denominator is usually the Least Common Multiple (LCM) of the original denominators. This step ensures you're working with parts of the same size.
Numerator Addition
Once you confirm the denominators are the same, you can add the numerators (the top numbers) directly. The numerator represents the number of the divided parts you have. So, in the example \(\frac{2}{5}+\frac{3}{5} \), you add the numerators 2 and 3 together: \(\frac{2+3}{5} = \frac{5}{5} \). Adding fractions with the same denominator is simply about combining how many parts you have.
Fraction Simplification
After adding the numerators and placing the result over the common denominator, you might end up with a fraction that can be simplified. Simplifying a fraction means reducing it to its simplest form by dividing the numerator and the denominator by their greatest common divisor. In the example \( \frac{5}{5} \), both the numerator and the denominator are 5. Since \( \frac{5}{5} \) equals 1, the fraction simplifies to 1. Always check if the numerator and the denominator can be divided evenly by the same number.

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Most popular questions from this chapter

Estimate each of the following as \(0, \frac{1}{2},\) or 1 . $$ \frac{19}{20} $$

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