/*! 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 115 $$\text { Find } \frac{2}{5} \te... [FREE SOLUTION] | 91影视

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Chapter 4: Problem 115

$$\text { Find } \frac{2}{5} \text { of } \frac{1}{5}$$

Short Answer

Expert verified
\( \frac{2}{25} \)

Step by step solution

01

Understand the Problem

The problem asks to find \( \frac{2}{5} \) of \( \frac{1}{5} \). The word 'of' in this context means multiplication.
02

Set Up the Multiplication

Write the problem as a multiplication of two fractions: \( \frac{2}{5} * \frac{1}{5} \).
03

Multiply the Numerators

Multiply the numerators together: \( 2 * 1 = 2 \).
04

Multiply the Denominators

Multiply the denominators together: \( 5 * 5 = 25 \).
05

Write the Result

Combine the results from Steps 3 and 4 to write the final fraction: \( \frac{2}{25} \).

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Key Concepts

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

fractions
Fractions represent parts of a whole. They consist of two main components - the numerator and the denominator. Understanding how to manipulate and work with fractions is key to solving many math problems. For example, in the exercise given, we are dealing with the fractions \( \frac{2}{5} \) and \( \frac{1}{5} \). By multiplying these fractions, we are essentially finding a portion of a portion, which is crucial in various areas of mathematics like ratios, proportions, and algebra.
numerator
The numerator is the top number in a fraction and represents how many parts of the whole we are considering. For instance, in the fraction \( \frac{2}{5} \), the numerator is 2. This means we are considering 2 parts out of 5 equal parts. In the multiplication of fractions, you multiply the numerators to find the new numerator of the resulting fraction. So when we multiply \( 2 \) by \( 1 \), we get \( 2 \). This is evident in Step 3 of the exercise.
denominator
The denominator is the bottom number in a fraction and indicates the total number of equal parts that make up the whole. In the fraction \( \frac{1}{5} \), the denominator is 5. This means the whole is divided into 5 equal parts. When multiplying fractions, you also need to multiply the denominators. In our example, \( 5 \) multiplied by \( 5 \) is \( 25 \). This helps us determine that our whole for the final fraction is divided into 25 parts.
multiplication
Multiplication of fractions involves multiplying the numerators together and the denominators together. The exercise given asks us to find \( \frac{2}{5} \) of \( \frac{1}{5} \). The word 'of' implies multiplication. To solve this, we multiply the numerators (2 and 1) to get 2, and the denominators (5 and 5) to get 25. The result is \( \frac{2}{25} \), meaning 2 parts out of 25. Understanding this method is essential for working with fractions efficiently.

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Most popular questions from this chapter

Convert the improper fraction to a mixed number. $$-\frac{27}{10}$$

Label the fraction as proper or improper. $$\frac{2}{3}$$

Simplify the expression. $$-\frac{3 m^{2} n}{9 m^{2} n^{4}}$$

Simplify. $$-\left(-\frac{7}{3}\right)$$

Jonathan and Jared both sold candy bars for a fundraiser. Jonathan sold 25 of his 35 candy bars, and Jared sold 24 of his 28 candy bars. a. What fractional part of his total number of candy bars did each person sell? b. Which person sold the greater fractional part?
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