/*! 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 99 Perform the operations and, if p... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 99

Perform the operations and, if possible, simplify. $$ \frac{1}{5} \cdot \frac{3}{5} $$

Short Answer

Expert verified
\(\frac{3}{25}\) is the simplified form.

Step by step solution

01

Multiply Numerators

To multiply fractions, start by multiplying the numerators. Here, multiply the numerators of \(\frac{1}{5}\) and \(\frac{3}{5}\): \[ 1 \times 3 = 3 \]
02

Multiply Denominators

Next, multiply the denominators. For the fractions \(\frac{1}{5}\) and \(\frac{3}{5}\): \[ 5 \times 5 = 25 \]
03

Write the Initial Product

Combine the product of the numerators and the product of the denominators to form a new fraction: \[ \frac{3}{25} \]
04

Simplify the Fraction

Check if the fraction \(\frac{3}{25}\) can be simplified further. Since 3 and 25 have no common factors other than 1, \(\frac{3}{25}\) is already in its simplest form.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

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

Fraction Simplification
Simplifying fractions means making a fraction as simple as possible. This means representing it with the smallest possible whole numbers. To check if a fraction can be simplified, you need to find the greatest common factor (GCF) of the numerator and the denominator. For instance:
  • If you have a fraction like \( \frac{6}{9} \), check the GCF which is 3, so you divide both numerator and denominator by 3, simplifying it to \( \frac{2}{3} \).
  • In the case of \( \frac{3}{25} \), the GCF is 1. So, it is already in its simplest form.
Understanding simplification helps tidy up mathematical expressions and is essential for efficient calculations in more complex problems.
Numerator and Denominator
Every fraction is made up of two parts: the numerator and the denominator. These parts are separated by a horizontal bar, often called the fraction bar.
  • The numerator is the top number and it tells how many parts we have. In \( \frac{1}{5} \), 1 is the numerator, indicating 1 part.
  • The denominator is the bottom number and it signifies the total number of equal parts something is divided into. For \( \frac{1}{5} \), 5 is the denominator, meaning the whole is divided into 5 parts.
Understanding these parts is crucial for performing operations like addition, subtraction, multiplication, and division of fractions.
Basic Fraction Operations
Operations on fractions include addition, subtraction, multiplication, and division. Each operation follows specific rules:For multiplication:
  • Multiply the numerators together.
  • Multiply the denominators together.
For example, to multiply \( \frac{1}{5} \) and \( \frac{3}{5} \), multiply the numerators (1 and 3) to get 3. Then multiply the denominators (5 and 5) to get 25, resulting in \( \frac{3}{25} \).Addition and subtraction require the denominators to be the same, while division of fractions involves multiplying by the reciprocal of the second fraction. Understanding these rules makes working with fractions more manageable and is a key foundation for further mathematical learning.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Simplify each expression, if possible. $$ -16 y+16 y $$

Simplify by combining like terms. $$ 9 z-7-z-19 z $$

Simplify each expression, if possible. $$ -(c+7)+2(c-3) $$

$$ \text { Add: }-3+(-4)+(-5)+4+3 $$

Simplify each expression, if possible. $$ -v-3 v+6 v+2 v $$
See all solutions

Recommended explanations on Math Textbooks

Statistics

Read Explanation

Calculus

Read Explanation

Pure Maths

Read Explanation

Probability and Statistics

Read Explanation

Discrete Mathematics

Read Explanation

Mechanics Maths

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.