/*! 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 Multiply, and write the answer i... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 4: Problem 99

Multiply, and write the answer in simplified form. \(\frac{2}{5} \cdot \frac{1}{3}\)

Short Answer

Expert verified
The simplified form is \(\frac{2}{15}\).

Step by step solution

01

Multiply the Numerators

Multiply the numerators of the two fractions together. In this case, multiply 2 by 1. \[2 \times 1 = 2\]
02

Multiply the Denominators

Multiply the denominators of the two fractions together. In this case, multiply 5 by 3. \[5 \times 3 = 15\]
03

Write the Result as a Fraction

Combine the results from steps 1 and 2 to form a new fraction. \[\frac{2}{15}\]
04

Simplify the Fraction (If Needed)

Check if the fraction \(\frac{2}{15}\) can be simplified further. In this case, it 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.

Numerators
A numerator is the top number of a fraction. It tells you how many parts of a whole you are dealing with. For example, in the fraction \(\frac{2}{5}\), the numerator is 2. This means you have 2 parts out of a total of 5 parts.

When multiplying fractions, you multiply the numerators together. For instance, in our exercise, we multiply the numerators of \(\frac{2}{5}\) and \(\frac{1}{3}\). So we perform the multiplication: \[2 \times 1 = 2\]
This produces the numerator of the resulting fraction.
Denominators
A denominator is the bottom number of a fraction. It shows the total number of equal parts in the whole. For example, in the fraction \(\frac{2}{5}\), the denominator is 5, meaning the whole is split into 5 equal parts.

In fraction multiplication, you also need to multiply the denominators together. For the given exercise \(\frac{2}{5} \times \frac{1}{3}\), you multiply the denominators: \[5 \times 3 = 15\]
This gives the denominator of the resulting fraction.
Simplifying Fractions
Simplifying fractions is the process of reducing the fraction to its simplest form where the numerator and the denominator are as small as possible while still maintaining the same value. To simplify, find the greatest common divisor (GCD) of the numerator and the denominator and divide both by that number.

In our exercise, we found \(\frac{2}{15}\). Here, the numerator is 2 and the denominator is 15. Since the GCD of 2 and 15 is 1 (the only common factor between them), \(\frac{2}{15}\) is already in its simplest form.

Always check your fractions to see if they can be simplified to make your calculations easier and your answers clearer.

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

In the following exercises, perform the indicated operation. $$ 6 \frac{2}{5}+7 \frac{3}{5} $$

In the following exercises, evaluate the given expression. Express your answers in simplified form, using improper fractions if necessary. 4\(p^{2} q\) when \(p=-\frac{1}{2}\) and \(q=\frac{5}{9}\)

In the following exercises, simplify. $$ -\frac{3}{4} \div \frac{x}{3} $$

In the following exercises, perform the indicated operation. $$ 3 \frac{5}{8}+3 \frac{7}{8} $$

In the following exercises, add. $$\frac{2}{5}+\frac{1}{5}$$
See all solutions

Recommended explanations on Math Textbooks

Pure Maths

Read Explanation

Decision Maths

Read Explanation

Mechanics Maths

Read Explanation

Geometry

Read Explanation

Discrete Mathematics

Read Explanation

Calculus

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.