/*! 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 119 Multiply: \(\frac{7}{8} \cdot \f... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 5: Problem 119

Multiply: \(\frac{7}{8} \cdot \frac{3}{5}\)

Short Answer

Expert verified
The product is \( \frac{21}{40} \).

Step by step solution

01

Multiply the Numerators

To multiply two fractions, first multiply the numerators (top numbers). For this exercise, multiply the numerators 7 and 3:\( 7 imes 3 = 21 \)
02

Multiply the Denominators

Next, multiply the denominators (bottom numbers). For this exercise, multiply the denominators 8 and 5:\( 8 imes 5 = 40 \)
03

Write the Fraction

Combine the results from Steps 1 and 2 to form a new fraction using the products from each step.So, the fraction becomes \( \frac{21}{40} \).
04

Simplify the Fraction (if needed)

Check if the resulting fraction can be simplified. In this case, the numerator 21 and the denominator 40 have no common factors other than 1, so \( \frac{21}{40} \) 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
When you look at a fraction, the number on the top is called the numerator. It tells you how many parts of a whole you have. For example, in the fraction \( \frac{7}{8} \), the numerator is 7, meaning you have 7 parts out of 8. It's important to multiply the numerators directly when you're multiplying fractions. So when multiplying two fractions, such as \( \frac{7}{8} \cdot \frac{3}{5} \), you take the numerators 7 and 3 and multiply them to get 21. Notice, only focus on the top numbers in this step. They represent the parts you have from the whole before combining them with the denominators.
Denominators
The number on the bottom side of a fraction is called the denominator. This part tells you the total number of equal parts the whole is divided into. In the example \( \frac{7}{8} \), the denominator is 8, which shows that there are 8 equal parts in a whole.
When multiplying fractions, you also multiply the denominators. With \( \frac{7}{8} \cdot \frac{3}{5} \), the denominators are 8 and 5. By multiplying them, you get 40. This number forms the new denominator of the product fraction.
  • The denominator helps understand the size of each part.
  • Always work with both the numerator and denominator when forming a new fraction.
Simplifying Fractions
Simplifying a fraction means making it as simple as possible, often by dividing both the numerator and the denominator by their greatest common factor. This doesn't change the value of the fraction, but it makes calculations easier and the fraction clearer. For instance, if you had \( \frac{28}{40} \), you would notice both numbers can be divided by 4 to get \( \frac{7}{10} \). However, not all fractions need simplifying.
In the exercise, the product \( \frac{21}{40} \) is already in its simplest form because 21 and 40 only share the number 1 as a common factor, which means it cannot be simplified further.
  • Simplifying reduces fractions to their lowest terms.
  • Always check if a fraction can be simplified after multiplying.
  • A simple fraction is usually easier to use in further calculations.

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

Perform the indicated operations to simplify each expression, if possible. a. \(\left(6 x^{2} z^{5}\right)-\left(-3 x z^{3}\right)\) b. \(\left(6 x^{2} z^{5}\right)\left(-3 x z^{3}\right)\)

Perform the operations. $$ (4 a-3)^{2}+(a+6)^{2} $$

Write an equation of the line with slope \(-\frac{11}{6}\) that passes through \((2,-6) .\) Write the answer in slope-intercept form.

Perform each division. $$ \frac{9 a^{4} b^{3}-16 a^{3} b^{4}}{12 a^{2} b} $$

Perform the indicated operations. a. \((x y)^{2}\) b. \((x+y)^{2}\)
See all solutions

Recommended explanations on Math Textbooks

Calculus

Read Explanation

Mechanics Maths

Read Explanation

Probability and Statistics

Read Explanation

Pure Maths

Read Explanation

Discrete Mathematics

Read Explanation

Decision 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.