/*! 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 3 Multiply. Write each answer in l... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 6: Problem 3

Multiply. Write each answer in lowest terms. \(\frac{4}{9} \cdot \frac{15}{16}\)

Short Answer

Expert verified
\frac{5}{12}

Step by step solution

01

- Multiply the Numerators

First, multiply the numerators of both fractions. For \(\frac{4}{9} \cdot \frac{15}{16}\), the numerators are 4 and 15. \(\text{Numerator: } 4 \cdot 15 = 60\).
02

- Multiply the Denominators

Next, multiply the denominators of both fractions. The denominators are 9 and 16. \(\text{Denominator: } 9 \cdot 16 = 144\).
03

- Write the Fraction

Combine the results from Steps 1 and 2 to write the fraction: \(\frac{60}{144}\).
04

- Simplify the Fraction

Simplify \(\frac{60}{144}\) to its lowest terms. Find the greatest common divisor (GCD) of 60 and 144, which is 12. Divide the numerator and denominator by 12. \(\frac{60 \div 12}{144 \div 12} = \frac{5}{12}\).

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 multiply fractions, the numerators are the numbers on the top of each fraction. They determine how many parts of the whole we are considering. In the exercise \(\frac{4}{9} \cdot \frac{15}{16}\), the numerators are 4 and 15.
The first step is to multiply these numerators together:
  • 4 \cdot 15 = 60
The numerator in the final fraction is 60. It's important to remember to handle numerators separately from denominators. This makes it easier to understand and perform fraction multiplication.
If you mix up numerators and denominators, or forget which is which, it can lead to errors. So let's keep them straight to make everything easier!
Denominators
Denominators are found at the bottom part of each fraction. They tell us how many equal parts the whole is divided into. For the fractions in our exercise, the denominators are 9 and 16.
Just like with the numerators, we need to multiply the denominators together:
  • 9 \cdot 16 = 144
This gives us the denominator for our resulting fraction, which is 144. Keeping our numerators and denominators organized lets us multiply fractions correctly.
After multiplying both the numerators and the denominators, we can write the new fraction.
This new fraction combines the results: \(\frac{60}{144}\).
Simplifying Fractions
Simplifying fractions means reducing them to their lowest terms. This makes them easier to understand and work with. In the example, we ended up with the fraction \(\frac{60}{144}\) after multiplying.
To simplify a fraction, find the greatest common divisor (GCD) of the numerator and the denominator. In this case, the GCD of 60 and 144 is 12. Divide both the numerator and the denominator by the GCD:
  • 60 \div 12 = 5
  • 144 \div 12 = 12
So, \(\frac{60}{144} \rightarrow \frac{5}{12}\). Always check if a fraction can be simplified further.
Continuing until you can't simplify anymore ensures the fraction is in its simplest form. Simplifying fractions helps keep numbers manageable and easy to use.

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

Solve each formula or equation for the specified variable. $$ \frac{t}{x-1}-\frac{2}{x+1}=\frac{1}{x^{2}-1} \text { for } t $$

A Concours d'Elegance is a competition in which a maximum of 100 points is awarded to a car based on its general attractiveness. The rational expression $$ \frac{9010}{49(101-x)}-\frac{10}{49} $$ approximates the cost, in thousands of dollars, of restoring a car so that it will win x points. 101\. Simplify the given expression by performing the indicated subtraction.

The fractions here are continued fractions. Simplify by starting at "the bottom" and working upward. $$ \frac{2 q}{7}-\frac{q}{6+\frac{8}{4+4}} $$

Simplify each complex fraction. Use either method. $$ \frac{a-\frac{5}{a}}{a+\frac{1}{a}} $$

Let \(P\), \(Q\), and \(R\) be rational expressions defined as follows. $$P=\frac{6}{x+3}, \quad Q=\frac{5}{x+1}, \quad R=\frac{4 x}{x^{2}+4 x+3}$$ Why is \((P \cdot Q) \div R\) not defined if \(x=0 ?\)
See all solutions

Recommended explanations on Math Textbooks

Pure Maths

Read Explanation

Probability and Statistics

Read Explanation

Mechanics Maths

Read Explanation

Applied Mathematics

Read Explanation

Statistics

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.