/*! 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 487 Simplify. $$ -\frac{5}{12} \... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 487

Simplify. $$ -\frac{5}{12} \div\left(-\frac{5}{9}\right) $$

Short Answer

Expert verified
The simplified form is \( \frac{3}{4} \).

Step by step solution

01

- Understand the Division of Fractions

When you divide by a fraction, it is the same as multiplying by the reciprocal of that fraction. The reciprocal of a fraction is obtained by swapping the numerator and the denominator.
02

- Find the Reciprocal

The given problem is \( -\frac{5}{12} \div\left(-\frac{5}{9}\right) \). First, find the reciprocal of \( -\frac{5}{9} \). The reciprocal is \( -\frac{9}{5} \).
03

- Rewrite the Division as Multiplication

Rewrite the problem using multiplication: \( -\frac{5}{12} \times -\frac{9}{5} \).
04

- Multiply the Numerators and Denominators

Multiply the numerators: \( (-5) \times (-9) = 45 \). Then, multiply the denominators: \( 12 \times 5 = 60 \). So, the expression becomes \( \frac{45}{60} \).
05

- Simplify the Fraction

Simplify \( \frac{45}{60} \) by finding the greatest common divisor (GCD) of 45 and 60, which is 15. Divide both numerator and denominator by 15: \( \frac{45 \div 15}{60 \div 15} = \frac{3}{4} \).

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.

Division of Fractions
Understanding how to divide fractions is essential. When you divide by a fraction, you actually multiply by its reciprocal. The reciprocal of a fraction is simply flipping its numerator and denominator. This rule makes the math simpler and is easy to remember.
For example, in the problem \(-\frac{5}{12} \div \left(-\frac{5}{9}\right)\), we begin by finding the reciprocal of \(-\frac{5}{9}\).
Reciprocal of a Fraction
The reciprocal of a fraction is obtained by swapping the numerator (top number) and the denominator (bottom number).
For example, the reciprocal of \(\frac{a}{b}\) is \(\frac{b}{a}\).
In our example, the reciprocal of \(-\frac{5}{9}\) is \(-\frac{9}{5}\).
By knowing this, we can transform division into multiplication, making our calculations simpler.
Multiplying Fractions
Once you have the reciprocal, you replace the division with multiplication. That leads to a new multiplication problem that is simpler to solve. For instance, our division problem \(-\frac{5}{12} \div \left(-\frac{5}{9}\right)\) becomes \(-\frac{5}{12} \times -\frac{9}{5}\).
Next, just multiply the numerators and denominators:
  • Numerators: \( -5 \times -9 = 45 \)
  • Denominators: \( 12 \times 5 = 60 \)

    • This turns our problem into \( \frac{45}{60} \).
Greatest Common Divisor (GCD)
The Greatest Common Divisor (GCD) is the largest number that divides both the numerator and the denominator without leaving a remainder. Finding the GCD helps to simplify fractions.
In our case, the GCD of 45 and 60 is 15. With that, we simplify \[ \frac{45}{60} \] by dividing both 45 and 60 by their GCD:
  • \( 45 \div 15 = 3 \)
  • \( 60 \div 15 = 4 \)

Thus, \[ \frac{45}{60} \] simplifies to \[ \frac{3}{4} \], which is our final answer.

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 using the distributive property. $$ 6(7 y+8)-(30 y-15) $$

Solve. Harry mailed 5 packages that weighed 420 grams each. What was the total weight of the packages in kilograms?

Simplify using the distributive property. $$ -3(x-6) $$

Convert the units. JJ's cat, Posy, weighs 14 pounds. Convert her weight to ounces.

Simplify using the distributive property. $$ -(5 p-4) $$
See all solutions

Recommended explanations on Math Textbooks

Discrete Mathematics

Read Explanation

Logic and Functions

Read Explanation

Pure Maths

Read Explanation

Decision Maths

Read Explanation

Probability and Statistics

Read Explanation

Geometry

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.