/*! 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 104 Perform the operations and, if p... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 104

Perform the operations and, if possible, simplify. $$ \frac{19}{35}-\frac{12}{35} $$

Short Answer

Expert verified
The result is \( \frac{1}{5} \).

Step by step solution

01

Ensuring Like Denominators

Both fractions have the same denominator of 35, so the subtraction can be performed directly.
02

Subtract the Numerators

Subtract the numerators while keeping the denominator the same: \( 19 - 12 = 7 \). Thus, the operation becomes \( \frac{19}{35} - \frac{12}{35} = \frac{7}{35} \).
03

Simplify the Fraction

Determine if \( \frac{7}{35} \) can be simplified. The greatest common divisor of 7 and 35 is 7. Divide both the numerator and the denominator by 7: \( \frac{7}{35} = \frac{1}{5} \).

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.

Simplifying Fractions
Understanding how to simplify fractions is essential for dealing with fractions effectively. Simplifying a fraction means reducing it to its simplest form, where the numerator and the denominator have no common divisors other than 1. This helps make calculations easier and results clearer.

When simplifying a fraction, follow these steps:
  • Identify the greatest common divisor (GCD) of the numerator and the denominator. This is the largest number that can divide both numbers without leaving a remainder.
  • Divide both the numerator and the denominator by their GCD.
For instance, in the exercise, we have the fraction \( \frac{7}{35} \). The GCD of 7 and 35 is 7, so dividing both by 7 simplifies the fraction to \( \frac{1}{5} \).

Practicing this skill will improve your ability to handle complex fraction operations with ease.
Subtraction of Fractions
Subtracting fractions can seem tricky at first, but it's all about ensuring the denominators are the same. Fractions with like denominators can be subtracted directly by working with the numerators.

Here's the step-by-step process:
  • Verify that the fractions have the same denominator. If they don't, find a common denominator.
  • Once the denominators match, subtract the numerators while keeping the denominator unchanged.
  • Consider simplifying the resulting fraction, if possible.
In our case, with \( \frac{19}{35} - \frac{12}{35} \), both fractions already have the same denominator, so we can proceed to subtract the numerators: \( 19 - 12 = 7 \). This gives us \( \frac{7}{35} \).

Understanding these steps prepares you for dealing with more complicated addition and subtraction problems in the future.
Greatest Common Divisor
The greatest common divisor (GCD) is an essential concept when simplifying fractions. It is the largest number that divides two or more integers without leaving a remainder.

Here's how you can find the GCD:
  • List the factors of each number.
  • Identify the largest factor that appears in both lists.
In the exercise, the numbers are 7 and 35:
  • Factors of 7: 1, 7
  • Factors of 35: 1, 5, 7, 35
The largest common factor is 7, which makes it the GCD. Using this, we reduce \( \frac{7}{35} \) to \( \frac{1}{5} \). Knowing how to find the GCD allows you to simplify fractions quickly, making your math work cleaner and more efficient.

Keep practicing finding the GCD and soon it will become second nature!

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. $$ 2 z+5(z-3)-10 $$

Evaluate each expression for \(x=-3\) and \(y=-5\) $$ \frac{2 y+1}{x}-x $$

Find the LCD for \(\frac{5}{12}\) and \(\frac{1}{15}\)

In this section, we substituted a number for a variable. List some other uses of the word substitute that you encounter in everyday life.

Write \(-3-(-5)\) as addition of the opposite.
See all solutions

Recommended explanations on Math Textbooks

Decision Maths

Read Explanation

Probability and Statistics

Read Explanation

Pure Maths

Read Explanation

Discrete Mathematics

Read Explanation

Applied 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.