Problem 87 Simplify to lowest terms by firs... [FREE SOLUTION]

91影视

Prealgebra

Julie Miller, Molly O鈥橬eill, Nancy Hyde

$Math Studyset 91影视 Explanations$ Math

1 Edition

Chapter 4: Problem 87

Simplify to lowest terms by first reducing the powers of 10. $$\frac{5100}{30,000}$$

Short Answer

Expert verified

$ \frac{17}{100} $

Step by step solution

- Identify the common factors

First, identify the common factors of the numerator (5100) and the denominator (30,000). Specifically, look for common factors of 10 to reduce the size of the numbers.

- Reduce the powers of 10

Both 5100 and 30,000 are divisible by 100. Simplify by dividing both the numerator and the denominator by 100: \[\frac{5100 \div 100}{30000 \div 100} = \frac{51}{300}\]

- Simplify the fraction

Next, simplify the fraction $ \frac{51}{300} $. Find the greatest common factor (GCF) of 51 and 300. The GCF is 3. Therefore, divide both the numerator and the denominator by 3: \[\frac{51 \div 3}{300 \div 3} = \frac{17}{100}\]

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.

common factors

Common factors are numbers that can evenly divide both the numerator and the denominator of a fraction. When simplifying fractions, identifying common factors is the first crucial step. Start with the smallest prime numbers such as 2, 3, 5, 7, etc., and see which ones can divide both numbers without leaving a remainder. For example, in the fraction given, $\frac{5100}{30000}$, both 5100 and 30000 have common factors of 2, 3, and 5. However, spotting the common power of 10 (100) makes simplification much easier.

greatest common factor

The greatest common factor (GCF) is the largest number that can divide both the numerator and the denominator without leaving a remainder. Finding the GCF is essential for fully simplifying fractions. In our example, after reducing the powers of 10, we have the fraction $\frac{51}{300}$. The GCF of 51 and 300 is 3. Dividing both the numerator and the denominator by the GCF, $\frac{51 \div 3}{300 \div 3} = \frac{17}{100}$, ensures the fraction is in its simplest form.

powers of 10

Simplifying large numbers can be made easier by reducing powers of 10. Numbers like 100, 1000, and 10000 are powers of 10, making them convenient for simplification. For the fraction $\frac{5100}{30000}$, we see that both numbers are divisible by 100, a power of 10. By dividing both 5100 and 30000 by 100, we simplify to $\frac{51}{300}$. This reduces the size of the numbers, making it easier to find common factors and further simplify.

numerator and denominator

The numerator is the top number in a fraction, representing how many parts of the whole are being considered. The denominator is the bottom number, indicating the total number of equal parts in the whole. For instance, in $\frac{5100}{30000}$, 5100 is the numerator, and 30000 is the denominator. When simplifying fractions, it's important to understand the roles of these components. By reducing both the numerator and the denominator by their common factors, we arrive at a simplified form of the fraction. In our example, reducing by powers of 10 first, then dividing by the GCF gives us $\frac{17}{100}$. Remember, always simplify both the numerator and the denominator equally.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

91影视

Simplify to lowest terms by first reducing the powers of 10. $$\frac{5100}{30,000}$$

Short Answer

Step by step solution

- Identify the common factors

- Reduce the powers of 10

- Simplify the fraction

Key Concepts

common factors

greatest common factor

powers of 10

numerator and denominator

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Discrete Mathematics

Logic and Functions

Decision Maths

Pure Maths

Calculus

Study anywhere. Anytime. Across all devices.