/*! 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 51 A jar of 20 coins contains 4 pen... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 51

A jar of 20 coins contains 4 pennies. What percent of the coins are pennies?

Short Answer

Expert verified
20%

Step by step solution

01

- Identify Total Number of Coins

Determine the total number of coins in the jar. The problem states that there are 20 coins in total.
02

- Identify Number of Pennies

Determine the number of pennies in the jar. The problem states that there are 4 pennies.
03

- Set Up the Fraction

Set up the fraction of pennies over the total number of coins: \ \[ \frac{4}{20} \]
04

- Simplify the Fraction

Simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor. \ \[ \frac{4 \div 4}{20 \div 4} = \frac{1}{5} \]
05

- Convert Fraction to Percent

Multiply the simplified fraction by 100 to find the percentage. \ \[ \frac{1}{5} \times 100 = 20\% \]

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.

fractions
Fractions are a way to represent parts of a whole. They consist of two numbers: a numerator and a denominator.
The numerator is the top number and indicates how many parts we have.
The denominator is the bottom number and shows how many equal parts the whole is divided into.
In the exercise, the fraction is set up as \(\frac{4}{20}\), where 4 (pennies) is the numerator and 20 (total coins) is the denominator.
Fractions are essential because they allow us to describe proportions and make comparisons easily.
simplifying fractions
Simplifying fractions means reducing them to their simplest form. This involves finding the greatest common divisor (GCD) of both the numerator and the denominator and then dividing both by this number.
In our example, the fraction is \(\frac{4}{20}\). First, find the GCD of 4 and 20, which is 4.
Next, divide both the numerator and the denominator by the GCD:
\[ \frac{4}{20} = \frac{4 \div 4}{20 \div 4} = \frac{1}{5} \]
This means that \(\frac{4}{20}\) simplifies to \(\frac{1}{5}\), making it easier to work with.
percentages
Percentages are a way to express a number as a fraction of 100. They help us understand ratios and proportions.
To convert a simplified fraction to a percentage, you multiply it by 100. In our case, the simplified fraction is \(\frac{1}{5}\).
To find the percentage, we perform this calculation:
\[ \frac{1}{5} \times 100 = 20\% \]
So, 20% of the coins in the jar are pennies. Percentages are very useful for quickly comparing different quantities and understanding their relationships.

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 equation or inequality. $$ |x-4|+5 \geq 4 $$

Bonnie earned scores of 90 and 82 on her first two tests in English literature. What score must she make on her third test to keep an average of 84 or greater?

The Jurassic Park Collection in Blu-Ray was on sale for $29.96 . The list price (full price) of this three-disc set was 44.98. To the nearest tenth, what was the percent discount?

Solve each investment problem. Mario earned \(\$ 12,000\) last year giving tennis lessons. He invested part of the money at \(3 \%\) simple interest and the rest at \(4 \% .\) In one year, he earned a total of \(\$ 440\) in interest. How much did he invest at each rate?

The base of the Great Pyramid of Cheops is a square whose perimeter is \(920 \mathrm{~m}\). What is the length of each side of this square?
See all solutions

Recommended explanations on Math Textbooks

Geometry

Read Explanation

Calculus

Read Explanation

Mechanics Maths

Read Explanation

Discrete Mathematics

Read Explanation

Decision Maths

Read Explanation

Statistics

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.