/*! 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 18 Translate to a proportion. Do no... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 6: Problem 18

Translate to a proportion. Do not solve. $$ 103 \text { is what percent of } 100 ? $$

Short Answer

Expert verified
\( \frac{103}{100} = \frac{x}{100} \)

Step by step solution

01

Identify the Key Components

Determine the parts of the sentence: 103 is the part, 100 is the whole, and we need to find the percent (unknown).
02

Set Up the Proportion

A proportion can be set up using the formula: the part / the whole = percent / 100.So, substitute the known values: \( \frac{103}{100} = \frac{x}{100} \).

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.

percent
The concept of percent is crucial in mathematics, especially when working with proportions.
A percent represents a part out of 100 and is symbolized by the % sign. For example, 50% means 50 parts out of 100, which can also be written as 50/100 or 0.50.
Understanding percent helps us compare different quantities on a common scale.

In the original exercise, the task is to find out '103 is what percent of 100'. This means figuring out how many parts out of 100 correspond to 103. This is a direct application of the percent concept.
Remember, finding a percent involves dividing the part by the whole and then multiplying the result by 100.
This leads to the next important concept: the part-whole relationship.
part-whole relationship
The part-whole relationship is a fundamental idea in mathematics.
It helps us understand how a particular quantity (the part) relates to a total quantity (the whole).
This relationship is essential for working with percentages, fractions, and proportions.

In the original exercise, 103 is the part, and 100 is the whole.
To find out what percent 103 is of 100, we are essentially comparing the part to the whole.
This comparison helps us understand how the quantities relate to each other.
The part-whole relationship can be expressed in a proportion, which is the next concept we'll discuss.
proportion equation
A proportion equation is a mathematical statement that shows two ratios are equal.
Ratios compare two quantities, and when they are set equal to each other, they form a proportion.

In the original exercise, the proportion equation is set up as follows:
Part/Whole = Percent/100.
Substituting the known values gives us: \ \( \frac{103}{100} = \frac{x}{100} \).
Here, 103 is the part, 100 is the whole, and x represents the unknown percent.

This proportion equation method allows us to find the unknown value when the other three values of the ratios are known.
By cross-multiplying and solving for x, we can determine the percent that 103 is of 100.
This is a very useful technique in many areas of mathematics and real-world applications.

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

The Arctic sea surface freezes in the winter, but the part of it that melts in the summer is increasing. In 1979,2,780,000 square miles of the Arctic sea were still ice-covered in September. Only 1,820,000 square miles were still ice-covered in September \(2016 .\) What was the percent decrease?

The effective yield is the yearly rate of simple interest that corresponds to a rate for which interest is compounded two or more times a year. For example, if \(P\) is invested at \(12 \%,\) compounded quarterly, we multiply \(P\) by \((1+0.12 / 4)^{4},\) or \(1.03^{4}\). Since \(1.03^{4} \approx 1.126\), the \(12 \%\) compounded quarterly corresponds to an effective yield of approximately \(12.6 \% .\) In Exercises 47 and \(48,\) find the effective yield for the indicated account. The account pays \(9 \%\) compounded monthly.

Find the LCM of 32 and 50 .

Convert to standard notation. $$ 4.03 \text { trillion } $$

Consumers are paying record amounts of fees for overdrawing their bank accounts. In \(2016,\) the largest 628 banks collected $$\$ 11,410,000,000$$ in overdraft fees, which is $$\$ 250,000,000$$ more than they collected in 2015\. What was the percent increase?
See all solutions

Recommended explanations on Math Textbooks

Mechanics Maths

Read Explanation

Discrete Mathematics

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.