/*! 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 6 Use the percent proportion to so... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 6: Problem 6

Use the percent proportion to solve each problem What is \(74 \%\) of \(56 ?\)

Short Answer

Expert verified
74% of 56 is 41.44.

Step by step solution

01

Identify the Proportion Formula

The percent proportion formula is \( \frac{x}{100} = \frac{a}{b} \), where \(x\) is the percentage, \(a\) is the part, and \(b\) is the whole.
02

Set Up the Equation

We need to find what number is \(74\%\) of \(56\). Based on the problem, \(x = 74\) and \(b = 56\). Thus, the equation is \( \frac{74}{100} = \frac{a}{56} \).
03

Cross-Multiply

Cross-multiply to solve for \(a\). This gives us \(74 \times 56 = 100 \times a\).
04

Calculate Cross-Multiplication

Calculate the left side: \(74 \times 56 = 4144\).
05

Solve for a

Now, solve for \(a\) by dividing both sides by \(100\): \(a = \frac{4144}{100} = 41.44\).

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.

Percentage Calculation
Percentage calculation is all about finding a part of a whole. In the context of the problem, we need to find 74% of 56. This means understanding that we are calculating 74 parts out of every 100 parts of 56.
  • To calculate percentages, you multiply the whole number by the percentage expressed as a decimal.
  • A percentage like 74% is converted to a decimal by dividing by 100, which means 74% becomes 0.74.
So, to find 74% of 56, you multiply 56 by 0.74, which ultimately gives you 41.44.
A precise understanding of this process aids in various situations, from determining discounts during shopping to calculating statistics.
Cross-Multiplication
Cross-multiplication is a mathematical technique mostly used to solve equations that involve two fractions set equal to each other. It helps to clear fractions quickly and allows us to solve linear equations more easily.
  • In our example, we use the percent proportion, \[\frac{74}{100} = \frac{a}{56},\] to set up a situation where cross-multiplication can effectively eliminate the fractions.
  • We multiply diagonally: 74 times 56 and 100 times \(a\).
  • This gives the equation: \(74 \times 56 = 100 \times a\).
This step simplifies solving the equation, as it reduces the original fraction equation into a more straightforward multiplication one.
Equation Solving
Equation solving is the final step in problems involving percent proportions and cross-multiplication.
Once the cross-multiplication step has provided us with the equation \(74 \times 56 = 100 \times a\), our task is to isolate \(a\) (the unknown variable we want to find).
Here鈥檚 how we tackle it:
  • Calculate the product of 74 and 56, resulting in 4144.
  • Next, we divide both sides of the equation by 100 to solve for \(a\).
  • Performing \(4144 \div 100\) provides the solution: \(a = 41.44\).
This stepwise isolation and simplification help in pinpointing the exact value of our unknown, ensuring accuracy and clarity in solutions.

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

Find each sum or difference. Write in simplest form. $$ \frac{25}{8}+\frac{7}{8} $$

Solve each equation. Check your solution. $$15=60 h$$

Write each decimal as a percent. $$0.89$$

Solve each equation. Check your solution. $$5=10 a$$

Solve each proportion. $$\frac{75}{8}=\frac{n}{100}$$
See all solutions

Recommended explanations on Math Textbooks

Statistics

Read Explanation

Geometry

Read Explanation

Mechanics Maths

Read Explanation

Decision Maths

Read Explanation

Discrete Mathematics

Read Explanation

Applied Mathematics

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.