/*! 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 412 Evaluate \(\frac{3}{16}\left(\fr... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 7: Problem 412

Evaluate \(\frac{3}{16}\left(\frac{16}{3} n\right)\) when \(n=42\)

Short Answer

Expert verified
The value is 42.

Step by step solution

01

Substitute the Value of n

First, substitute the given value of \(n = 42\) into the expression \( \frac{3}{16}\bigg(\frac{16}{3} n \bigg) \). This gives us: \[ \frac{3}{16}\bigg(\frac{16}{3} \times 42 \bigg) \]
02

Simplify Inside the Parentheses

Simplify the expression inside the parentheses first: \[ \frac{16}{3} \times 42 = \frac{16 \times 42}{3} = \frac{672}{3} = 224 \]. So the expression now is: \[ \frac{3}{16} \times 224 \]
03

Multiply the Fractions

Multiply the two fractions: \[ \frac{3}{16} \times 224 \]. This can be written as: \[ \frac{3 \times 224}{16} \]. Simplify the fraction by dividing: \[ \frac{3 \times 224}{16} = \frac{672}{16} = 42 \]

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.

Substitution
Substitution in algebra involves replacing a variable with its given value. This is the first step in evaluating an algebraic expression. In the exercise, the value provided is 42 for the variable \( n \). So, our first task is to plug 42 in place of \( n \) inside the given expression.

Let's start by writing the expression: \( \frac{3}{16}\bigg(\frac{16}{3} n \bigg) \). By substituting \( n = 42 \), we get:

- \( \frac{3}{16} \bigg(\frac{16}{3} \times 42 \bigg) \).

Now the expression is ready for the next steps. Always remember to carefully replace the variable to avoid confusion.
Simplifying Fractions
To simplify fractions means to reduce them to their lowest terms or to handle operations inside them. After substitution, our expression looks like this: \( \frac{3}{16} \bigg(\frac{16}{3} \times 42 \bigg) \).

First, handle the multiplication inside the parentheses. Here, we multiply \( \frac{16}{3} \) by 42. This works out as:
- \( \frac{16}{3} \times 42 \)
- Which is \( \frac{16 \times 42}{3} \).

Now compute the numerator: \( 16 \times 42 = 672 \) and form the fraction: \( \frac{672}{3} \).

Next, simplify the fraction by dividing 672 by 3, giving us 224. So, \( \frac{16}{3} \times 42 = 224 \), and our expression is now simplified to \( \frac{3}{16} \times 224 \).
Multiplication of Fractions
Multiplying fractions involves multiplying the numerators together and the denominators together. Here, our task is to carry out: \( \frac{3}{16} \times 224 \).

First, rewrite 224 as a fraction: \( \frac{224}{1} \). Now we have:
- \( \frac{3}{16} \times \frac{224}{1} \).

Multiply the numerators: \( 3 \times 224 = 672 \). Similarly, multiply the denominators: 16 \times 1 = 16. This forms the new fraction: \( \frac{672}{16} \).

To get the final result, divide: \( 672 \text{ by } 16 = 42 \). Hence, \( \frac{3}{16} \times 224 = 42 \).

Remember, for multiplying fractions:
  • Always multiply straight across (numerator with numerator, and denominator with denominator).
  • Then simplify the resulting fraction if necessary.

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

In the following exercises, find the multiplicative inverse. $$ -\frac{4}{9} $$

In the following exercises, simplity using the distributive property. $$ -3(6 m-1) $$

In the following exercises, simplity using the distributive property. $$ \frac{1}{3}(15 n-6) $$

In the following exercises, simplify the given expression. $$ \frac{1}{4}(8 a+12) $$

In the following exercises, simplify using the commutative and associative properties. $$ \frac{14}{11} \cdot \frac{35}{9} \cdot \frac{14}{11} $$
See all solutions

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Read Explanation

Decision Maths

Read Explanation

Geometry

Read Explanation

Statistics

Read Explanation

Mechanics Maths

Read Explanation

Logic and Functions

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.