/*! 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 91 Find the missing value. $$ 4... [FREE SOLUTION] | 91影视

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Chapter 4: Problem 91

Find the missing value. $$ 439.57 \times 0.01 \div 1000 \times \square=4.3957 $$

Short Answer

Expert verified
The missing value is 1000.

Step by step solution

01

- Rewrite the Equation

Rewrite the given equation including the missing value as a variable. Let the missing value be represented by \( x \). The equation becomes: \[ 439.57 \times 0.01 \times \frac{1}{1000} \times x = 4.3957 \]
02

- Simplify the Multiplications

Simplify the multiplication of the constants on the left-hand side of the equation.First, compute \( 439.57 \times 0.01 \): \[ 439.57 \times 0.01 = 4.3957 \]Next, compute \( 4.3957 \times \frac{1}{1000} \): \[ 4.3957 \times \frac{1}{1000} = 0.0043957 \]So the equation simplifies to:\[ 0.0043957 \times x = 4.3957 \]
03

- Solve for \( x \)

To find the value of \( x \), divide both sides of the equation by 0.0043957:\[ x = \frac{4.3957}{0.0043957} \]Perform the division:\[ x = 1000 \]

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Multiplication
Multiplication is one of the basic arithmetic operations. The process involves finding the product when you combine groups of equal size. For instance, when you multiply 439.57 by 0.01, you essentially find what 439.57 is when multiplied by 1/100.
To perform this, we move the decimal point two places to the left, giving us 4.3957. Multiplication helps in scaling numbers and is extensively used in equations to simplify and solve for unknown variables.
Division
Division is another fundamental arithmetic operation that involves splitting a number into equal parts. It is the inverse operation of multiplication. In our step-by-step solution, we encounter division when simplifying the equation to isolate the variable.
To understand division better, consider the problem \(4.3957 \times \frac{1}{1000}\). Here, multiplying by \(\frac{1}{1000}\) is the same as dividing 4.3957 by 1000. This results in 0.0043957, explaining how division can simplify equations and solve for unknowns.
Equation Solving
Equation solving is the process of finding the value of unknown variables that satisfy a given mathematical condition. In our exercise, the goal was to find the missing value (\(x\)) in the equation.
The primary method involves simplifying the equation step-by-step by performing arithmetic operations and isolating \(x\). For example, transforming \(0.0043957 \times x = 4.3957\) to \(x = \frac{4.3957}{0.0043957}\). This step helps us to determine that \(x\) equals to 1000.
Variables
Variables are symbols that represent unknown values. In our exercise, we used \(x\) to describe the missing value in the equation. Variables allow for flexibility and generalization of problems, making them an essential concept in algebra.
By writing and solving equations with variables, we can figure out the value they represent. This process is crucial in understanding and mastering algebraic equations.

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Most popular questions from this chapter

A recipe for bread calls for \(\frac{2}{3}\) cup of water, \(\frac{1}{4}\) cup of milk, and \(\frac{1}{8}\) cup of oil. How many cups of liquid ingredients does the recipe call for?

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Subtract. $$ 3.801-2.81 $$

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