/*! 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 56 \(\frac{8}{7}=\frac{?}{42}\)... [FREE SOLUTION] | 91影视

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Chapter 6: Problem 56

\(\frac{8}{7}=\frac{?}{42}\)

Short Answer

Expert verified
x = 48

Step by step solution

01

Identify the relationship

Notice that the given equation is a proportion of two fractions. The aim is to find the unknown value in the fraction on the right-hand side.
02

Set up the proportion equation

The equation can be written as \ \ \ \ \(\frac{8}{7} = \frac{x}{42}\)

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Key Concepts

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

proportions
Proportions are equations that show two ratios or fractions are equal. In this exercise, we have the proportion \(\frac{8}{7}=\frac{x}{42}\). Understanding proportions helps you solve for unknowns when you only know part of the ratio. To solve a proportion, you cross-multiply. This means you multiply the numerator of one fraction by the denominator of the other fraction, and do the same for the remaining numerator and denominator. This gives you an equation that you can solve for the unknown variable.
fractions
Fractions represent parts of a whole. In this exercise, both sides of the equation are fractions. The fraction \(\frac{8}{7}\) represents 8 parts out of 7, and \(\frac{x}{42}\) represents x parts out of 42.
To solve for x, you need to understand how fractions work in proportion. When fractions are equal, their cross-products are also equal.
Cross-multiplying our fractions, we get: \ 8 \times 42 = 7 \times x. This is an algebraic equation that we can solve for the unknown value x.
algebraic equations
Algebraic equations consist of variables and constants. In this problem, x represents an unknown value, and we set up our equation by cross-multiplying the fractions to get: \ 8 \times 42 = 7 \times x\.
Simplify the left side: \ 336 = 7x.
To isolate x, we divide both sides of the equation by 7:
\ \frac{336}{7}=x. \ This simplifies to x = 48.
So, the unknown value x in the fraction \( \frac{x}{42} \) is 48.

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Most popular questions from this chapter

Let \(P\), \(Q\), and \(R\) be rational expressions defined as follows. $$P=\frac{6}{x+3}, \quad Q=\frac{5}{x+1}, \quad R=\frac{4 x}{x^{2}+4 x+3}$$ Solve the equation \(P+Q=R\).

Let \(P\), \(Q\), and \(R\) be rational expressions defined as follows. $$P=\frac{6}{x+3}, \quad Q=\frac{5}{x+1}, \quad R=\frac{4 x}{x^{2}+4 x+3}$$ Find the \(L C D\) for \(P, Q,\) and \(R\).

\(\frac{15 m^{2}}{8 k}=\frac{?}{32 k^{4}}\)

Simplify each complex fraction. Use either method. $$ \frac{\frac{1}{x^{3}-y^{3}}}{\frac{1}{x^{2}-y^{2}}} $$

Simplify each complex fraction. Use either method. $$ \frac{q+\frac{1}{q}}{q+\frac{4}{q}} $$
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