\frac37 = \frac9x - Blask
Solving the Proportion: \frac{3}{7} = \frac{9}{x}
Solving the Proportion: \frac{3}{7} = \frac{9}{x}
Understanding how to solve equations involving fractions is a fundamental skill in algebra. One common type of problem students encounter is solving proportions—statements that two ratios are equal. In this article, we’ll walk through how to solve the equation:
\[
\frac{3}{7} = \frac{9}{x}
\]
Understanding the Context
This equation presents a proportion where a fraction with numerator 3 and denominator 7 equals another fraction with numerator 9 and unknown denominator \( x \). Let’s break down the steps to find \( x \) and explain the logic behind it.
What Is a Proportion?
A proportion sets two fractions equal to each other, meaning the ratio on the left matches the ratio on the right. The equation:
\[
\frac{a}{b} = \frac{c}{d}
\]
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Key Insights
can be solved by cross-multiplication, so long as \( b \) and \( d \) are not zero.
Step-by-Step Solution
Start with the given equation:
\[
\frac{3}{7} = \frac{9}{x}
\]
To eliminate denominators, cross-multiply:
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\[
3 \cdot x = 7 \cdot 9
\]
Simplify both sides:
\[
3x = 63
\]
Now divide both sides by 3 to isolate \( x \):
\[
x = \frac{63}{3} = 21
\]
Final Answer
\[
\boxed{x = 21}
\]
This means that when \( x = 21 \), the proportion \(\frac{3}{7} = \frac{9}{21}\) holds true.
Why This Works: A Quick Check
Plug \( x = 21 \) back into the original proportion:
