Question
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Tutor-Verified Answer
Answer
\( x = 10 \)
Solution
Given the equation:
\[
\frac{4}{x} = \frac{0.22}{0.55}
\]
**Step 1: Simplify the right-hand side**
Convert the decimals to fractions:
\[
\frac{0.22}{0.55} = \frac{22}{55}
\]
Simplify by dividing numerator and denominator by \(11\):
\[
\frac{22 \div 11}{55 \div 11} = \frac{2}{5}
\]
So, the equation becomes:
\[
\frac{4}{x} = \frac{2}{5}
\]
**Step 2: Solve for \( x \)**
Cross-multiply to eliminate the fractions:
\[
4 \cdot 5 = 2 \cdot x
\]
This gives:
\[
20 = 2x
\]
Divide both sides by \(2\):
\[
x = \frac{20}{2} = 10
\]
Thus, the solution is:
\[
x = 10
\]
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Simplify this solution Extra Insights
To solve for \( x \) in the equation \( \frac{4}{x}=\frac{0.22}{0.55} \), you first simplify the right side. The fraction \( \frac{0.22}{0.55} \) simplifies to \( \frac{2}{5} \). Now, rewrite the equation as \( \frac{4}{x} = \frac{2}{5} \). Cross-multiply to get \( 4 \cdot 5 = 2 \cdot x \), leading to \( 20 = 2x \). Dividing both sides by 2 gives \( x = 10 \). Remember to always check your solution! Plugging \( x = 10 \) back into the original equation confirms it holds true, thus guaranteeing your answer is correct. Now you can calmly tackle similar problems knowing the trick of simplification can often lead you to the solution faster!
