Question
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Answer
\( \frac{6}{8} = \frac{42}{56} \)
Solution
To solve the proportion \( \frac{6}{8}=\frac{?}{56} \), we can use cross-multiplication.
1. Set up the equation based on the proportion:
\[
6 \times 56 = 8 \times ?
\]
2. Calculate \( 6 \times 56 \):
\[
6 \times 56 = 336
\]
3. Now, we have:
\[
336 = 8 \times ?
\]
4. To find \( ? \), divide both sides by 8:
\[
? = \frac{336}{8}
\]
5. Calculate \( \frac{336}{8} \):
\[
? = 42
\]
Thus, the answer is \( 42 \).
So, \( \frac{6}{8}=\frac{42}{56} \).
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Simplify this solution Extra Insights
To solve for the missing numerator, you can set up a proportion. Cross-multiply: \(6 \times 56 = 8 \times ?\) which simplifies to \(336 = 8?\). Now, divide both sides by 8 to get \(? = 42\). So, the fraction simplifies to \( \frac{6}{8}=\frac{42}{56} \) — both are equivalent! If there’s any confusion, remember that simplifying fractions and setting up proportions are great tools! Also, common mistakes often include forgetting to simplify both sides after solving, so double-check your work to ensure clarity in your solutions!
