\frac{2}{6} = \frac{u}{3}
Understand the Problem
The question is asking us to solve the proportion \frac{2}{6} = \frac{u}{3} for the variable u. To approach this, we can use cross-multiplication to find the value of u.
Answer
$u = 1$
Answer for screen readers
The value of $u$ is $1$.
Steps to Solve
- Set up the proportion for cross-multiplication
We have the equation
$$ \frac{2}{6} = \frac{u}{3} $$
To solve for $u$, we can use cross-multiplication.
- Perform cross-multiplication
Cross-multiplication involves multiplying the numerator of one fraction by the denominator of the other. This gives us:
$$ 2 \cdot 3 = 6 \cdot u $$
- Simplify the equation
Now we simplify the left side:
$$ 6 = 6u $$
- Isolate the variable u
To isolate $u$, we divide both sides of the equation by 6:
$$ u = \frac{6}{6} $$
- Solve for u
Simplifying the right side gives us:
$$ u = 1 $$
The value of $u$ is $1$.
More Information
This problem illustrates how cross-multiplication can simplify solving proportions. In many practical applications, proportions are used to compare relationships between two quantities.
Tips
One common mistake is forgetting to cross-multiply properly, which can lead to incorrect equations. Always double-check your multiplication to ensure accuracy.
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