Question
What is the method used to solve a proportional equation like the following?
X/8 = 5/16
X/8 = 5/16
Answers
GPT-4o mini
To solve a proportional equation like \( \frac{X}{8} = \frac{5}{16} \), you can use cross-multiplication. This method involves multiplying the numerator of one fraction by the denominator of the other fraction.
Here are the steps:
1. **Cross-Multiply**: Multiply the numerator of the first fraction by the denominator of the second fraction and the numerator of the second fraction by the denominator of the first fraction.
\[
X \cdot 16 = 5 \cdot 8
\]
2. **Calculate the Products**: Simplify both sides of the equation:
\[
16X = 40
\]
3. **Solve for X**: Divide both sides by 16 to isolate \( X \):
\[
X = \frac{40}{16}
\]
4. **Simplify if necessary**:
\[
X = \frac{5}{2} = 2.5
\]
So, the solution to the equation \( \frac{X}{8} = \frac{5}{16} \) is \( X = 2.5 \).
Here are the steps:
1. **Cross-Multiply**: Multiply the numerator of the first fraction by the denominator of the second fraction and the numerator of the second fraction by the denominator of the first fraction.
\[
X \cdot 16 = 5 \cdot 8
\]
2. **Calculate the Products**: Simplify both sides of the equation:
\[
16X = 40
\]
3. **Solve for X**: Divide both sides by 16 to isolate \( X \):
\[
X = \frac{40}{16}
\]
4. **Simplify if necessary**:
\[
X = \frac{5}{2} = 2.5
\]
So, the solution to the equation \( \frac{X}{8} = \frac{5}{16} \) is \( X = 2.5 \).