Solving Ratio Containing Fractions

\(1\frac{1}{2}:3=x:21\)

Answer:

First and foremost, make any mixed fractions into improper.

Therefore, \(1\frac{1}{2}\rightarrow \frac{3}{2}\)

\(\frac{3}{2}:3=x:21\)

Convert each side of the ratio into a fraction for ease of reading:

\(\frac{\frac{3}{2}}{3}=\ \frac{x}{21}\)

⭐ Now you cross-multiply:

\(21\left(\frac{3}{2}\right)=3x\)

⭐ Simplify the left-side:

\(21\left(\frac{3}{2}\right)\) is the same as \(21\times \frac{3}{2}\), and that's the same as:

\(\frac{21}{1}\times \frac{3}{2}\)

To multiply fractions, multiply all the numerators at once, and all the denominators at once. If you do that correctly, we get:

\(\frac{21}{1}\times \frac{3}{2}=\frac{63}{2}\)

Therefore, our simplified ratio is now:

\(\frac{63}{2}=3x\)

⭐ Divide both sides by 3:

\(\frac{\frac{63}{2}}{3}=x\)

This gives us an answer of: 10.5 or \(\frac{21}{2}\)