To simplify the ratio [tex]\( 5.2 : 8.6 \)[/tex] into a fraction in its simplest form, follow these steps:
1. Convert the Ratio to a Fraction:
The ratio [tex]\( 5.2 : 8.6 \)[/tex] can be written as the fraction [tex]\( \frac{5.2}{8.6} \)[/tex].
2. Eliminate the Decimal by Scaling:
To get rid of decimals, multiply both the numerator and the denominator by 10 (since there is one decimal place in both numbers):
[tex]\[
\frac{5.2 \times 10}{8.6 \times 10} = \frac{52}{86}
\][/tex]
3. Find the Greatest Common Divisor (GCD):
Determine the GCD of 52 and 86. The GCD of 52 and 86 is 2.
4. Simplify the Fraction:
Divide both the numerator and the denominator by the GCD to simplify the fraction:
[tex]\[
\frac{52 \div 2}{86 \div 2} = \frac{26}{43}
\][/tex]
5. Convert Back to Decimal Representation if needed:
To ensure the fraction is correct in decimal form, you can check that [tex]\( \frac{26}{43} \)[/tex] simplifies back to values proportional to 5.2 and 8.6:
[tex]\[
\frac{26}{43} \approx 0.60465 \quad \text{and} \quad \frac{5.2}{8.6} \approx 0.60465
\][/tex]
Thus, the ratio [tex]\( 5.2 : 8.6 \)[/tex] is equivalent to the fraction [tex]\( \frac{26}{43} \)[/tex] in its simplest form.
