Write the ratio 12 gal to 40 gal as a fraction in simplest form.
Understand the Problem
The question is asking to express the ratio of 12 gallons to 40 gallons as a fraction in simplest form.
Answer
The simplified ratio of 12 gallons to 40 gallons is $\frac{3}{10}$.
Answer for screen readers
The ratio of 12 gallons to 40 gallons in simplest form is $\frac{3}{10}$.
Steps to Solve
- Write the Ratio as a Fraction
Express the ratio of 12 gallons to 40 gallons as a fraction: $$ \frac{12}{40} $$
- Find the Greatest Common Divisor (GCD)
Identify the GCD of the numerator (12) and the denominator (40). The GCD of 12 and 40 is 4.
- Divide the Numerator and Denominator by the GCD
Divide both the numerator and the denominator by the GCD: $$ \frac{12 \div 4}{40 \div 4} = \frac{3}{10} $$
- Final Form
The fraction is now in its simplest form: $$ \frac{3}{10} $$
The ratio of 12 gallons to 40 gallons in simplest form is $\frac{3}{10}$.
More Information
Ratios can often be simplified by finding common factors. Understanding how to reduce fractions helps with various mathematical applications, such as scaling recipes or determining proportions.
Tips
- Forgetting to simplify the fraction. Always check for common factors.
- Incorrectly calculating the GCD. Make sure to find the highest number that divides both values evenly.
