Write the ratio: 21 to 70 as a fraction in lowest terms.

To simplify the ratio 21 to 70 as a fraction, you start by writing it as 21/70. Next, find the greatest common divisor (GCD) of 21 and 70, which is 7. Divide both the numerator and the denominator by 7. So, 21 ÷ 7 = 3 and 70 ÷ 7 = 10. The simplified fraction is 3/10. Now, let's explore how this simplification process has roots in ancient mathematics. The Greeks were some of the first to document methods for reducing fractions and ratios, employing their knowledge of prime factors and common divisors to create simpler forms of fractions for easier calculation and understanding. In real-world applications, understanding ratios and their simplifications is crucial, especially in fields like cooking, chemistry, or finance. For instance, when adjusting a recipe, using the simplified ratio helps you scale ingredients accurately, ensuring your dish turns out just right—no more guessing how much of that crucial spice to add!