Express each ratio as a fraction in its simplest form. 1 1 2 1\frac12 to 2 1 4 2\frac14

Here, we need to express this ratio as a fraction in its simplest form, and the ratio we have is 11/2 to 2 1/4. So first, writing it as a fraction, we have 1 1/2 in the numerator, and 2 1/4 in our denominator. Now, since we have mixed fractions here, both in the numerator and the denominator, I'm going to convert these into improper fractions in order to simplify. So writing 1 and 1/2 as an improper fraction, I take 1, multiply it by 2 to get 2, and then add 1 to get 3. So 1 and 1/2 as an improper fraction is 3 halves. Now we do the same thing for 21 1/4. 2 times 4 is 8, plus 1 is 9, so 21 1/4 is equal to 9/4. Now I have a fraction over a fraction, and I know that to simplify this, I take the bottom fraction, flip it, and multiply. So I'll have 3 halves times 4/9. And since these are two fractions being multiplied, I can combine them into one fraction and multiply the numerators and the denominators. Simplifying, I know that 4 is divisible by 2, so 4 will reduce to 22 will reduce to 1, and 9 is divisible by 3. So 9 will reduce to 3, and 3 will reduce to 1, leaving us with 1 times 2 up top, which is 2. And 1 times 3 below, which is 3, and since 2 and 3 are prime, this is now our ratio in its simplest form, 2 to 3.