Express each ratio as a fraction in its simplest form. 2.4 2.4 bags to 3 1 4 3\frac14 bags.

For this problem, we need to express this ratio as a fraction in its simplest form, and we have the ratio of 2.4 bags to 3 and 1/4 bag. So writing this as a fraction, we'll have 2.4 bags up top. And 3 and 14 bags down below. Since we have the same units, bags over bags, these are going to divide out and reduce to one, leaving us with 2.4 over 314. Now, first, to simplify this, I'm going to take my mixed number here of 3 and 14 and write it as an improper fraction. So doing that, we have 2.4 up above, and 3 times 4 is 12, plus 1 is 13, so 134 below. Next, I'm going to clear the decimal up top, and to do that, since we have just a tense value here, I'm going to multiply both the numerator and denominator by 10. Giving us 24 in the numerator, and 13 times 10 is 130, it's 1304 in our denominator. Next, since I have a value being divided by a fraction, I know that to simplify, I take the 1st 2 fraction, multiply it by the reciprocal, which is 4/130. So I have 24 times 4/130. Now 24 is the same as 24 divided by 1, and with a fraction being multiplied by a fraction, I can combine these into one fraction and multiply the numerators and the denominators. Next, I'm going to take a look at my factors in the numerator and denominator in order to simplify. I know that 24 is equal to 6 times 4, so we have 6 times 4 times a 2nd 4 in our numerator. And 130 is equal to 13 times 10, so I'll have 1 times 13 times 10, which I know that 10 further breaks down into 2 times 5. Since 4 is divisible by 2. I can reduce this to a 2 up top and 1 below. And since none of our factors in the numerator are divisible by 5 or 13, this is as simple as this can get. So recombining our values, we have 6 times 4 is 24, 24 times 2 is 48 in our numerator. 1 x 13 is 13, and 13 times 5 is 65. So our ratio of 2.4 bags to 3.14 bags simplifies to the ratio of 4/8 to 65.