write each of the following as the ratio of two integers in lowest terms:

2 and 3/4

Any integer n can be written as n/1. If the ratio of two integers is in lowest terms then the greatest common divisor or gcd of them is 1. What is the gcd of 3 and 4?

To find the greatest common divisor (gcd) of 3 and 4, you can use a variety of methods, such as the Euclidean algorithm or by listing the factors of each number. Let's use the latter approach:

Factors of 3: 1, 3
Factors of 4: 1, 2, 4

Looking at the factors, we can see that the only common factor between 3 and 4 is 1. Therefore, the gcd of 3 and 4 is 1.

Now, to write 2 and 3/4 as a ratio of two integers in lowest terms, you can multiply the whole number part (2) by the denominator (4) and add the numerator (3), which gives us a new numerator of 11. The denominator remains the same.

So, 2 and 3/4 can be written as the ratio 11/4 in lowest terms because the gcd of 11 and 4 is 1.