In math, fractions represent how many equal parts of a whole. For example, when you slice a pizza, you get fractions. If you slice the pizza into 8 pieces, and you get 1 piece, you get a fraction, which is 1/8 of the whole pizza. If your brother gets 3 pieces, he gets a fraction, which is 3/8 of the whole pizza.

In above example, the top number - the numerator - specifies how many slices you get, and the bottom number - the denominator - specifies how many equal slices the whole is cut into.

It is easy when adding fractions when they have common denominators: For example, to find out the fraction of pizza you and your brother together get:

When adding fractions with different denominators, you first need to convert the fractions to make them have common denominator.

Reciprocal

In math, reciprocal is a special fraction. To get the reciprocal of a number, we just divide 1 by the number. For example the reciprocal of 8 is 1/8 (and of course, the reciprocal of 1/8 is 8).

A ratio is basically a fraction, or two numbers expressed as a quotient, such as 5/7 or 170/385, etc. But a ratio is a special kind of fraction, which is used to compare 2 related quantities. For example, if there are 5 boys and 8 girls in a classroom, the ratio of boys to girls is 5 to 8, which can be written 5/8 or 5:8.

What are the common ratio problems? Here is an example. Suppose you go to a restaurant 5 times in a 30-day month. Assume you go to a restaurant no more than 1 time a day, what is the ratio of restaurant days to non-restaurant days in this month?

The answer is not 5:30. Instead, you need to subtract your restaurant days from the total days in the month to get non-restaurant days, which is the required second part of your ratio. The answer is therefore 5:25 (or 5/25).

You can further simplify the above ratio by crossing out the ?common factors?, and you will get a ratio of 1:5 (or 1/5).

A proportion is just a numeric expression setting two ratios equal to each other, for example 3/4 = 12/16, a/b = c/d, etc.

What are the common proportion problems? Here is an example.

In a math class, the ratio of passing grades to failing grades is 7 to 5. How many of the 36 students failed the course?

In this example, the ratio 7/5 tells us that for every 7 students with a passing grade, 5 students will have a failing grade. This means if we have a group of 12 students, 7 students would pass, and 5 students would fail. Now, since we have 36 students, the question is essentially asking how many students would fail in a group of 36 students?

We can assume the number of failing students in a group of 36 is X, and we will have a proportion as below:

Now all we have to do is to solve the above proportion:

So the answer is: of the 36 students in the class, 15 students got a failing grade.