A denominator is the bottom number in a fraction. It shows the equal number of parts something is divided into. For example, four would be the denominator if we had the fraction 3/4. We would call the three the numerator. The numerator is how many equal parts there are, and the denominator is how many parts the whole can be divided.
Find the Denominator: Numerators and Denominators
The denominator of a fraction shows you how many parts are equal to a whole. At the same time, the fraction’s numerator tells you how many of those equal parts the fraction contains. Simply put, the denominator is the number at the bottom of the fraction, and the numerator is the number on top.
Find the Denominator: Common Denominators
The first step in adding or subtracting fractions is always to make sure your denominators are the same. It means you must find the common denominator. Then, once you have found the common denominator, you can add together or subtract the numerators.
Equations where the denominators are the same, are very straightforward, as you don’t have to find the denominator they share in common. The common denominator is already given. For example:
1/4 + 2/4 = 3/4
In the case of this equation, 4 is the common denominator. Therefore, you can put four at the bottom of the fraction and add the numerators together, giving you 3/4.
This rule is the same for subtracting fractions. For example:
5/7 – 2/7 = 3/7
In this equation, 7 is the common denominator. Therefore, you can put seven at the bottom of the fraction and subtract the numerators. Giving you 3/7.
Things get much more tricky when the denominators in an equation are different. In this instance, you have to find the denominator in common before you start trying to solve the equation.
To find the denominator in common for two fractions, multiply the numerator and denominator of each fraction by the denominator of the other. For example, if you are trying to find the common denominator of 1/4 and 1/5, multiply both the numerator and denominator of 1/4 by 5 (the denominator of 1/5). Then, multiply the numerator and denominator of 1/5 by 4 (which is the denominator of 1/4). This equation will look like this:
(1 × 5) / (4 × 5) = 5/20
(1 × 4) / (5 × 4) = 4/20
Now you’ve got two new fractions with the same denominator that can be easily added or subtracted!
Find the Denominator: How to find the unknown denominator
First, when the numerator or denominator is strange in a fraction, you must cross-multiply the numerators and denominators. To cross-multiply, you must multiply each numerator by the denominator in the opposite fraction. Resulting in a brand-new equation for you to work with that is not a fraction.
So, how do you use cross multiplication to find the denominator when it is unknown? In algebraic equations, an unknown denominator will be represented by an ‘x.’
You can solve X (i.e., find the unknown denominator) by carrying out these super easy steps:
Let’s take the equation x/3 = 3/4 as an example.
Step 1: Cross Multiply the Fraction
The first step is to cross-multiply the fractions, as explained above. It will create a new equation that is much easier to solve.
For example:
(4 × x) = (3 × 3), this means that 4x = 9
Step Two: Solve the Equation
After cross-multiplying your fractions, you must solve the equation you created. The first step is to get x on its own. You do this by dividing both sides of the equation by the number in front of the x.
For example:
4x = 9
4x ÷ 4 = x
9 ÷ 4 = 9/4
x = 9/4
Step Three: Reduce the Fraction
The last of the three steps is to reduce the fraction. To do this, you must first find the most common factor of the numerator and denominator. Then, once you have done this, divide the numerator and denominator by the common factor.
If the fraction’s numerator is greater than 1, it is a good idea to turn it into a mixed number. To do this, you have to divide the numerator by the denominator. It will leave you with a whole number and a fraction, where the remainder will be the numerator, and the original denominator is the denominator.
For example:
9 ÷ 4 cannot be simplified into a mixed number.
It leaves us with 2 and a remainder of 1. As the original denominator in the fraction was 4, we are left with the following:
2 1/4
Multiplying Mixed Fractions by Mixed Fractions
There are simple steps to take when multiplying mixed fractions (fractions featuring whole numbers).
Let’s take the equation 2 1/4 × 3 1/2 as an example.
Step 1: Convert everything into improper fractions
The first step in multiplying mixed fractions is eliminating the whole numbers and turning everything into improper fractions. To change one of the mixed fractions, multiply the denominator by the actual number. Then, after you have done this, add the numerator. This number then goes to the top of the fraction, and the denominator remains the same.
For example:
2 1/4 × 3 1/2 becomes (2 × 4 = 8 + 1)/4 = 9/4 × 3 1/2
9/4 x (3 × 2 = 6 + 1)/2 = 9/4 × 7/2
Step 2: Multiply the numerators of the improper fractions
Now that we have 2 improper fractions to work with, we can begin the next step. It is to multiply the numerators of the improper fractions.
For example:
The numerators of our fractions are 9 and 7.
9 × 7 = 63
Step 3: Multiply the denominators of the improper fractions
Now we’ve sorted the numerators, we have to deal with the denominators. The next step in this process is multiplying the denominators by one another.
For example:
The denominators of our fractions are 4 and 2.
4 × 2 = 8
It makes our new fraction 63/8
Step 4: Turn the answer into a mixed fraction
Suppose the numerator of the new fraction is larger than the denominator. In that case, we can turn it into a mixed number by seeing how many times the denominator will go into the numerator. What is left over becomes the remainder.
For example:
7 7/8
