Dealing with fractions could be a nightmare for many students who just started learning the concept. Even though fraction calculations become easy after learning the concept but you may get exhausted during the learning process.
Fractions are complicated when we are dealing with very small numbers. In school, you may have been taught the concept by using pizza or cake as an example. Which is; if there are 8 pieces in a pizza and you have eaten one piece, then 7/8 is remaining, right?
In this post, we will take solving fractions to another level by using mathematical examples with real values. We will discuss what are fractions, how you can add, subtract, multiply, or divide them, and what tools you can use to pace up your fraction calculations on the way to your school.
What exactly are fractions?
Fractions are a way to represent a number that cannot be represented in the whole form. Fractions are used to read or write quantity in comparison to the whole quantity. For example, if there are 3 apples and 5 oranges in a basket, then there are 3/8 oranges if we have to calculate the ratio of oranges as compared to the total number of fruits.
According to Splash Learn, the fraction can be defined as,
A fraction is a number that represents a whole number that has been divided into equal parts. When spoken in everyday English, a fraction describes how many parts of a specific size are there.
The upper part of the fraction is known as the numerator which is placed on top of the slash “/.” Whereas, the number or digit placed under the slash is known as the denominator.
For Example: 2/5, 3/4, 5/10, etc.
How many types of fractions are there?
There are generally three types of fractions.
1. Proper Fractions
A proper fraction is a type of fraction where the denominator is greater than the numerator. In other words, the numerator (the upper part) is smaller than the denominator (the lower part). These fractions are part of a whole.
Here are few examples:
3/4, 1/3, 2/8, etc.
All of the above fractions are proper fractions.
2. Improper Fractions
Improper fractions are the reverse case of proper fractions. In this type of fraction, the numerator is greater than the denominator. The part on the top of the slash will be greater than the part below the fraction slash. These fractions are greater than the whole.
Here are few examples:
7/2, 4/1, 5/3, etc.
3. Mixed Fractions
A mixed fraction is the combination of proper fraction and whole. In simple words, mixed fractions form when we write a whole and proper fraction together.
How to use a fraction calculator to solve fractions?
We will show a way to solve fractions step by step. For that purpose, we will use an online fraction calculator by CalculatorSchool.com. This tool is free to use and you can solve fractions on the go.
To solve fractions,
- Enter the numerator and denominator of the first fraction.
- Enter the numerator and denominator of the second fraction.
- Select the mode of operation i.e., addition, subtraction, etc.
- Press the Calculate button to get the answer.
- Use the Reset button to enter new values.
It shows you step-by-step calculations for fraction addition, subtraction, multiplication, and division. You can enter values for both fractions in the designated input boxes and select the operation you want to perform on those fractions.
You will get all the steps of the calculation and you can use these steps to learn the whole process.
How to solve fractions by hand?
Solving fractions is not that complicated if you know the types of fractions we discussed above. To handle the fractions, you should know which type of fractions you are dealing with. Either it’s a proper fraction, a mixed one, or an improper fraction. However, if you are dealing with proportions, solving proportions calculator can save you a lot of time.
In this section, we will add, subtract, multiply, and divide fractions by using examples.
Fractions: 4/5 and 3/2.
Add, Subtract, Multiply, and Divide above fractions.
1. Fraction Addition
To add two fractions, follow the below steps.
Step 1: Write both fractions and place an addition sign between them.
= 4/5 + 3/2
Step 2: Make the denominator of both fractions the same. To do that, we will multiply both fractions with a number so that the denominator will be the same after multiplication.
Multiply numerator and denominator of the first fraction with 2 and the second fraction with 5.
= 4/5 × 2/2 + 3/2 × 5/5
= 8/10 + 15/10
You can see, the denominator of both fractions is the same. I.e., 10.
Step 3: We can take the denominator common and add both numerators.
= 1/10 (8 + 15)
= 1/10 (23)
= 23/10
Now you can add two or more fractions by using the above method. Could you tell what type of the resultant fraction is? Look out for the numerator. It is greater than the denominator. This means it is an improper fraction.
2. Fraction Subtraction
To subtract two fractions, follow the below steps.
Step 1: Write both fractions and place a subtraction sign between them.
= 4/5 – 3/2
Step 2: Make the denominator of both fractions the same. To do that, follow the method explained in the previous example. i.e., make the denominator of both fractions identical.
Multiply numerator and denominator of the first fraction with 2 and the second fraction with 5.
= 4/5 × 2/2 – 3/2 × 5/5
= 8/10 – 15/10
Step 3: Take the denominator common and subtract both numerators.
= 1/10 (8 – 15)
= 1/10 (-7)
= -7/10
As you can see, the addition and subtraction of a fraction are similar.
3. Fraction multiplication
To multiply two fractions, follow these steps.
Step 1: Write both fractions and place a multiplication sign between them.
= 4/5 × 3/2
Step 2: Multiply the numerator of the first fraction with the numerator of the second fraction. In the same way, multiply the denominator of the first fraction with the denominator of the second fraction.
= 4/5 × 3/2
= 12/10
Step 3: Simply the fraction by dividing with a common number.
= 12÷2/10÷2
= 6/5
4. Fraction division
Fraction division is as simple as multiplication.
Step 1: Write both fractions and place a division sign between them.
= 4/5 ÷ 3/2
Step 2: Get the reciprocal of 2nd fraction to replace the “÷” sign with “×”.
= 4/5 × 2/3
Step 3: Multiply the numerator of 1st fraction with the numerator of 1st fraction. Also, multiply the denominator of the 2nd fraction with the denominator of 2nd fraction.
= 8/15