Calculating the fraction of a whole number is a very useful skill to learn that helps students to understand the nature of numbers and their interactions. In this article, we'll explain how to calculate 1/2 of 78 with step-by-step-examples.
Looking for fractions of whole number worksheets? Click here to see all of our free fraction of a number worksheets.
Calculating the Answer as a Number
The simple rule to remember whenever you want to find a fraction of an amount is to divide the amount by the fraction's denominator, and then multiply that answer by the fraction. Using this rule, you'll be able to work out the fractional amount of the original number. Let's work it out together.
First we take the amount, 78, and divide it by the denominator, 2:
Next, we take the answer, 39, and multiply it by the numerator, 1:
As you can see, the answer to the question "what is 1/2 of 78?" as a number is 39.
Increase or Decrease an Amount by a Fraction
What if you wanted to increase or decrease 78 by 1/2? Once you have calculated the answer above, 39, you deduct that amount from the whole number to decrease it by 1/2 and you add it to increase:
Increase = 78 + 39 = 117
Decrease = 78 - 39 = 39
Calculating the Answer as a Fraction
Sometimes, you might want to show your answer as another fraction. In that case, we can do the following.
First, we take the whole number and turn it into a fraction by using 1 as the fraction denominator:
Now that we have two fractions, we can multiply the numerators and denominators together to get our answer in fraction form:
We can simplify this new fraction down to lower terms. To do that we need to know something in math which is called the GCD, or greatest common divisor.
I won't go through the steps of finding the GCD here as we'll cover it in a future article, but for now all you need to know is that the greatest common divisor of 78 and 2 is 2.
Using the GCD, we can divide the new numerator (78) and the denominator (2) by 2 to simplify the fraction:
78 ÷ 2 = 39
2 ÷ 2 = 1
Finally, we can put the fraction answer together:
Now you might have noticed that the fraction we have has a numerator that is larger than the denominator. This is called a mixed or improper fraction and means that there is a whole number involved. We can simplify this down to a mixed number.
We'll put together a blog post on converting improper fractions to a mixed number to explain those steps in more detail, but for the purposes of this article, we'll go ahead and just give you the mixed number answer:
Hopefully this article helps you to understand how you can work with fractions of whole numbers and work this out quickly for yourself whenever you need it.
Practice Fraction of Number Worksheets
Like most math problems, finding the fraction of a number is something that will get much easier for you the more you practice the problems and the more you practice, the more you understand.
Whether you are a student, a parent, or a teacher, you can create your own fractions of a whole number worksheets using our fraction of a number worksheet generator. This completely free tool will let you create completely randomized, differentiated, fraction of a number problems to help you with your learning and understanding of fractions.
Practice Fractions of a Number Using Examples
If you want to continue learning about how to calculate the fraction of a whole number, take a look at the quick calculations and random calculations in the sidebar to the right of this blog post.
We have listed some of the most common fractions in the quick calculation section, and a selection of completely random fractions as well, to help you work through a number of problems.
Each article will show you, step-by-step, how to work out the fraction of any whole number and will help students to really learn and understand this process.
Calculate Another Fraction of a Number
Enter your fraction in the A and B boxes, and your whole number in the C box below and click "Calculate" to calculate the fraction of the number.