What is 78/40 as a mixed number?
Trying to find out how to convert 78/40 into a mixed number or fraction? Have I got the answer for you! In this guide, we'll walk you through the step-by-step process of converting an improper fraction, in this case 78/40, to a mixed number. Read on!
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Before we begin, let's revisit some basic fraction terms so you understand exactly what we're dealing with here:
- Numerator. This is the number above the fraction line. For 78/40, the numerator is 78.
- Denominator. This is the number below the fraction line. For 78/40, the denominator is 40.
- Improper fraction. This is a fraction where the numerator is greater than the denominator.
- Mixed number. This is a way of expressing an improper fraction by simplifying it to whole units and a smaller overall fraction. It's an integer (whole number) and a proper fraction.
Now let's go through the steps needed to convert 78/40 to a mixed number.
Step 1: Find the whole number
We first want to find the whole number, and to do this we divide the numerator by the denominator. Since we are only interested in whole numbers, we ignore any numbers to the right of the decimal point.
78/40= 1.95 = 1
Now that we have our whole number for the mixed fraction, we need to find our new numerator for the fraction part of the mixed number.
Step 2: Get the new numerator
To work this out we'll use the whole number we calculated in step one (1) and multiply it by the original denominator (40). The result of that multiplication is then subtracted from the original numerator:
78 - (40 x 1) = 38
Step 3: Our mixed fraction
We've now simplified 78/40 to a mixed number. To see it, we just need to put the whole number together with our new numerator and original denominator:
Step 4: Simplifying our fraction
In this case, our fraction (38/40) can be simplified down further. In order to do that, we need to calculate the GCF (greatest common factor) of those two numbers. You can use our handy GCF calculator to work this out yourself if you want to. We already did that, and the GCF of 38 and 40 is 2.
We can now divide both the new numerator and the denominator by 2 to simplify this fraction down to its lowest terms.
38/2 = 19
40/2 = 20
When we put that together, we can see that our complete answer is:
Hopefully this tutorial has helped you to understand how to convert any improper fraction you have into a mixed fraction, complete with a whole number and a proper fraction. You're free to use our calculator below to work out more, but do try and learn how to do it yourself. It's more fun than it seems, I promise!
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