Hello. In this mathematics guide, I go over converting improper fractions to mixed numbers and the other way around. The reader should be familiar with multiplication and long division.
Review Of Improper Fractions & Mixed Numbers
With improper fractions and mixed numbers we are dealing with ways to represent values that contain wholes and parts greater than one.
An improper fraction contains a numerator and a denominator. The denominator of a fraction represents the number of equal pieces in a whole. The numerator (top number) is larger than the denominator and represents the amount of shaded/taken pieces. An example of an improper fraction is seven quarters or 7/4.
A mixed number contains how many whole parts that are there along with the remaining parts of a whole. The number two and a half is an example of a mixed number. It is written as
Improper Fractions To Mixed Numbers
Going from an improper fraction to a mixed number requires division. We would like to know how many of the denominator amount goes into the numerator number. This is done through long division. The remainder from this long division is used as a numerator for the fractional part in the mixed number.
Let's look at a few examples.
Example One
What is eleven halves as a mixed number?
We do long division of eleven divided by two which gives 5 with a remainder of one. The remainder of one is the numerator of the fractional part. In the fractional part, the denominator is two as the denominator from the improper fraction was 2.
Example Two
Let's go with some larger numbers. What would fourty-nine fifths be a mixed number?
Dividing 49 by 5 gives 9 with a remainder of 4. As a mixed number, this is written as
Example Three
Doing one hundred thirds gives a mixed number of
Mixed Numbers To Improper Fractions
When it comes to algebra purposes mixed numbers are annoying to work with. It is preferable to use improper fractions for solving equations and combining like terms.
Going from mixed numbers to improper fractions does not involve division. It involves multiplication and addition.
Example One
Convert
Find how many halves are there in three wholes. This can be done by multiplying the big three with denominator of 2 to obtain 6. Then add one from the numerator to obtain the numerator of the improper fraction. The denominator of the improper fraction is still 2.
Example Two
Practice Problems
Part One - Convert the improper fractions into mixed numbers.
11/3
9/4
88/5
100/ 7
Part Two - Convert the mixed numbers into improper fractions.
7 1/2
8 3/4
100 3/7
21 7/9
Solutions To Practice Problems
Part One
11/3 = 3 2/3
9/4 = 2 1/4
88/5 = 17 3/5
100/7 = 14 2/7
Part Two
7 1/2 = 15/2
8 3/4 = 35/4
100 3/7 = 703/7
21 7/9 = 196/9
Thank you for reading.