Writing Mixed Numbers As Improper Fractions
Fractions
Fractions represent part of a whole number. Fractions, decimals and percentages can all have the same values and you may find it useful to know how to convert between them.
Mixed numbers and improper fractions
A whole number can be written as \(\frac{2}{2}\) , \(\frac{3}{3}\) , \(\frac{4}{4}\) , etc.
So \(1 \frac{2}{3}\) can be written as:
\[\frac{3}{3} + \frac{2}{3} = \frac{5}{3}\]
Mixed numbers
\(1\frac{2}{3}\) is known as a mixed number , because it is made up of a whole number and a fraction.
Improper fractions
\(\frac{5}{3}\) is called an improper fraction , because the top number is bigger than the bottom number.
Converting from a mixed number to an improper fraction
You can write the whole number part as a fraction, with the same denominator as the other fraction, and then add the fractions together.
Example
\[1 \frac{2}{3} = \frac{3}{3} + \frac{2}{3} = \frac{5}{3}\]
Here is another example:
\[2 \frac{1}{4} = 1 + 1 + \frac{1}{4} = \frac{4}{4} + \frac{4}{4} + \frac{1}{4} = \frac{9}{4}\]
Converting from improper fractions to mixed numbers
You can separate the fraction into as many whole numbers as possible, with a smaller remaining fraction.
Example
\[\frac{17}{5}= \frac{5}{5} + \frac{5}{5} + \frac{5}{5} + \frac{2}{5} = 3 \frac{2}{5}\]
Another way to convert an improper fraction is to find how many whole numbers you get, by using a division.
For example let's convert \(\frac{17}{5}\) to a mixed number again.
We start by dividing the top number by the bottom number.
\({17}\) divided by \({5}\) is \({3}\) remainder \({2}\) .
So the whole number part is \({3}\) , and the remainder \({2}\) means there are \(\frac{2}{5}\) left over.
So the answer is \(\frac{17}{5} = 3 \frac{2}{5}\)
- Question
-
Write \(\frac{20}{7}\) as a mixed number.
-
Method 1:
\[\frac{20}{7} = \frac{7}{7} + \frac{7}{7} + \frac{6}{7} = {2}\frac{6}{7}\]
Method 2:
\(\frac{20}{7} = 20 \div 7 = 2\) remainder \({6}\) , so:
\[\frac{20}{7} = 2 \frac{6}{7}\]
Using a calculator
If your calculator has a fraction button you can use this to convert from improper fractions to mixed numbers. Type in the improper fraction, press ' \({=}\) ', and the calculator will convert it to a mixed number.
Writing Mixed Numbers As Improper Fractions
Source: https://www.bbc.co.uk/bitesize/guides/zt6p34j/revision/5
Posted by: lawsontheast.blogspot.com
0 Response to "Writing Mixed Numbers As Improper Fractions"
Post a Comment