A Mixed Number is made of a fraction and a whole number.
There are 1 and a half cups of food.
Read it as one and a half and write it as 1 ½
Example: Represent the following as a mixed number.
Solution: It is written as 1 ½ and 1$\frac{9}{16}$
Comparison of Mixed Numbers
We can compare the mixed numbers just like we compare the fractions.
Example: Compare 1 ½ and 1$\frac{1}{3}$
Solution: First draw a fraction bar to represent each of these mixed numbers and then place them one below the other.
Next compare the two rows of the fraction bars. The longer fraction bar is greater than the shorter one.
Hence, 1 ½ > 1$\frac{1}{3}$
Example: Compare 4 ¼ and 3 ½ using a number line.
Solution: First place the mixed numbers on the number line
The mixed number that is farther away to the right is the greater mixed number. Here, 4 ¼ is farther to the right than 3 ½ and hence 4 ½ > 3 ½
Renaming Fraction as Mixed Numbers and Mixed Numbers as Fractions
In a fraction, when the Numerator is less than the denominator, the fraction is a Proper Fraction. When the Numerator is bigger than the denominator or is equal to the denominator, the fraction is called an Improper Fraction. When the numerator of a fraction is greater than the denominator, it has a value greater than one and hence, can be renamed as a Mixed Number.
Example: Rewrite $\frac{13}{4}$ as a mixed number
Solution: First let us draw a model for the mixed number.
There are 13 fourths shown here. There are 3 full and a fourth. Hence, the mixed number is 3 ¼
$\frac{13}{4}$ actually means 13 ÷ 4 and hence, we can use division to rename the fraction into a mixed number.
13 ÷ 4 = 3 Remainder 1
Write the quotient as the whole number, the remainder as numerator and the divisor as denominator.
Hence, $\frac{13}{4}$ has been renamed as a mixed number 3 ¼
We can also rename a mixed number as a fraction.
Example: Rewrite 1 $ \frac{4}{5}$ as a fraction.
Solution: We can use fraction bars to rename mixed numbers as fractions.
Let us first model 1 $ \frac{4}{5}$ as fraction bars.
Now place the $\frac{1}{5}$ bars under the 1 bar
Now count the number of $\frac{1}{5}$ bars. There are 9 of them. Hence, the numerator of the fraction is 9 and the denominator is 5. Hence, the mixed number 1 $\frac{4}{5}$ is renamed as $\frac{9}{5}$
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