Mixed Fractions

Example 1:
Convert the following fraction \(\frac{23}{5}\) into a mixed number.

Solution:
Given improper fraction = \(\frac{23}{5}\)

After dividing the numerator with the denominator, we get the remainder = 3 and quotient = 4

Hence, the mixed number is \(4\frac{3}{5}\).

Example 2:
Michael has \(2\frac{1}{2}\) liters of milk. He needs to share \(1\frac{1}{2}\) liters of milk with his brother John. Calculate the quantity of milk he will be left with after sharing the milk with his brother.

Solution:
The quantity of milk Michael has = \(2\frac{1}{2}\) liters

The quantity of milk Michael needs to share with John = \(1\frac{1}{2}\) liters

Quantity of milk left = (Quantity of milk Michael has) – (Quantity of milk shared)

Quantity of milk left = \(2\frac{1}{2}\ – \ 1\frac{1}{2}\)

First, let’s subtract the whole numbers = 2 – 1
= 1

Then, we need to subtract the fractional part = \(\frac{1}{2}\ – \ \frac{1}{2}\)
= 0

Now, add both the whole number and fractional parts.
That is, 1 + 0 = 1.

Therefore, Michael will be left with 1 liter of milk after sharing it with his brother.

Example 3:
John walks \(3\frac{1}{2}\) km every day. What is the distance he covers in the month of November?

Solution:

Distance covered by John in 1 day = \(3\frac{1}{2}\) km

Number of days in the month of November = 30

Thus, the total distance covered by John can be calculated by multiplying the distance walked in one day by the number of days in November, that is,

= \(3\frac{1}{2}\ \times\ 30\)

= \(\frac{7}{2}\ \times\frac{30}{1}\)    [Converting mixed number to improper fraction]

= \(\frac{7\ \times\ 30}{2\ \times\ 1}\)        [Multiplying both the numerators and denominators]

= \(7\times15\)      [Simplify]

= 105

Hence, John covers a total of 105 km in the month of November.

Example 4:
Find the result for the equation \(3\frac{1}{4}-1\frac{1}{2}\).

Solution:
The equation we have is \(3\frac{1}{4}-1\frac{1}{2}\)

Subtract the whole numbers = 3 – 1
= 2

Now, subtract the fractional parts = \(\frac{1}{4}-\frac{1}{2}\)

Since the given fractions have different denominators, let’s use equivalent fractions to make them same.

As we know, 4 is a multiple of 2, rewrite \(\frac{1}{2}\) as \(\frac{2}{4}\) by multiplying 4 with both numerator and denominator.

= \(\frac{1}{4}-\frac{2}{4}\)   [Rewrite \(\frac{1}{2}\) as \(\frac{2}{4}\) and simplify]

= \(\frac{-1}{4}\)

Then, add the whole number parts and fractional parts.

= \(2+(\frac{-1}{4})\)

= \(\frac{2}{1}-\frac{1}{4}\)

= \(\frac{8}{4}-\ \frac{1}{4}\)   [Rewrite \(\frac{2}{1}\) as \(\frac{8}{4}\) and simplify]

= \(\frac{7}{4}\)

Therefore, the result for the equation \(3\frac{1}{4}-1\frac{1}{2}\) is \(\frac{7}{4}\).