Question

Can anybody explain how to subtract mixed fractions?

Answer 1

How do we subtract mixed fractions?

To subtract mixed fractions, we must follow the steps:

1. Convert the mixed fraction to improper fraction.

2. Multiply the denominator and the numerator by the LCM of the denominators to make the denominators same. P.S: (If the denominators are the same, you can skip this step).

3. Simplify the fractions. (The denominators do not change).

4. (Optional) Convert the fractions to mixed fraction.

Solving an example:

Let's take an example.

• ⇒
  `4 (2)/(5) - 3 (3)/(8)`

Step-1: Convert the fractions to improper fraction:

• ⇒
  `4 (2)/(5) - 3 (3)/(8)`
• ⇒
  `((4)(5) + 2)/(5) - ((3)(8) + 3)/(8)`
• ⇒
  `(20 + 2)/(5) - (24+ 3)/(8)`
• ⇒
  `(22)/(5) - (27)/(8)`

Step-2: Make the denominators same:

• ⇒
  `(22)/(5) - (27)/(8)`
• ⇒
  `((22)(8))/((5)(8)) - ((27)(5))/((8)(5))`
• ⇒
  `(176)/(40) - (135)/(40)`

Step-3: Subtract:

• ⇒
  `(176)/(40) - (135)/(40)`
• ⇒
  `(41)/(40)`

Step-4: Convert the fraction to mixed fraction:

• ⇒
  `(41)/(40)`
• ⇒
  `(40)/(40) + (1)/(40)`
• ⇒
  `1 + (1)/(40)`
• ⇒
  `1(1)/(40)`

Answer 2

• convert the mixed fractions to improper fractions (where the numerator is greater than or equal to the denominator): multiply the whole number part by the fraction's denominator, add that to the numerator, write the result on top of the denominator.
• if the denominators are not the same, work out the common denominator and rewrite the fractions with the same denominators
• subtract by subtracting the numerators and writing the result over the denominator
• convert back to mixed fractions by dividing the numerator by the denominator, write down the whole number answer, write down the remainder above the denominator.

Example

`3\frac23-1\frac45`

convert to improper fractions:

`(3 * 3+2)/(3)-(1 * 5+4)/(5)=(11)/(3)-(9)/(5)`

common denominator = 3 × 5 = 15, so:

`(11)/(3)-(9)/(5)=(11* 5)/(3* 5)-(9* 3)/(5* 3)=(55)/(15)-(27)/(15)`

subtract:

`(55)/(15)-(27)/(15)=(55-27)/(15)=(28)/(15)`

convert back to mixed fractions:

`28 / 15=1 \textsf{ remainder }13=1 (13)/(15)`