Answer :

semsee45

Answer:

  • 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

[tex]3\frac23-1\frac45[/tex]

convert to improper fractions:

[tex]\dfrac{3 \times 3+2}{3}-\dfrac{1 \times 5+4}{5}=\dfrac{11}{3}-\dfrac{9}{5}[/tex]

common denominator = 3 × 5 = 15, so:

[tex]\dfrac{11}{3}-\dfrac{9}{5}=\dfrac{11\times 5}{3\times 5}-\dfrac{9\times 3}{5\times 3}=\dfrac{55}{15}-\dfrac{27}{15}[/tex]

subtract:

[tex]\dfrac{55}{15}-\dfrac{27}{15}=\dfrac{55-27}{15}=\dfrac{28}{15}[/tex]

convert back to mixed fractions:

[tex]28 \div 15=1 \textsf{ remainder }13=1 \frac{13}{15}[/tex]

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.

  • ⇒ [tex]4 \frac{2}{5} - 3 \frac{3}{8}[/tex]

Step-1: Convert the fractions to improper fraction:

  • ⇒ [tex]4 \frac{2}{5} - 3 \frac{3}{8}[/tex]
  • ⇒ [tex]\frac{(4)(5) + 2}{5} - \frac{(3)(8) + 3}{8}[/tex]
  • ⇒ [tex]\frac{20 + 2}{5} - \frac{24+ 3}{8}[/tex]
  • ⇒ [tex]\frac{22}{5} - \frac{27}{8}[/tex]

Step-2: Make the denominators same:

  • ⇒ [tex]\frac{22}{5} - \frac{27}{8}[/tex]
  • ⇒ [tex]\frac{(22)(8)}{(5)(8)} - \frac{(27)(5)}{(8)(5)}[/tex]
  • ⇒ [tex]\frac{176}{40} - \frac{135}{40}[/tex]

Step-3: Subtract:

  • ⇒ [tex]\frac{176}{40} - \frac{135}{40}[/tex]
  • ⇒ [tex]\frac{41}{40}[/tex]

Step-4: Convert the fraction to mixed fraction:

  • ⇒ [tex]\frac{41}{40}[/tex]
  • ⇒ [tex]\frac{40}{40} + \frac{1}{40}[/tex]
  • ⇒ [tex]1 + \frac{1}{40}[/tex]
  • ⇒ [tex]1\frac{1}{40}[/tex]