How will you subtract multiply and divide fraction and mixed numbersexamples?

Answer 1

To add or subtract fractions the denominators must be the same.

If the denominators are different, convert them into equivalent fractions with the same denominator. Ideally the new denominator should be the lowest common multiples of the denominators, but a simple solution is to use the "butterfly" method:

1. Multiply the denominators together to create the new denominator

2. Multiple the numerator of the first fraction by the denominator of the second fraction to get the new first numerator

3. Multiple the numerator of the second fraction by the numerator of the first fraction to get the new second numerator.

The fractions are then added/subtracted by keeping the denominator and adding/subtracting the denominators, and simplify the result (by dividing the numerator and denominator by any common factors until the only common factor is 1).

eg 2/3 - 1/6 = (2x6)/(3x6) - (1x3)/(3x6) = 12/18 - 3/18 = (12-3)/18 = 9/18 = (1x9)/(2x9) = 1/2

To multiply fractions multiply the numerators together and multiply the denominators together and simplify.

eg 2/3 × 1/6 = (2×1)/(3×6) = 2/18 = (1x2)/(9x2) = 1/9

To divide fractions, invert the divisor and multiply as above.

eg 4/7 ÷ 2/3 = 4/7 × 3/2 = (4×3)/(7×2) = 12/14 = (2x6)/(2x7) = 6/7

To work with mixed numbers, it is easier to convert them into an improper fractions, solve as above, and convert any improper fraction back to a mixed number.

To convert a mixed number into an improper fraction multiply the whole number by the denominator and add the numerator to get the new numerator and keep the denominator.

eg 2 3/4 = (2x4+3)/4 = 11/4

To convert an improper fraction into a mixed number divide the numerator by the denominator to get a quotient and a remainder; the quotient is the whole number and the remainder is the numerator over the original denominator.

eg 11/4: 11 ÷ 4 = 2 r 3 → 11/4 = 2 3/4

This can be written as the reverse of the above conversion:

eg 11/4 = (2x4+3)/4 = 2 3/4

Though, normally only the first and last steps would be shown.

eg 4 1/5 ÷ 3/7 = (4x5+1)/5 ÷ 3/7 = 21/5 ÷ 3/7 = 21/5 × 7/3 = (21x7)/(5x3) = (3x7x7)/(5x3) = 49/5 = (9x5+4)/5 = 9 4/5