Describe how to add, subtract, multiply and divide rational numbers.
To add, subtract, multiply and divide rational numbers, follow the steps below:
1. To add or subtract rational numbers, make sure the denominators are the same. If not, find the least common multiple (LCM) of the denominators and convert each fraction to an equivalent fraction with the common denominator. Then add or subtract the numerators and simplify the fraction if possible.
Example:
To add 2/3 and 1/4, find the LCM of 3 and 4, which is 12. Convert the fractions to have a denominator of 12:
2/3 = 8/12 and 1/4 = 3/12
Then add the numerators:
8/12 + 3/12 = 11/12
2. To multiply rational numbers, multiply the numerators together and the denominators together. Simplify the fraction if possible.
Example:
To multiply 2/3 and 5/4:
2/3 x 5/4 = (2 x 5)/(3 x 4) = 10/12 = 5/6
3. To divide rational numbers, invert the second fraction (the divisor) and multiply it by the first fraction (the dividend). Simplify the resulting fraction if possible.
Example:
To divide 2/3 by 5/4:
2/3 ÷ 5/4 = 2/3 x 4/5 = (2 x 4)/(3 x 5) = 8/15