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What is the rule for adding fractions?
They have to have a common denominator
What is the state rule for dividing fractions?
Take the 2nd fraction, switch the denominator with the numerator, multiply across, simplify.
Changing fractions into percents?
To change a fraction to a percent you must first divide! Say you have 1/4 as your fraction. You have to divide the top number by the bottom number, which will give you 0.25. From there, to find a percent from a decimal, you always have to move the decimal point to the right TWICE. So, following that rule, you'll find the percent, which in this case is 25%. :) Hope this helped!
Why must mixed numbers be converted to improper fractions before multiplying or dividing?
You do not need to convert them, but it makes the calculation much simpler. For example to multiply 31/4 by 71/5: 31/4 = 3 + 1/4 71/5 = 7 + 1/5 31/4 x 71/5 = (3 + 1/4) x (7 + 1/5) = 3 x 7 + 3 x 1/5 + 1/4 x 7 + 1/4 x 1/5 = 21 + 3/5 + 1 3/4 + 1/20 = 21 + 12/20 + 1 + 15/20 + 1/20 = 22 + 18/20 = 232/5 Or, using improper fractions: 3 1/4 = 13/4 71/5 = 36/5 31/4 x 71/5 = 13/4 x 36/5 = (13 x 36)/(4 x 5) = (13 x 9)/5 = 117/5 = 232/5 Which with less calculations to be done is simpler and less liable to incur a mistake. With division the calculations would be horrendous whereas with improper fractions the "invert divisor and multiply" rule can be used very effectively: 31/4 / 71/5 13/4 / 36/5 = 13/4 x 5/36 = 65/144
Why should you simplify each radical in a radical expression before adding?
It is easier to work with simplified radicals just as it is easier to work with simplified fractions. A fundamental rule for math is to simplify whenever possible, as much as possible.
