alt="math"/> has the larger denominator and can be written as Q.
A. First find the common denominator, 24, and then complete the addition:
Q.
A. You need a common denominator of 30:
The whole number parts are separated from the fractional parts to keep the numbers in the computations smaller. Be sure to apply the subtraction to both the whole number and fraction when needed.
Q.
A. In this problem, you see another option: you can change both mixed numbers to improper fractions. The common denominator is 56:
27
28
29
30
31
Multiplying and dividing fractions
Multiplying fractions is really a much easier process than adding or subtracting fractions, because you don’t have to find a common denominator. Furthermore, you can take some creative steps and reduce the fractions before you even multiply them.
When multiplying fractions, you can pair up the numerator of any fraction in the problem with the denominator of any other fraction; then divide each by the same number (reduce). Doing so saves you from having large numbers to multiply and then to reduce later.
Yes, multiplying fractions is a tad easier than adding or subtracting them. Multiplying is easier because you don’t need to find a common denominator first. The only catch is that you have to change any mixed numbers to improper fractions. Then, at the end, you may have to change the fraction back again to a mixed number. Small price to pay.
When multiplying fractions, follow these steps:
1 Change all mixed numbers to improper fractions.
2 Reduce any numerator-denominator combinations, if possible.
3 Multiply the numerators together and the denominators together.
4 Reduce the answer if necessary.
Here’s an example: Suppose Sadie worked
Write the problem as
The product
But
Dividing fractions is as easy as (dividing) pie — that is, dividing the pie into enough pieces so that everybody at your table gets an equal share. Actually, dividing fractions uses the same techniques as multiplying fractions, except that there’s an additional “first step”: the numerator and the denominator of the second fraction first have to change places — the fraction does a “flip.”
When dividing fractions:
1 Change all mixed numbers to improper fractions.
2 Flip the second fraction, placing the bottom number on top and the top number on the bottom.
3 Change the division sign to multiplication.
4 Continue as with the multiplication of fractions.
The flip of a fraction is called its reciprocal. All real numbers except 0 have a reciprocal. The product of a number and its reciprocal is equal to 1.
Consider this example: If you buy
