Algebra I All-in-One For Dummies. Mary Jane Sterling
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Название: Algebra I All-in-One For Dummies

Автор: Mary Jane Sterling

Издательство: John Wiley & Sons Limited

Жанр: Математика

Серия:

isbn: 9781119843061

isbn:

СКАЧАТЬ alt="math"/> has the larger denominator and can be written as math or math or math, and so on. You can stop at math because 3 divides 21 evenly: math and math. Add the numerators to get the total designation to charity in Jane’s will: math. Subtract that total from the whole of Jane’s proceeds to find what portion is allotted to her children: math. Jane’s children will be awarded math of her estate.

      Q. math

      A. First find the common denominator, 24, and then complete the addition:

math

      Q. math

      A. You need a common denominator of 30:

math

      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.

math

      Q. math

      A. In this problem, you see another option: you can change both mixed numbers to improper fractions. The common denominator is 56:

math

      27yourturn math

      29 math

      30 math

      31 math

      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 math hours at time-and-a-half. How many hours will she get paid for?

      Write the problem as math and then rewrite the mixed numbers as improper fractions. math. Reducing the fractions before multiplying can make multiplying the fractions easier. Smaller numbers are more manageable, and if you reduce the fractions before you multiply, you don’t have to reduce them afterward.

      The product math has a 32 in the first numerator and a 2 in the second denominator. Even though the 32 and 2 aren’t in the same fraction, you can reduce them because this is a multiplication problem. Multiplication is commutative, meaning that it doesn’t matter what order you multiply the numbers. You can pretend that the 32 and 2 are in the same fraction. So, dividing the first numerator by 2 and the second denominator by 2, you get

math

      But math has a 3 in the first denominator and a 3 in the second numerator, so you can divide by 3: math.

      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 math pounds of sirloin steak and СКАЧАТЬ