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Operations Study Guide: GED Math

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Updated on Mar 23, 2011

Practice problems for these concepts can be found at:

Numbers and Operations Practice Problems: GED Math

Choosing an Operation

Often a problem will tell you exactly which operation you should do. However, sometimes you will have to translate the words in a word problem into the operations. Look for these clues when you have to choose the operations.

You add (+) when you are asked to

• find a sum
• find a total
• combine amounts
Key words to look for:
• sum
• total
• all together

You subtract (–) when you are asked to

• find a difference
• take away an amount
• compare quantities
Key words to look for:
• difference
• take away
• how many more than
• how many fewer than
• how much less than
• how much is left over

You multiply (×) when you are asked to

• find a product
• add the same number over and over
Key words to look for:
• product
• times

You divide (÷) when you are asked to

• find a quotient
• split an amount into equal parts
Key words to look for:
• quotient
• per
Examples
1. Add the product of 6 and 3 to the sum of 10 and 4.
2. To solve this problem, begin by translating the words into math symbols. You know from the list of clues that the word product indicates multiplication. So you will need to multiply 6 and 3. You also know that sum indicates addition.You could write the problem like this: 6 × 3 + 10 + 4.

Now, follow the order of operations. Multiply 6 and 3: 18 + 10 + 4.

Add in order from left to right: 28 + 4 = 32. The answer is 32.

3. Missy and Amy went to a movie at the theater. They shared a large popcorn. Each girl paid for her own drink. The movie cost \$6.25. The popcorn cost \$4.50. Each drink cost \$2. How much did each girl pay?
4. Begin by translating the words into math symbols. The cost of the popcorn should be divided between the two girls. So, each girl paid the following: \$6.25 + (\$4.50 ÷ 2) + \$2.

Now, follow the order of operations. Do operations in parentheses first: \$6.25 + (\$2.25) + \$2. Add in order from left to right: \$8.50 + \$2 = \$10.50.

Each girl paid \$10.50 for the movie and refreshments.

Order of Operations

The basic operations of real numbers include addition, subtraction, multiplication, division, and exponentiation. Often, in expressions, there are grouping symbols—usually shown as parentheses—which are used to make a mathematical statement clear. In math, there is a predefined order in which you perform operations. This is an agreed-upon order that must be used. For the five basic operations, the order is:

• First, perform all operations enclosed in parentheses.
• Second, evaluate all exponents. (See Chapter 5 for a discussion of exponents.)
• Third, perform any multiplication and division, in order, working from left to right.
• Finally, evaluate any addition and subtraction, in order, working from left to right.

Examples
1. 8 + 15 × 3
2. There are no parentheses or exponents, so evaluate multiplication first: 15 × 3 = 45. Now perform the addition: 8 + 45 = 53.

3. 7 + 24 ÷ 6 × 10
4. There are no parentheses or exponents, so evaluate multiplication and division from left to right. First, do the division: 24 ÷ 6 = 4. Next, perform multiplication: 4 × 10 = 40. Finally, perform addition: 7 + 40 = 47.

5. (36 + 64) ÷ (18 – 20)
6. First, evaluate the parentheses, from left to right: (36 + 64) = 100 and (18 – 20) = –2. Now, do the division: 100 ÷ –2 = –50.

Practice problems for these concepts can be found at:

Numbers and Operations Practice Problems: GED Math

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