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Numbers Properties

by Sandi
(GA)











































Match the name of the number property used to get to each step from the previous step.

-5 + (1/2 + 5) · 2

1. -5 + (5 + 1/2 ) · 2 inverse property of multiplication
2. (-5 + 5) + 1/2 · 2 associative property
3. 0 + 1/2 · 2 commutative property
4. 1/2 · 2 identity property of addition
5. 1 inverse property of addition

Comments for Numbers Properties

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Apr 21, 2011
Numbers Properties
by: Staff


The question:

by Sandi
(GA)

Match the name of the number property used to get to each step from the previous step.

-5 + (1/2 + 5) • 2

1. -5 + (5 + 1/2 ) • 2 inverse property of multiplication
2. (-5 + 5) + 1/2 • 2 associative property
3. 0 + 1/2 • 2 commutative property
4. 1/2 • 2 identity property of addition
5. 1 inverse property of addition



The answer:

The steps shown 1 through 5 are not correct.


To simplify this expression, use the PEMDAS order of operations.

PEMDAS order tells you what to do first, second, . . . etc.

PEMDAS stands for: parentheses, exponents, multiplication, division, addition, subtraction

Step 1: evaluate PARENTHESES

PEMDAS order of evaluation: PARENTHESES, exponents, multiplication, division, addition, subtraction

(1/2 + 5) = 5.5


Step 2: evaluate EXPONENTS


PEMDAS order of evaluation: parentheses, EXPONENTS, multiplication, division, addition, subtraction

There area no exponents to evaluate.


Step 3: MULTIPLICATION


PEMDAS order of evaluation: parentheses, exponents, MULTIPLICATION, division, addition, subtraction

There is one multiplication process in your expression: (5.5) • 2

(5.5) • 2 = 11


At this stage in the simplification process, your expression now looks like this: -5 + 11



Step 4: DIVISION


PEMDAS order of evaluation: parentheses, exponents, multiplication, DIVISION, addition, subtraction

There are no parts of your expression which require division.


Step 5: evaluate ADDITION & SUBTRACTION

PEMDAS order of evaluation: parentheses, exponents, multiplication, division, ADDITION, SUBTRACTION

-5 + 11

= 6



The final answer is:

-5 + (1/2 + 5) • 2 = 6


Here are some parts of your original steps, along with the property associated with each:
(keep in mind that the 5 steps shown in your statement of the problem are not correct)



(1/2 + 5) = (5 + 1/2), Commutative PROPERTY

(5 + 1/2) • 2 = (5 * 2) + [(1/2) * 2], Distributive PROPERTY

[(1/2) * 2] = 1, multiplicative inverse



Thanks for writing.


Staff
www.solving-math-problems.com


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