1. |-6 - 10| 2. 3 + 4(8 (3.5 - 20) - 41) 3. 6 + 1/8 / 3/8 4. (13 - 5(3 - 7)^2 ) Help! Please explain & show the work.This is 9th grade math

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ishpiro's profile pic

ishpiro | College Teacher | (Level 1) Educator

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1) |-6 - 10| = ?

In this expression, the straight lines || mean "absolute value". The absolute value of a number is the distance from that number on the number line to 0. Thus, it is always positive.

To evaluate any expression containing absolute value, always calculate whatever is inside the absolute value lines first. In respect to the order of operations, absolute value is a grouping symbol, just like parenthesis.

Here, inside the absolute value lines is the expression -6 - 10 = -16.

-16 is the negative number, located 16 units to the left of 0 on the number line. The distance between -16 and 0 is 16 units.

|-16| = 16

|-6 - 10| = 16

2) 3 + 4(8(3.5 - 20) - 41)

This expression contains parenthesis within the parenthesis. According to the order of operations agreement, the inside parenthesis needs to be evaluated first:

3.5 - 20 = - 16.5

Now the outside parenthesis contain 8(-16.5) - 41

8(-16.5) =  -132

-132 - 41 = -173

The original expression now becomes 3 + 4(-173). Perform multiplication first, according to the order of operations:

4(-173) = -692

3 + (-692) = -689

3 + 4(8(3.5 - 20) - 41) = -689

3) `6 + (1/8)/(3/8)`

This expression contains two operations: addition and division. According to the order of operations, perform the division of two fractions first.

To divide two fractions, multiply the first fraction by the reciprocal of the second fraction:

`(1/8)/(3/8) = (1/8)*(8/3) = (1*8)/(8*3)`

The common factor of 8 cancels from the denominator and the numerator, so the result is

`(1/8)/(3/8) = 1/3`

Now the addition can be performed: `6 + 1/3 = 6 1/3`

`6 + (1/8)/(3/8) = 6 1/3`

4) 13 - 5(3 - 7)^2

To evaluate this expression, recall the order of operations agreement:

1) Parenthesis

2) Exponents

3) Multiplication/Division, from left to right

4) Addition/Subtraction, from left to right

Consider the expression above:

1) Parenthesis: (3 - 7) = -4

The expression is now 13 - 5(-4)^2

2) Exponent: (-4)^2 = (-4)(-4) = 16

The expression is now 13 - 5(16)

3) Multiplication: 5(16) = 80

4) Finally, subtraction: 13 - 80 = -67.

Thus, 13 - 5(3 - 7)^2 = -67.

atyourservice's profile pic

atyourservice | Student, Grade 11 | (Level 3) Valedictorian

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1. |-6 - 10|

Those lines around the problem are absolute value lines. This line indicates that when you get an answer, the result should be turned into a positive number. Why? Because absolute value means how far from zero a number is, and you can't be a negative away from zero.  -10 is 10 spaces away from 0 just like 10 is 10 spaces away from 0

first you solve the number inside:

-6 - 10 = -16

since it is  l-16l  the answer will be 16 because -16 is 16 spaces away from 0

2. 3 + 4(8 (3.5 - 20) - 41)

the first thing you do is take care of the parenthesis:

(8 (3.5 - 20) - 41)

distribute the 8 to 3.5 and -20, you will end up with:

((28 - 160) - 41)

now get rid of the parenthesis around 28 and -160

(28-160-41)

solve this:

-173

now look at the problem as a whole again:

2. 3 + 4(-173)

Distribute the 4 to -173

3 + (-692)

which is the same as:

3 - 692 = -689

3. 6 + (1/8) / (3/8)

Since we are dividing a fraction by a fraction we flip the reciprocal and multiply:

`1/8 xx 8/3 = 8/24 = 1/3`

6 + `1/3 ` = `6 ` `1/3`

or you can turn 1/3 into a decimal:

1/3 = .33

6 + .33 = 6.33

4. (13 - 5(3 - 7)^2 ) 

You use pemdas for a problem like this. Pemdas stands for Parentheses,Exponents,(Multiplication,Division),(Addition,Subtraction)

the reason i put parentheses around m,d & a,s is because it doesnt matter what order you do those paired together if you have them in a problem:

Take care of the parentheses:

5(3 - 7)^2

5(-4)^2

Exponent:

(13 -5(16))

Multiplication -5(16):

(13-80)

Subtraction:

-67 

udonbutterfly's profile pic

udonbutterfly | Student, College Freshman | (Level 1) Valedictorian

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1) |-6 - 10|

Anything that happens to be inside absolute value will always be positive so |-a| will always equal a. So with this question you are going to add the contents inside together since they are both negative. Sometimes it helps for people to see the question asked as -6 + (-10) so the answer will be -16 which is inside absolute value so |-16|= 16

2) 3 + 4(8 (3.5 - 20) - 41)

Let's take this problem step by step using Please Excuse My Dear Aunt Sally which stands for: Parentheses, Exponents, Multiplication, Division, Addition, and Subtraction. 

First we are going to subtract 3.5 from - 20 you will get -16.5

then you are going to multiply -16.5 by 8 which will give you -132

3 + 4(-132 - 41) You will then add the -132 and the -42

3 + 4(-173) Now multiply 4 by 173

3 + (-692) Now add subtract the -692 by the positive 3 and you'll get

-689

3) 6 + 1/8 / 3/8

This is simple we are going to take the second fraction and flip that way you can multiply it.

6 + 1/8 x 8/3

6 + 8/24 Simplify it!

6 + 1/3 Turn 6 into a fraction by multiplying it by 3 and making 3 the denominator

18/3 + 1/3 add them!

19/3 is your answers.

4) (13 - 5(3 - 7)^2 )

Again we're going to use PEMDAS again and start with what's I the parentheses

(13 - 5(-4)^2 ) Now square the -4

(13 - 5(16) multiply the 16 by 5

13 -80 subtract

-67 is your answer

malkaam's profile pic

malkaam | Student, Undergraduate | (Level 1) Valedictorian

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1. |-6 - 10|

|-16|

16 Answer

2. 3 + 4(8 (3.5 - 20) - 41)

The rule of BODMAS ( Brackets of Division Multiplication Addition Subtraction) is applied.

3+4(8(-16.5)-41)

3+4(-132-41)

3+4(-173)

3-692

-689 Answer

3. 6 + 1/8 / 3/8

6+1/8*8/3

6+1/3

18/3+1/3

19/3

6.33 Answer

4. (13 - 5(3 - 7)^2 )

(13-5(-4)^2)

(13-5(16))

13-80

-67 Answer

glendamaem's profile pic

glendamaem | Student | (Level 1) Honors

Posted on

1. |-6 - 10|

    |-16| = 16

2. 3 + 4(8 (3.5 - 20) - 41)

    3 + 4(8(-16.5)-41)

    3 + 4((-132)-41)

    3 + 4(-173)

    3 + (-692) = -689

3. 6 + 1/8 / 3/8

    6 + (1/8 x 8/3)

    6 + (1/3)

    18/3 + 1/3

    19/3 = 6 1/3 or 6.33

4. (13 - 5(3 - 7)^2 )

     (13-5(-4)^2)

    (13-5(16))

    (13-80)

    (-67) = -67

rachellopez's profile pic

rachellopez | Student, Grade 12 | (Level 1) Valedictorian

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1. |-6 - 10|

The bars around this problem are called absolute value bars. All you do is solve the problem like normal and whatever value you get will be made positive.

-6-10=-16

|-16|=16

2. 3 + 4(8 (3.5 - 20) - 41)

If you follow the gulls of PEMDAS, you solve things in the parentheses first.

2.3+4(8(-16.5)-41)

For the next step, you want to stay in the parentheses, but do the multiplication BEFORE the subtraction. 

2.3+4(-132-41)

2.3+4(-173)

Now multiply the -173 and the 4. 

2.3+(-692)

=-689.7

3. 6 + 1/8 / 3/8

For this problem you need to put the 6 over 1, so you'll have all fractions and then get a common denominator. 

`(6)/(1) + ((1)/(8))/((3)/(8))`

you can fix the fraction over a fraction by multiplying 1/8 by the reciprocal (flipped fraction) 8/3.

`(6)/(1)+((1)/(8))((8)/(3))`

`(6)/(1)+(8)/(24)`

`(6)/(1)+(1)/(3)`

To get the common denominator, you will only have to multiply 6/1 by 3/3. 

`((6)/(1))((3)/(3))+(1)/(3)`

`(18)/(3)+(1)/(3)`

`=(19)/(3)` or `6((1)/(3))`

4. (13 - 5(3 - 7)^2 )

This problem also requires the rules of PEMDAS. Parentheses first, then exponents, multiplication, and so on. (Do the parentheses that are on the inside first). 

(13-5(-4)^2)

Now the exponent

(13-5(16))

Multiplication

(13-(80))

=-67

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