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Translate the phrase into an algebraic expression: “the quotient of 3 x and 8 .”

Solution

The keyword is quotient ; it tells us that the operation is division. Look for the words of and and to find the numbers to divide.

The quotient of 3 x and 8 .

This tells us that we need to divide 3 x by 8 . 3 x 8

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Translate the phrase into an algebraic expression: the quotient of 9 s and 14 .

9 s 14

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Translate the phrase into an algebraic expression: the quotient of 5 y and 6 .

5 y 6

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Translate the phrase into an algebraic expression: the quotient of the difference of m and n , and p .

Solution

We are looking for the quotient of the difference of m and , and p . This means we want to divide the difference of m and n by p .

m n p
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Translate the phrase into an algebraic expression: the quotient of the difference of a and b , and c d .

a b c d

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Translate the phrase into an algebraic expression: the quotient of the sum of p and q , and r .

p + q r

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Simplify complex fractions

Our work with fractions so far has included proper fractions, improper fractions, and mixed numbers. Another kind of fraction is called complex fraction    , which is a fraction in which the numerator or the denominator contains a fraction.

Some examples of complex fractions are:

6 7 3 3 4 5 8 x 2 5 6

To simplify a complex fraction, remember that the fraction bar means division. So the complex fraction 3 4 5 8 can be written as 3 4 ÷ 5 8 .

Simplify: 3 4 5 8 .

Solution

3 4 5 8
Rewrite as division. 3 4 ÷ 5 8
Multiply the first fraction by the reciprocal of the second. 3 4 · 8 5
Multiply. 3 · 8 4 · 5
Look for common factors. 3 · · 2 · 5
Remove common factors and simplify. 6 5
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Simplify: 3 7 6 11 .

11 14

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Simplify a complex fraction.

  1. Rewrite the complex fraction as a division problem.
  2. Follow the rules for dividing fractions.
  3. Simplify if possible.

Simplify: 6 7 3 .

Solution

6 7 3
Rewrite as division. 6 7 ÷ 3
Multiply the first fraction by the reciprocal of the second. 6 7 · 1 3
Multiply; the product will be negative. 6 · 1 7 · 3
Look for common factors. · 2 · 1 7 ·
Remove common factors and simplify. 2 7
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Simplify: 8 7 4 .

2 7

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Simplify: 3 9 10 .

10 3

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Simplify: x 2 x y 6 .

Solution

x 2 x y 6
Rewrite as division. x 2 ÷ x y 6
Multiply the first fraction by the reciprocal of the second. x 2 · 6 x y
Multiply. x · 6 2 · x y
Look for common factors. · 3 · · · y
Remove common factors and simplify. 3 y
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Simplify: a 8 a b 6 .

3 4 b

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Simplify: p 2 p q 8 .

4 q

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Simplify: 2 3 4 1 8 .

Solution

2 3 4 1 8
Rewrite as division. 2 3 4 ÷ 1 8
Change the mixed number to an improper fraction. 11 4 ÷ 1 8
Multiply the first fraction by the reciprocal of the second. 11 4 · 8 1
Multiply. 11 · 8 4 · 1
Look for common factors. 11 · · 2 · 1
Remove common factors and simplify. 22
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Simplify: 5 7 1 2 5 .

25 49 .

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Simplify: 8 5 3 1 5 .

1 2

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Simplify expressions with a fraction bar

Where does the negative sign go in a fraction? Usually, the negative sign is placed in front of the fraction, but you will sometimes see a fraction with a negative numerator or denominator. Remember that fractions represent division. The fraction 1 3 could be the result of dividing −1 3 , a negative by a positive, or of dividing 1 −3 , a positive by a negative. When the numerator and denominator have different signs, the quotient is negative.

Negative 1 over positive 3 is equal to negative one third. Negative over positive equals negative. Positive 1 over negative 3 is equal to negative one third. Positive over negative equals negative.

If both the numerator and denominator are negative, then the fraction itself is positive because we are dividing a negative by a negative.

Questions & Answers

show that the set of all natural number form semi group under the composition of addition
Nikhil Reply
what is the meaning
Dominic
explain and give four Example hyperbolic function
Lukman Reply
_3_2_1
felecia
⅗ ⅔½
felecia
_½+⅔-¾
felecia
The denominator of a certain fraction is 9 more than the numerator. If 6 is added to both terms of the fraction, the value of the fraction becomes 2/3. Find the original fraction. 2. The sum of the least and greatest of 3 consecutive integers is 60. What are the valu
SABAL Reply
1. x + 6 2 -------------- = _ x + 9 + 6 3 x + 6 3 ----------- x -- (cross multiply) x + 15 2 3(x + 6) = 2(x + 15) 3x + 18 = 2x + 30 (-2x from both) x + 18 = 30 (-18 from both) x = 12 Test: 12 + 6 18 2 -------------- = --- = --- 12 + 9 + 6 27 3
Pawel
2. (x) + (x + 2) = 60 2x + 2 = 60 2x = 58 x = 29 29, 30, & 31
Pawel
ok
Ifeanyi
on number 2 question How did you got 2x +2
Ifeanyi
combine like terms. x + x + 2 is same as 2x + 2
Pawel
x*x=2
felecia
2+2x=
felecia
×/×+9+6/1
Debbie
Q2 x+(x+2)+(x+4)=60 3x+6=60 3x+6-6=60-6 3x=54 3x/3=54/3 x=18 :. The numbers are 18,20 and 22
Naagmenkoma
Mark and Don are planning to sell each of their marble collections at a garage sale. If Don has 1 more than 3 times the number of marbles Mark has, how many does each boy have to sell if the total number of marbles is 113?
mariel Reply
Mark = x,. Don = 3x + 1 x + 3x + 1 = 113 4x = 112, x = 28 Mark = 28, Don = 85, 28 + 85 = 113
Pawel
how do I set up the problem?
Harshika Reply
what is a solution set?
Harshika
find the subring of gaussian integers?
Rofiqul
hello, I am happy to help!
Shirley Reply
please can go further on polynomials quadratic
Abdullahi
hi mam
Mark
I need quadratic equation link to Alpa Beta
Abdullahi Reply
find the value of 2x=32
Felix Reply
divide by 2 on each side of the equal sign to solve for x
corri
X=16
Michael
Want to review on complex number 1.What are complex number 2.How to solve complex number problems.
Beyan
yes i wantt to review
Mark
16
Makan
x=16
Makan
use the y -intercept and slope to sketch the graph of the equation y=6x
Only Reply
how do we prove the quadratic formular
Seidu Reply
please help me prove quadratic formula
Darius
hello, if you have a question about Algebra 2. I may be able to help. I am an Algebra 2 Teacher
Shirley Reply
thank you help me with how to prove the quadratic equation
Seidu
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Opoku
what is math number
Tric Reply
4
Trista
x-2y+3z=-3 2x-y+z=7 -x+3y-z=6
Sidiki Reply
can you teacch how to solve that🙏
Mark
Solve for the first variable in one of the equations, then substitute the result into the other equation. Point For: (6111,4111,−411)(6111,4111,-411) Equation Form: x=6111,y=4111,z=−411x=6111,y=4111,z=-411
Brenna
(61/11,41/11,−4/11)
Brenna
x=61/11 y=41/11 z=−4/11 x=61/11 y=41/11 z=-4/11
Brenna
Need help solving this problem (2/7)^-2
Simone Reply
x+2y-z=7
Sidiki
what is the coefficient of -4×
Mehri Reply
-1
Shedrak
A soccer field is a rectangle 130 meters wide and 110 meters long. The coach asks players to run from one corner to the other corner diagonally across. What is that distance, to the nearest tenths place.
Kimberly Reply
Jeannette has $5 and $10 bills in her wallet. The number of fives is three more than six times the number of tens. Let t represent the number of tens. Write an expression for the number of fives.
August Reply
What is the expressiin for seven less than four times the number of nickels
Leonardo Reply
How do i figure this problem out.
how do you translate this in Algebraic Expressions
linda Reply
why surface tension is zero at critical temperature
Shanjida
I think if critical temperature denote high temperature then a liquid stats boils that time the water stats to evaporate so some moles of h2o to up and due to high temp the bonding break they have low density so it can be a reason
s.
Need to simplify the expresin. 3/7 (x+y)-1/7 (x-1)=
Crystal Reply
. After 3 months on a diet, Lisa had lost 12% of her original weight. She lost 21 pounds. What was Lisa's original weight?
Chris Reply
Practice Key Terms 1

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Source:  OpenStax, Prealgebra. OpenStax CNX. Jul 15, 2016 Download for free at http://legacy.cnx.org/content/col11756/1.9
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