All categories

3 years ago

What is the least common denominator for adding the fractions 4/15, 1/12, and 3/8

2 answers:

5 0

I think you want the least common multipule (exg LCM of 2,3,4 is 12)

so we find the factors and include all of them so like this

15=3 times 5
12=2 times 2 times 3
8=2 times 2 times 2

so to include all of them we include 3 2's, 1 3 and 1 5 or 2 times 2 times 2 times 3 times 5 or 8 times 15 or 4 times 30 or 120

the LCM is 120

so 4/15=32/120
1/12=10/120
3/8=45/120

add 32/120+10/120+45/120=(32+10+45)/120=87/120

sladkih [1.3K]3 years ago

3 0

The least common denominator would be the least common multiple (LCM) of the denominators, 15 12 and 8.

To find the LCM, multiply two of the numbers together and test to see if the third one divides evenly into it.

15 x 8 = 120

120 ÷ 12 = 10

Because all three numbers go evenly into 120 (and 120 is the smallest number for which that is true), the least common denominator would be 120.

You might be interested in

A roulette wheel has 38 slots total, 36 of which are numbered 1 through 36, and 2 green slots labeled "0" and "00." For any spin

Morgarella [4.7K]

Answer:

Probability (Roulette ball not landing on red) = 10 / 19

Step-by-step explanation:

Given:

Number of total slots = 38

Number of red slots = 18

Number of black slots = 18

Number of green slots = 2

Find:

Probability (Roulette ball not landing on red)

Computation:

Probability (Roulette ball not landing on red) = 1 - Probability (Roulette ball landing on red)

Probability (Roulette ball not landing on red) = 1 - (18 / 38)

Probability (Roulette ball not landing on red) = 20 / 38

Probability (Roulette ball not landing on red) = 10 / 19

7 0

3 years ago

Pls, help me it has been a missing assignment for too long :/

Natasha2012 [34]

Answer:

Snail A: 0, 5, 10, 15, 20, 25, 30

Snail A travels at a rate of 30 inches in 1 hour or 30 inches per hour.

Snail B: 0, 3, 6, 9, 12, 15, 18

Snail B travels at a rate of 18 inches in 1 hour or 18 inches per hour.

Snail C: 0, 6, 12, 18, 24, 30, 36

Snail C travels at a rate of 36 inches in 1 hour or 36 inches per hour.

Snail D: 0, 4, 8, 12, 16, 20, 24

Snail D travels at a rate of 24 inches in 1 hour or 24 inches per hour.

3 0

3 years ago

A+b=180 A=-2x+115 B=-6x+169 What is the value of B?

natulia [17]

The answer is: " 91 " .
___________________________________________________
→ " B = 91 " .
__________________________________________________

Explanation:
__________________________________________________
Given:
__________________________________________________
" A + B = 180 " ;

"A = -2x + 115 " ; ↔ A = 115 − 2x ;

"B = - 6x + 169 " ; ↔ B = 169 − 6x ;
_____________________________________________________
METHOD 1)
_____________________________________________________
Solve for "x" ; and then plug the solved value for "x" into the expression given for "B" ; to solve for "B"
_____________________________________________________

(115 − 2x) + (169 − 6x) =

115 − 2x + 169 − 6x = ?

→ Combine the "like terms" ; as follows:

+ 115 + 169 = + 284 ;

− 2x − 6x = − 8x ;
_________________________________________________________
And rewrite as:

" − 8x + 284 " ;
_________________________________________________________
→ " - 8x + 284 = 180 " ;

Subtract: "284" from each side of the equation:

 → " - 8x + 284 − 284 = 180 − 284 " ;

to get:

→ " -8x = -104 ;

Divide EACH SIDE of the equation by "-8 " ;
to isolate "x" on one side of the equation; & to solve for "x" ;

→ -8x / -8 = -104/-8 ;

→ x = 13
__________________________________________________________
Now, to find the value of "B" :
__________________________________________________________
 "B = - 6x + 169 " ; ↔ B = 169 − 6x ;

↔ B = 169 − 6x ;

= 169 − 6(13) ; ===========> Plug in our "solved value, "13", for "x" ;

= 169 − (78) ;

= 91 ;

 B = " 91 " .
__________________________________________________
The answer is: " 91 " .
____________________________________________________
→ " B = 91 " .
____________________________________________________
Now; let us check our answer:
____________________________________________________
→ A + B = 180 ;
____________________________________________________
Plug in our "solved answer" ; which is "91", for "B" ; as follows:
________________________________________________________

→ A + 91 = ? 180? ;

↔ A = ? 180 − 91 ? ;

→ A = ? -89 ? Yes!
________________________________________________________
→ " A = -2x + 115 " ; ↔ A = 115 − 2x ;

Plug in our solved value for "x"; which is: "13" ;

" A = 115 − 2x " ;

→ A = ? 115 − 2(13) ? ;

→ A = ? 115 − (26) ? ;

→ A = ? 29 ? Yes!
_________________________________________________
METHOD 2)
_________________________________________________
Given:
__________________________________________________
" A + B = 180 " ;

"A = -2x + 115 " ; ↔ A = 115 − 2x ;

"B = - 6x + 169 " ; ↔ B = 169 − 6x ;

→ Solve for the value of "B" :
_______________________________________________________
A + B = 180 ;

→ B = 180 − A ;

→ B = 180 − (115 − 2x) ;

→ B = 180 − 1(115 − 2x) ; ==========> {Note the "implied value of "1" } ;
__________________________________________________________
Note the "distributive property" of multiplication:__________________________________________________ a(b + c) = ab + ac ; AND:
a(b − c) = ab − ac .________________________________________________________
Let us examine the following part of the problem:
________________________________________________________
→ " − 1(115 − 2x) " ;
________________________________________________________

→ " − 1(115 − 2x) " = (-1 * 115) − (-1 * 2x) ;

= -115 − (-2x) ;

= -115 + 2x ;
________________________________________________________
So we can bring down the: " {"B = 180 " ...}" portion ;

→and rewrite:
_____________________________________________________

→ B = 180 − 115 + 2x ;

→ B = 65 + 2x ;
_____________________________________________________
Now; given: "B = - 6x + 169 " ; ↔ B = 169 − 6x ;

→ " B = 169 − 6x = 65 + 2x " ;
______________________________________________________
→ " 169 − 6x = 65 + 2x "

Subtract "65" from each side of the equation; & Subtract "2x" from each side of the equation:

→ 169 − 6x − 65 − 2x = 65 + 2x − 65 − 2x ;

to get:

→ " - 8x + 104 = 0 " ;

Subtract "104" from each side of the equation:

→ " - 8x + 104 − 104 = 0 − 104 " ;

to get:

→ " - 8x = - 104 ;

Divide each side of the equation by "-8" ;
to isolate "x" on one side of the equation; & to solve for "x" ;

→ -8x / -8 = -104 / -8 ;

to get:

→ x = 13 ;
______________________________________________________

Now, let us solve for: " B " ; → {for which this very question/problem asks!} ;

→ B = 65 + 2x ;

Plug in our solved value, " 13 ", for "x" ;

→ B = 65 + 2(13) ;

= 65 + (26) ;

→ B = " 91 " .
_______________________________________________________
Also, check our answer:
_______________________________________________________
Given: "B = - 6x + 169 " ; ↔ B = 169 − 6x = 91 ;

When "x = 13 " ; does: " B = 91 " ?

→ Plug in our "solved value" of " 13 " for "x" ;

→ to see if: "B = 91" ; (when "x = 13") ;

→ B = 169 − 6x ;

= 169 − 6(13) ;

= 169 − (78)______________________________________________________
→ B = " 91 " .
______________________________________________________

6 0

3 years ago

Unit of Measurement, a punk/disco band, was signed up to play a benefit

vova2212 [387]

D because they played for two days so that makes you multiply the number of seconds by the same number

7 0

3 years ago

A newspaper carrier has $5.40 in change. He has six more quarters than dimes but five times as many nickles as quarters. How man

BigorU [14]

X= number of dimes
x+6= number of quarters
5(x+6)= number of nickels
$5.40= 540 cents

Add the number of each coin and set it equal to the total in cents.

x + (x + 6) + 5(x + 6)= $5.40
multiply 5 by parentheses; change dollar total to cents

x + (x + 6) + (5 * x) + (5 * 6)= 540

x + (x + 6) + 5x + 30= 540
combine like terms

7x + 36= 540
subtract 36 from both sides

7x= 504
divide both sides by 7

x= 72 dimes

x + 6= 78 quarters

5(x + 6)= 390 nickels

CHECK
72 + 78 + 390= 540
540= 540

ANSWER: There are 72 dimes, 78 quarters and 390 nickels.

Hope this helps! :)

5 0

3 years ago