When would the product of the denominators and the least common denominator of the denominators be the same?

Answers

Answer 1

Answer:

Example 1:

Find the common denominator of the fractions.

16 and 38

We need to find the least common multiple of 6 and 8 . One way to do this is to list the multiples:

6,12,18,24−−,30,36,42,48,...8,16,24−−,32,40,48,...

The first number that occurs in both lists is 24 , so 24 is the LCM. So we use this as our common denominator.

Listing multiples is impractical for large numbers. Another way to find the LCM of two numbers is to divide their product by their greatest common factor ( GCF ).

Example 2:

Find the common denominator of the fractions.

512 and 215

The greatest common factor of 12 and 15 is 3 .

So, to find the least common multiple, divide the product by 3 .

12⋅153=3 ⋅ 4 ⋅ 153=60

If you can find a least common denominator, then you can rewrite the problem using equivalent fractions that have like denominators, so they are easy to add or subtract.

Example 3:

Add.

512+215

In the previous example, we found that the least common denominator was 60 .

Write each fraction as an equivalent fraction with the denominator 60 . To do this, we multiply both the numerator and denominator of the first fraction by 5 , and the numerator and denominator of the second fraction by 4 . (This is the same as multiplying by 1=55=44 , so it doesn't change the value.)

512=512⋅55=2560215=215⋅44=860

512+215=2560+860                 =3360

Note that this method may not always give the result in lowest terms. In this case, we have to simplify.

=1130

The same idea can be used when there are variables in the fractions—that is, to add or subtract rational expressions .

Example 4:

Subtract.

12a−13b

The two expressions 2a and 3b have no common factors, so their least common multiple is simply their product: 2a⋅3b=6ab .

Rewrite the two fractions with 6ab in the denominator.

12a⋅3b3b=3b6ab13b⋅2a2a=2a6ab

Subtract.

12a−13b=3b6ab−2a6ab                   =3b − 2a6ab

Example 5:

Subtract.

x16−38x

16 and 8x have a common factor of 8 . So, to find the least common multiple, divide the product by 8 .

16⋅8x8=16x

The LCM is 16x . So, multiply the first expression by 1 in the form xx , and multiply the second expression by 1 in the form 22 .

x16⋅xx=x216x38x⋅22=616x

Subtract.

x16−38x=x216x−616x                  =x2 − 616x\


Related Questions

What is 54/72 in simplest form?

Answers

Answer:

3/4

Step-by-step explanation:

Answer:

3/4

Step-by-step explanation:

state if the three numbers can be the lengths of the sides of a triangle 7, 19, 9​

Answers

Answer:

Well i am not sure on that but i do know that the angle measures have to add up to 180 degrees hope that helps at least a little

Step-by-step explanation:

What are the roots of the equation x2 – 10x + 21 = 0?

Answers

Answer:

Step-by-step explanation:

H

alex is w years old. His sister claudia is three years younger than Alex. The product of their ages is 180 a) set up an equation to represent this information b) solve your equation (from a) to find alex's age​

Answers

Answer: The equation is w*(w-3)= 180 & Alex is 15 years old

Step-by-step explanation:

Alex= w years old

Claudia= (w-3) years old

a) Equation, w*(w-3)= 180

b) Now,

         w*(w-3)= 180

      ⇒ w²-3w-180= 0

      ⇒ (w+12)*(w-15)= 0

      ⇒ w= 15

Alex is 15 years old

Claudia is (15-3) = 12 years old

 

x intercepts of -12x^2+108x=h and the y intercept

Answers

Answer:

x: 0 or 9

y-int: 0

1. Un representante de ventas debe visitar 6 ciudades durante un viaje. a) Si hay 10 ciudades en el área geográfica que va a visitar ¿Cuántos grupos diferentes de seis ciudades podrá seleccionar? b) Suponga que las seis ciudades por visitar han sido designadas, pero no la secuencia en que se han de visitar ¿Cuántas secuencias posibles existen para las seis ciudades designadas?

Answers

Answer:

a) Hay 210 grupos diferentes de seis ciudades que el representante de ventas podrá seleccionar.

b) Hay 720 secuencias posibles existen para las seis ciudades designadas.

Step-by-step explanation:

a)  Se llama combinaciones de m elementos tomados de n en n a todas las agrupaciones posibles que pueden hacerse con los m elementos de forma que no entran todos los elementos , no importa el orden  y no se repiten los elementos. La combinación se calcula como:

[tex]C=\frac{m!}{n!*(m-n)!}[/tex]

En este caso m corresponde a las 10 ciudades en el área geográfica que va a visitar, mientras que n corresponde a las 6 ciudades que debe visitar un representante de venta durante un viaje.

Entonces:

[tex]C=\frac{10!}{6!*(10-6)!}=\frac{10!}{6!*4!}[/tex]

Considerando que el factorial ! indica que se deben multiplicar todos los números enteros y positivos que hay entre el número que aparece en la fórmula y el número 1, entonces la combinación dará como resultado:

C= 210

Hay 210 grupos diferentes de seis ciudades que el representante de ventas podrá seleccionar.

b) Se llama permutación de n elementos a cada una de las diferentes ordenaciones  que se pueden hacer con esos elementos.

Si se tiene un grupo de n objetos distintos, el número de maneras diferentes que podemos tomar un número r de objetos (r < n) del grupo, está dado por la fórmula de la permutación:

[tex]P=\frac{n!}{(n-r)!}[/tex]

Si m=n para calcular el total de permutaciones se utiliza la fórmula:

P= n!

En este caso se utiliza esta última expresión, ya que se desea calcular las permutaciones de 6 ciudades en 6 posiciones:

P=6!

P=720

Hay 720 secuencias posibles existen para las seis ciudades designadas.

Please help asap! I attached the image.

Answers

Step-by-step explanation:

[tex] {5}^{2} = {x}^{2} + {x}^{2} \\ {5}^{2} = {x}^{4} \\ 5 = \sqrt{ {x}^{4} } \\ 5 = {x}^{2} \\ x = \sqrt{5} =2.236068\\ [/tex]

At costco food court a family can purchase 4 hot dog meals for 6$ what is the cost per person

Answers

Answer:

$1.50

Step-by-step explanation:

Answer:

$1.5

Explanation:

6 / 4?

An architect built a scale model of a sports stadium using a scale in which 2 inches represents 30 feet. The height of the sports stadium is 180 feet. What is the height of the scale model in inches?

Answers

Answer:

12 inches

Step-by-step explanation:

Given the conversion factor;

2inches = 30feet

if the height of the building is 180feet, we are to find the height of the scale model in inches.

Let x = 180 feet.

Equating both;

2inches = 30feet

x inches = 180feet

Cross multiply;

30 * x = 2 * 180

30x = 360

x = 360/30

x = 12inches

Hence the height of the scale model in inches is 12inches

Answer: 60 in

Step-by-step explanation:Let x = 180 feet.

Equating both;

2 inches = 30 feet

x inches = 180 feet

Cross multiply;

30 * x = 2 * 180

30 x = 360

x = 360/30

x = 60 inches

What is the slope of all lines parallel to the line 4x - 5y = -1?

Answers

4/5 is the slope of all lines parallel
I only found one and the Slop is 4/5

Find the values of r and t.

Answers

The answer is b, r=24 and t = 24\|3

The perimeter of a rectangle is 37cm find X

Answers

I think the answer is 16=x

Which of the following equations has a slope of -3 and a y-intercept of 8?

y=−8−3x


y=8−3x

y=8x−3

y=−8x−3

Answers

Format: y = mx + b
m = slope, b = y intercept
Solution: y = -3x + 8
the second one, y=8-3x

Trying to get a 100 on every assigment because I wanna be top student in class :) So please help ​

Answers

Answer:

About 30%

Hope this helps :)

Answer:

30%

Step-by-step explanation:

5 times 4 = 20 (area)

100 divided by 20 = 5

5 times 6(the amount of shaded blocks) = 30

therefore its 30% of 100

multiple choice, plz help

Answers

B will be the correct answer

HELPPPP!!!!!!! TIMEDDDDD!!!!!!!! ASPPP!!!!!!

Which of the following is an arithmetic sequence?
3, 4, 6, 9, 13
1, 3, 6, 10, 15, 21
2, 5, 8, 11, 14
1, 2, 4, 8, 16

Answers

Answer:

1, 2, 4, 8, 16

Step-by-step explanation:

Each gets higher everytime you multiply by 2

Answer:

C or 3

Step-by-step explanation:

It is the only one going in a pattern or arithmetic sequence

2 + 3 = 5

5 + 3 = 8

8 + 3 = 11

11 + 3 = 14

The relationship is 3

Find the first four terms of the sequence given by the following.
a₁ = -3.5"-1 n=1, 2, 3

Answers

the first four terms of the sequence is 51,51.8,52.6,53.4

we can find first four terms by using formula given by

[tex]a_{n} =a_{1} +(n-1) *d[/tex]

[tex]a_{n}[/tex] = the nᵗʰ term in the sequence

[tex]a_{1[/tex] = the first term in the sequence

d = the common difference between terms

Arithmetic progression is a progression in which every term after the first is obtained by adding a constant value, called the common difference (d). So, to find the nth term of an arithmetic progression, we know an = a1 + (n – 1)d. a1 is the first term, a1 + d is the second term, the third term is a1 + 2d, and so on

an=51 + (n-1)*0.8, n=1, 2, 3...

a1 = 51 + (1 -1 ) * 0.8

a1 = 51

a2 = 51 + (2 - 1)*0.8

a2 = 51 + 0.8

a2 = 51.8

a3 = 51 + (3 - 1)*0.8

a3 = 51 + 2*0.8

a3 = 51 + 1.6

a3 = 52.6

a4 = 51 + (4 - 1)*0.8

a4 = 51 + 2.4

a4 = 53.4

Hence , the first four terms of the sequence is 51,51.8,52.6,53.4

the complete question is

Find the first four terms of the sequence given by the following.

an=51 + (n-1)*0.8, n=1, 2, 3...

learn more of sequence here

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If FGH=QRS, find the measure of Q.

Answers

Answer: 28

Step-by-step explanation: i got the same test

A parallelogram is drawn such that the diagonals are congruent. Which shape below would not fit this description?

Answers

some shape is defined by the shape of the object in which the shape is a sphere and not a triangle

The shape that would not fit this description is a trapezoid.

What is a trapezium?

It is a quadrilateral that has one pair of parallel sides and a height.

The area is calculated as 1/2 x the sum of the parallel sides x height.

Examples:

Area of a trapezium that has the parallel sides as 3 cm and 4 cm and a heght o 5 cm.

Area = 1/2 x (3 + 4) x 5

Area = 1/2 x 7 x 5

Area = 35/2 = 17.5 cm^2

We have,

A parallelogram is a four-sided shape where opposite sides are parallel and congruent.

If a parallelogram has diagonals that are congruent, it must be a rectangle.

Therefore, the shape that would not fit this description is any shape that is not a rectangle.

Out of the shapes given,

A trapezoid is not a rectangle and does not have diagonals that are congruent.

Therefore,

The shape is a trapezoid.

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the difference of 3 times a number and 7 is written how ?

Answers

3x-7 or Three x minus seven

What is the perimeter of the shape below?

Answers

Answer:

what are the units?

Step-by-step explanation:

depends on the side of 1 square

if it is 1 unit, perimeter is 22 units

Write a system of equations and solve. A chemist wants to make a 10% solution of fertilizer. How much water and how much of a 30% solution should the chemist mix to get 30 L of a 10% solution?

Answers

Answer:

x=10 L of .30 solution

x+y=30

y=20 L water

Step-by-step explanation:

what is 200 times 350=
pleser help

Answers

Answer:

70000

Step-by-step explanation:

im new to this btw ill give you crown

Answers

The slope of the graphed linear equation is a = 3/4.

What is the slope of the graphed linear function?

A general linear equation is of the form:

y = a*x + b

Where a and b are real numbers, a is the slope, and b is the y-intercept.

If a line passes through two points (x₁, y₁) and (x₂, y₂), then the slope of that linear equation is given by:

a = (y₂ - y₁)/(x₂ - x₁)

Now, we can look at the graph to identify two points on the line, we can use (20, 40) and (60, 70), using the above formula we can get the slope:

a = (70 - 40)/(60 - 20)

a = 30/40 = 3/4

The slope of the graphed linear equation is a = 3/4.

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YOU HAVE A SWELLING INJURY. DO YOU USE….
Heat or ice?

Answers

Answer:

Ice would be the correct answer.

Answer:

if u want go to the doctor but use ice but if its to cold use a little heat not too much tho

Step-by-step explanation:

If you have injured your neck and are experiencing swelling, you should ice the area for at least 72 hours. After icing, you can use heat to help any lingering pain. Tight neck muscles and old injuries can benefit from heat only, as long as there isn’t any swelling.

A contractor needs to buy nails to build a house. The nails come in small boxes and large boxes. Each small box has 50 nails and each large box has 400 nails. The contractor bought six more small boxes than large boxes, which altogether had 1200 nails. Create a system of equations to represent this situation. Define the variables that you use to write the system.

Answers

Answer:

https://brainly.com/question/14526835?referrer=searchResults#

some one already answered the question you have  

Step-by-step explanation:

A line contains the points (82, −96) and (87, −86).

What is the slope of the line in simplified form?

Answers

Answer:

The slope is 2.

Step-by-step explanation:

ΔX = X2 - X1 = 87 - 82 = 5

ΔY = Y2 - Y1 = -86 - (-96) = -86 + 96 = 10

ΔY/ΔX = 10/5 = 2/1 = 2


Hello, I am struggling a bit with this question please help

Answers

Answer:

-7.4

-2/3

⅔-0.1

0

4/8

2.7

5 1/9

29/4

Step-by-step explanation:

I hope this helped and if it did I would appreciate it if you marked me Brainliest. Thank you and have a nice day!

Answer:

Step-by-step explanation:

first put everything in decimal

-0.1,2.7,0.25,7.25,0,-7.4,5.667

lowest to greatest

-0.1,-7.5,0,0.25,2.7,5.667,7.25

-0.1,-7.25,0,4/8,2.7,51/9,29/4

What is equivalent to (6xp)+3

Answers

Answer:

1(6xp+3)

Step-by-step explanation:

Multiply

PLEASE HELP FAST!
Determine the domain of the relation graph below.

A.) (-4,2]
B.) [-4,2)
C.) [-1,5)
D.) [1,5]

Answers

Answer: The answer is option A.

Step-by-step explanation: A white, non colored dot means always use a ( bracket. A solid, colored dot means use the [ bracket. Now it's farthest left at -4, and farthest right at 2. Thus, option A

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