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3 years ago

What is 8/12 in simplest form

Mathematics

2 answers:

DedPeter [7]3 years ago

5 0

Divide both by the least common denominator which is 4
The answer is 2/3

devlian [24]3 years ago

5 0

Hi, Minecraftwarrior!
2/3 is the simplest form for 8/12.
Divide the denominator and numerator by 4. You get 2/3! It cannot be simplified anymore!
I hope this helps;)

You might be interested in

which of the following is equivalent to 3 sqrt 32x^3y^6 / 3 sqrt 2x^9y^2 where x is greater than or equal to 0 and y is greater

Nutka1998 [239]

Answer:

$\frac{\sqrt[3]{16y^4}}{x^2}$

Step-by-step explanation:

The options are missing; However, I'll simplify the given expression.

Given

$\frac{\sqrt[3]{32x^3y^6}}{\sqrt[3]{2x^9y^2} }$

Required

Write Equivalent Expression

To solve this expression, we'll make use of laws of indices throughout.

From laws of indices $\sqrt[n]{a} = a^{\frac{1}{n}}$

So,

$\frac{\sqrt[3]{32x^3y^6}}{\sqrt[3]{2x^9y^2} }$ gives

$\frac{(32x^3y^6)^{\frac{1}{3}}}{(2x^9y^2)^\frac{1}{3}}$

Also from laws of indices

$(ab)^n = a^nb^n$

So, the above expression can be further simplified to

$\frac{(32^\frac{1}{3}x^{3*\frac{1}{3}}y^{6*\frac{1}{3}})}{(2^\frac{1}{3}x^{9*\frac{1}{3}}y^{2*\frac{1}{3}})}$

Multiply the exponents gives

$\frac{(32^\frac{1}{3}x*y^{2})}{(2^\frac{1}{3}x^{3}*y^{\frac{2}{3}})}$

Substitute $2^5$ for 32

$\frac{(2^{5*\frac{1}{3}}x*y^{2})}{(2^\frac{1}{3}x^{3}*y^{\frac{2}{3}})}$

$\frac{(2^{\frac{5}{3}}x*y^{2})}{(2^\frac{1}{3}x^{3}*y^{\frac{2}{3}})}$

From laws of indices

$\frac{a^m}{a^n} = a^{m-n}$

This law can be applied to the expression above;

$\frac{(2^{\frac{5}{3}}x*y^{2})}{(2^\frac{1}{3}x^{3}*y^{\frac{2}{3}})}$ becomes

$2^{\frac{5}{3}-\frac{1}{3}}x^{1-3}*y^{2-\frac{2}{3}}$

Solve exponents

$2^{\frac{5-1}{3}}*x^{-2}*y^{\frac{6-2}{3}}$

$2^{\frac{4}{3}}*x^{-2}*y^{\frac{4}{3}}$

From laws of indices,

$a^{-n} = \frac{1}{a^n}$ ; So,

$2^{\frac{4}{3}}*x^{-2}*y^{\frac{4}{3}}$ gives

$\frac{2^{\frac{4}{3}}*y^{\frac{4}{3}}}{x^2}$

The expression at the numerator can be combined to give

$\frac{(2y)^{\frac{4}{3}}}{x^2}$

Lastly, From laws of indices,

$a^{\frac{m}{n} = \sqrt[n]{a^m}$ ; So,

$\frac{(2y)^{\frac{4}{3}}}{x^2}$ becomes

$\frac{\sqrt[3]{(2y)}^{4}}{x^2}$

$\frac{\sqrt[3]{16y^4}}{x^2}$

Hence,

$\frac{\sqrt[3]{32x^3y^6}}{\sqrt[3]{2x^9y^2} }$ is equivalent to $\frac{\sqrt[3]{16y^4}}{x^2}$

8 0

3 years ago

I need help with this

lorasvet [3.4K]

I think the last one is right hope this helps

7 0

3 years ago

Underline all the ordered pairs (x,y) that are solutions to the equation y=2x+1.

Romashka [77]

Answer:

(3,7) (7,3) (−1,14) (0,1) (12,25)

(5,11) (0,12) (1,8) (12,0) (−1,−1)

Step-by-step explanation:

We have the following function:

$y = 2x+1$ .

We are going to check if each ordered pair is a solution.

(3,7)

If when $x = 3, y = 7$ , it is a solution.

$y = 2x + 1 = 2(3) + 1 = 7$

This ordered pair is a solution.

(7,3)

If when $x = 7, y = 3$ , it is a solution.

$y = 2x + 1 = 2(7) + 1 = 15$

This ordered pair is not a solution.

(-1,14)

If when $x = -1, y = 14$ , it is a solution.

$y = 2x + 1 = 2(-1) + 1 = -1$

This ordered pair is not a solution.

(0,1)

If when $x = 0, y = 1$ , it is a solution.

$y = 2x + 1 = 2(0) + 1 = 1$

This ordered pair is a solution.

(12,25)

If when $x = 12, y = 25$ , it is a solution.

$y = 2x + 1 = 2(12) + 1 = 25$

This ordered pair is a solution.

(5,11)

If when $x = 5, y = 11$ , it is a solution.

$y = 2x + 1 = 2(5) + 1 = 11$

This ordered pair is a solution.

(0,12)

If when $x = 0, y = 12$ , it is a solution.

$y = 2x + 1 = 2(0) + 1 = 1$

This ordered pair is not a solution.

(1,8)

If when $x = 1, y = 8$ , it is a solution.

$y = 2x + 1 = 2(1) + 1 = 3$

This ordered pair is not a solution.

(12,0)

If when $x = 12, y = 0$ , it is a solution.

$y = 2x + 1 = 2(12) + 1 = 25$

This ordered pair is not a solution.

(-1,-1)

If when $x = -1, y = -1$ , it is a solution.

$y = 2x + 1 = 2(-1) + 1 = -1$

This ordered pair is a solution.

3 0

3 years ago

How many liters of 80% alcohol solution and 30% alcohol solution must be mixed to obtain 15 liters of 50% alcohol solution?

Margaret [11]

set up a table (multiply across and add down - don't add the middle column). Use the equation created by the "Total" row to solve for the variable.

Quantity (times) % equals Total

Sol'n 1: x * .80 = (x)(.8)

Sol'n 2: 15 - x * .30 = (15 - x)(.3)

Total: 15 * .50 = .8x + .3(15 - x)

15(.5) = .8x + 4.5 - .3x

7.5 = .5x + 4.5

3.0 = .5x

6 = x

Answer: 6 liters of 80% and 9 liters of 30%

5 0

3 years ago

5. A monument casts a 78 ft. shadow at the same time that a vertical yardstick casts a 4.5 ft. shadow. How high is the monument?

rodikova [14]

Hello,

Using Thalès 's theorem:

Let's h the height of the monument.

$\dfrac{1}{h} =\dfrac{4.5}{78} \\\\h=\dfrac{78}{4.5} =\dfrac{156}{9} \approx{17.3\ (ft)}$

If you don't know what is the Thalès's theorem,

imagine that the similar triangles.

5 0

3 years ago