How to combine fraction

Answers

Answer 1

Answer: $\Large \frac { x }{ y }$ $\begin{matrix} \rightarrow numerator \n \rightarrow denominator \end{matrix}$

If two (or more) fractions have the same number as their denominator, you can just go ahead and add their numerators, without changing the denominator. For example:

$\frac { 1 }{ 2 }$ and $\frac { 4 }{ 2 }$ has the same number (2) as their denominator. So we will add their numerators, without changing the denominator.

$\frac { 1 }{ 2 } +\frac { 4 }{ 2 } \quad =\quad \frac { 1+4 }{ 2 } \quad =\quad \frac { 5 }{ 2 }$

So we added the numerators (1 + 4 = 5) and kept the denominator same (2) and we got ( $(5)/(2)$

This was the case where the fractions' denominator was same. What if it's not ?

If their denominator isn't equal, we're gonna have to equalize them ourself. How to do that ?

Let's show it with an example :

$\frac { 1 }{ 2 }$ and $\frac { 3 }{ 4 }$ do no have the same number as their denominator. To be able to add them, we have to equalize their denominators.

$\frac { 1 }{ 2 }$ 's denominator is 2 and $\frac { 3 }{ 4 }$ 's is 4

What can we do to equalize them ? Well, 4 is two times 2 ( $4 = 2\cdot 2$ ) So we cane multiply the denominator of $\frac { 1 }{ 2 }$ (which is 2) with 2 , to equal it to $\frac { 3 }{ 4 }$ 's denominator (which is 4).

But, there is a catch here. When multiplying a fraction's denominator before adding it to another, you should make sure that you're preserving its ratio. What does that mean ?

Let's take the number $\frac { 4 }{ 6 }$

(1) if we multiply only its numerator with a number (let it be 3)

$\frac { 3\cdot 4 }{ 6 } \quad =\quad \frac { 12 }{ 6 } \quad =\quad 2$

You got a new fraction with a different ratio than $(4)/(6)$ . And it is also equal to 2, but $(4)/(6)$ isn't equal to 2.

(2) if we multiply only its denominator with a number (let it be 3 again)

$\frac { 4 }{ 3\cdot 6 } \quad =\quad \frac { 4 }{ 18 }$

You got a new fraction again, with a different ration than $(4)/(6)$ .

How can we know that ? Well, if you simplify these two numbers to the simplest number, you'll get a different fraction or integer. Let's do so.

$\frac { 4 }{ 6 } \quad =\quad \frac { 2\cdot 2 }{ 2\cdot 3 } \quad =\quad \frac { 2 }{ 2 } \cdot \frac { 2 }{ 3 } \quad =\quad 1\cdot \frac { 2 }{ 3 } \quad =\quad \frac { 2 }{ 3 }$

So the simplified form of $(4)/(6)$ in the fraction form is $(2)/(3)$

$\frac { 4 }{ 18 } \quad =\quad \frac { 2\cdot 2 }{ 2\cdot 9 } \quad =\quad \frac { 2 }{ 2 } \cdot \frac { 2 }{ 9 } \quad =\quad 1\cdot \frac { 2 }{ 9 } \quad =\quad \frac { 2 }{ 9 }$

And the simplest form of $(4)/(18)$ as a fraction is $(2)/(9)$ , which is not equal to $(2)/(3)$

$\frac { 2 }{ 3 } \quad \neq \quad \frac { 2 }{ 9 }$

So what to do, to preserve the ratio ? Simle. We'll multiply also the numerator with the same number we're going to multiply the denominator with.

Let's get back to our example.

Adding $\frac { 1 }{ 2 }$ and $\frac { 3 }{ 4 }$

We were going to multiply $(1)/(2)$ 's denominator with 2. Now that we know, the ratio must not change, we'll also multiply the numerator with 2.

$\frac { 2\cdot 1 }{ 2\cdot 2 } \quad =\quad \frac { 2 }{ 4 }$

Now we've got a number which has the same denominator as $\frac { 3 }{ 4 }$

We can add them now,

$\frac { 2 }{ 4 } \quad +\quad \frac { 3 }{ 4 } \quad =\quad \frac { 2+3 }{ 4 } \quad =\quad \frac { 5 }{ 4 }$

$\boxed { \frac { 1 }{ 2 } \quad +\quad \frac { 3 }{ 4 } \quad =\quad \frac { 5 }{ 4 } }$

I hope this was clear, if not please ask and I'll try to explain.

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On a given morning the temperature was 71°F. The temperature dropped 5°F and then rose 8°F. How much does the temperature need to rise or fall to return to the initial temperature of 71°F?A) Fall 8°F
B) Fall 3°F
C) Rise 8°F
D) Rise 5°F

Answers

Fall 3°F to return to the initial temperature of 71°F so option (B) will be correct.

What is the arithmetic operator?

Arithmetic operators are four basic mathematical operations in which summation, subtraction, division, and multiplication involve.,

Summation = addition of two or more numbers or variable

For example = 2 + 8 + 9

Subtraction = Minus of any two or more numbers with each other called subtraction.

For example = 4 - 8

Division = divide any two numbers or variable called division.

For example 4/8

Multiplication = to multiply any two or more numbers or variables called multiplication.

For example 5 × 7.

Given that,

Initial temperature = 71°F

The temperature dropped 5°F = 71 - 5 = 66°F

Then rose of 8°F = 66 + 8 = 74°F

So,

The temperature has risen by 3°F so it needs to fall to match the initial temperature.

Hence "Fall 3°F to return to the initial temperature of 71°F".

To learn more about the arithmetic operators,

brainly.com/question/25834626

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Answer: The answer is B)Fall 3 F

A number, n, is added to 15 less than 3 times itself. The result is 101. Which of the following can be an equation can be used to find the value of n?a.n + (3n - 15) = 101
b.4n - 15 = 101

Answers

Answer:

Option a and b both are correct.

Step-by-step explanation:

We have been given the information that is: n is added to 15 less than 3 times itself.

The result is 101.

So, the number is 15 less than 3 times to itself means: 3n-15

And n is added to it that means:

n+(3n-15)

And its result is 101 so,

n+(3n-15)=101

After simplification of above expression gives:

4n-15=101.

Therefore, Option a and b both are correct.

For the function y = 9x, what is the output value if 5 is the input value?y = 4
y = 14
y = 45
y = 95

Answers

Answer:

Step-by-step explanation:

y=9x

y=9(5)

y=45

Answer: 45

Step-by-step explanation:

y=9x

y=9(5)

y=45

Step-by-step explanation:

The product of 9 and a number is 12 less than three times that number.What is the number?

Giving 20 Points....

Answers

9n = 3n-12
-3n= -3n
6n= -12
divide by 6 = -2 =n

to check.. 9 times -2 = -18 soo.. 3 times -2= -6-12= -18

so it is correct!!

hope it helps :)

Decompose -6x/(x+4)(x-4) into partial fractions

Answers

Hello,

Integration fractions?

-6x/((x+4)(x-4))=A/(x+4)+B/(x-4)=((A+B)x-4A+4B)/((x+4)(x-4))
==> A+B=-6 and -4A+4B=0
==>A=B=-3

Answer -3/(x+4)-3/(x-4)

What is 15 divided by 390

Answers

So,

15/390 = 5/130 = 1/26

In decimal form, that is 0.03846153846...

The answer to 15 divided by 390 is 0.038461538

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