All categories

3 years ago

Add the following rational number = 3/11 and -5/12

Mathematics

1 answer:

tatiyna3 years ago

4 0

Answer:

-19/132

Step-by-step explanation:

To add fractions, find the lowest common multiple of the two denominators and multiply accordingly to make both denominators the same. In this case, the lowest common multiple of 11 and 12 is 132, so we need to multiply the first number by 12 and the second by 11. So we get $\frac{36}{132} + (-\frac{55}{132} )$ = $\frac{36-55}{132}$ = $\frac{-19}{32}$ $-\frac{19}{132}$

You might be interested in

One positive number is 14 less than another positive number. If the reciprocal of the smaller number is added to five times the

Kipish [7]

Let's call the two numbers $s$ and $l$ .

Given these variables, we can say: $s = l - 14$ , based on the first sentence in the problem.

Also, remember that the reciprocal of a number is simply 1 divided by the number. Thus, we can say that:

$\dfrac{1}{s} + 5\Big( \dfrac{1}{l} \Big) = \dfrac{1}{4}$

To solve, we can simply substitute $l -14$ in for $s$ in the second equation and solve.

$\dfrac{1}{l - 14} + \dfrac{5}{l} = \dfrac{1}{4}$

Set up

$\dfrac{l}{l(l - 14)} + \dfrac{5(l - 14)}{l(l - 14)} = \dfrac{1}{4}$

Get terms on the left side to a common denominator for easier addition

$\dfrac{l + 5l - 70}{l(l - 14)} = \dfrac{1}{4}$

Simplify

$4(6l - 70) = l(l - 14)$

Cross multiplication ( $\frac{a}{b} = \frac{c}{d} \Rightarrow ad = bc$ )

$24l - 280 = l^2 - 14l$

Simplify

$l^2 - 38l + 280 = 0$

Subtract $24l - 280$ from both sides of the equation

$(l - 10)(l - 28) = 0$

Factor left side of the equation

$l = 10, 28$

Zero Product Property

Now, notice that we have found two solutions, but the problem is only asking for one. This <em>likely </em>means that one of our solutions is extraneous. Let's take a look. Remember that the smaller positive number is equal to 14 less than the larger number. However,

$s = 10 - 14 = -4$ ,

Since $s$ is not positive in this case, $l = 10$ is not a solution.

Thus, $l = 28$ is our only solution. In this case,

$s = 28 - 14 = 14$ ,

which means that the smaller number is 14 and the larger number is 28.

5 0

3 years ago

Which expression can be used to solve 3/5 divide by 7/10

kramer

Answer:

$\frac{3}{5} *\frac{10}{7}$

= $\frac{30}{35} =\frac{6}{7}$

7 0

3 years ago

− 96 , 48 , − 24 , 12 , − 6 . what is the ratio of the geometric sequece

snow_tiger [21]

Answer:

-1/2

Step-by-step explanation:

it has to be a negative number since

every other number is negative

its a fraction since the numbers are decreasing

96 divided by 48 is 2

so the number being multiplied or ration must be -1/2

7 0

2 years ago

Using what you know about angles and triangles, what is the measure of angle 6?

zvonat [6]

∠4 = 90 (verticallyopposite)
∠2 = 68 (verticallyopposite)

∠6 = ∠2 + ∠4 (exterior angles = sum of opposite angles)

∠6 = 68 + 90 = 158°

Answer: 158°

7 0

3 years ago

Determine whether the results below appear to have statistical significance, and also determine whether the results have practi

pantera1 [17]

Answer:

Step-by-step explanation:

Given that in a study of a weight loss program, 4 subjects lost an average of 48 lbs.

It is found that there is about a 32% chance of getting such results with a diet that has no effect.

The results do not appear to have statistical significance. The reasons are

1) Sample size of 4 is very small not even meeting the bare minimum

2) Sample of 4 cannot be taken to represent the population

3) Whether bias was there in the selection of sample is not known.

4) Std deviation is not considered which is very important while concluding results.

5 0

3 years ago