Prove the sum of two rational numbers is rational where a,b,c and,d are integers and b and d cannot be zero

1. Find the product. Simplify. 13/14 of 10/9. A. 15/42 B. 5/21 C. 2/7 D. 5/6 2. Andy has 5 pots, and each pot can hold 3/8 pound

Rufina [12.5K]

1) Resultant fraction: $\frac{65}{63}$

2) Total soil: $1\frac{7}{8}$ pounds

3) Result of the product: $\frac{35}{2}$

Step-by-step explanation:

1)

In this problem, we want to find the product between the two fractions

$\frac{13}{14}$

and

$\frac{10}{9}$

In order to find this product, we have to multiply the numerators of each fraction and the denominators of each fraction. We get:

$\frac{13}{14}\cdot \frac{10}{9}=\frac{13\cdot 10}{14\cdot 9}=\frac{130}{126}$

Now we simplify, dividing both numerator and denominator by 2:

$\frac{130/2}{126/2}=\frac{65}{63}$

And the fraction cannot be further simplified.

2)

Here we have:

n = 5 (number of pots that Andy has)

$s=\frac{3}{8}$ (amount of soil (in pounds) that each pot can contain)

In order to find the amount of soil that Andy needs to fill all the pots, we have to multiply the number of pots (n) by the amount of soil that each pot can contain (s).

If we do so, we find:

$t=n \cdot s = 5 \cdot \frac{3}{8}=\frac{5\cdot 3}{8}=\frac{15}{8}$

Which can be rewritten as a mixed fraction as:

$\frac{15}{8}=\frac{8+7}{8}=\frac{8}{8}+\frac{7}{8}=1\frac{7}{8}$

3)

Here we want to find the result of the following product:

$4\frac{2}{3}\cdot 3\frac{3}{4}$

In order to do so, we first have to rewrite each fraction as an improper fraction.

For the 1st fraction:

$4\frac{2}{3}=\frac{4\cdot 3+2}{3}=\frac{12+2}{3}=\frac{14}{3}$

For the 2nd fraction:

$3\frac{3}{4}=\frac{3\cdot 4+3}{4}=\frac{12+3}{4}=\frac{15}{4}$

Now we can finally find the product of the two fractions:

$\frac{14}{3}\cdot \frac{15}{4}=\frac{14\cdot 15}{3\cdot 4}=\frac{210}{12}=\frac{35}{2}$

Where in the last step, we divide both the numerator and the denominator by 6.

Learn more about fractions:

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6 0

3 years ago

In a recent student government election, the ratio of students who voted for the winner to all the students who voted was 0.55

Temka [501]

The ratio being 0.55 means 55% of students voted for the person who ended up winning. If there were 40 people who voted, just find 55% of 40.
This is done by 0.55 • 40, which equals 22.
So 22 students voted for the person who ended up winning.

3 0

3 years ago

Read 2 more answers

If f(x) = x-1/3 and g(x) = 3x+1 what is (fog)(x)

marin [14]

Answer:

if you meant f(x) = (x - 1) /3 then f (g(x) ) = x

of if you meant f(x) = x - (1/3) then f(g (x)) = 3x + 2/3

Step-by-step explanation:

f(x) = x-1/3 and g(x) = 3x+1 what is (fog)(x)

f ( g(x) ) = (3x + 1) - (1/3) = 3x + 2/3

Or

if you meant f(x) = (x - 1) /3 then f (g(x) ) = x

of if you meant f(x) = x - (1/3) then f(g (x)) = 3x + 2/3

3 0

3 years ago

(-3,-14) and (0-9) Pls help!!!

andreyandreev [35.5K]

Answer:

y = (5/3)x - 9

Step-by-step explanation:

First, find the slope (rise over run):

m = (-9 - (-14)) / (0 - (-3)) = (-9 + 14) / (0 + 3) = 5/3

Use the point-slope form equation with the given points (-3, -14):

y + 14 = (5/3)(x + 3)

or optionally in slope intercept form:

y = (5/3)x - 9

3 0

2 years ago

Write 10934 meters as an integer

tia_tia [17]

You just add the negative sign -10934 meters

7 0

3 years ago