Is 1/6 a rational number or a integer number

Mathematics

1 answer:

ss7ja [257]3 years ago

7 0

Answer:

1/6 is a rational number

Explanation:

The integer numbers are not fractions. Integer numbers are the whole numbers (1, 2, 3, 4, 5, ...) which are positive, and their negatives (-1, -2, -3, -4, -5, ...). Zero is also included in the set of the integer numbers, so they are:

. . . , - 5, - 4, - 3, - 2, - 1, 0, 1, 2, 3, 4, 5, . . .

The fractions are rational numbers. Per definition a rational number is the ratio of two integer numbers.

The rational numbers include the integer numbers but is a bigger set, i.e. every integer number is a rational number but not every rational numbers are integer. So, 1/6 is an example of an rational number that is not an integer number.

Any fraction that can be simplified to an integer number is an integer (and also a rational number); any fraction that cannot be simplified to an integer is a rational number but not an integer.

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A huge suspended LED screen is the centerpiece of The Place, a popular mall in Beijing, China. Find the length and width of a si

dusya [7]

The length and width of the similar rectangular screen are 110 meters and 35 meters respectively.

SOLUTION:

Given, A huge suspended LED screen is the centerpiece of The Place, a popular mall in Beijing, China.

We have to find the length and width of a similar rectangular screen

We are also given that the length is 5 meters more than 3 times its width,

Let width of rectangle be "b" meters, the its length will be 5 + 3b meters

And, the viewable area is 3,850 square meters.

$\begin{array}{l}{\text { So, area }=3850} \\\\ {\text { Length } \times \text { width }=3850} \\\\ {(5+3 b) \times b=3850} \\\\ {5 b+3 b^{2}=3850} \\\\ {3 b^{2}+5 b-3850=0}\end{array}$

Now,let us use quadratic formula:

$\begin{array}{l}{\mathrm{x}=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}} \\\\ {\text { Then, } \mathrm{b}=\frac{-5 \pm \sqrt{5^{2}-4 \times 3 \times(-3850)}}{2 \times 3}}\end{array}$

$\begin{array}{l}{\mathrm{b}=\frac{-5 \pm \sqrt{25+46200}}{6}} \\\\ {\mathrm{b}=\frac{-5 \pm \sqrt{46225}}{6}} \\\\ {\mathrm{b}=\frac{-5 \pm 215}{6}} \\\\ {\mathrm{b}=\frac{-5+215}{6} \text { or } \frac{-5-215}{6}} \\\\ {\mathrm{b}=\frac{210}{6} \mathrm{or} \frac{-220}{6}}\end{array}$