1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Rama09 [41]
3 years ago
9

Exercise 2.4.2: Proving statements about rational numbers with direct proofs. About Prove each of the following statements using

a direct proof. (a) The product of two rational numbers is a rational number. Solution (b) The quotient of a rational number and a non-zero rational number is a rational number. Solution (c) If x and y are rational numbers then is also a rational number.
Mathematics
1 answer:
IgorLugansk [536]3 years ago
8 0

Answer:

See Explanation

Step-by-step explanation:

(a) Proof: Product of two rational numbers

Using direct proofs.

Let the two rational numbers be A and B.

Such that:

A = \frac{1}{2}

B = \frac{2}{3}

The product:

A * B = \frac{1}{2} * \frac{2}{3}

A * B = \frac{1}{1} * \frac{1}{3}

A * B = 1 * \frac{1}{3}

A * B = \frac{1}{3}

Proved, because 1/3 is rational

(b) Proof: Quotient of a rational number and a non-zero rational number

Using direct proofs.

Let the two rational numbers be A and B.

Such that:

A = \frac{1}{2}

B = \frac{2}{3}

The quotient:

A / B = \frac{1}{2} / \frac{2}{3}

Express as product

A / B = \frac{1}{2} / \frac{3}{2}

A / B = \frac{1*3}{2*2}

A / B = \frac{3}{4}

Proved, because 3/4 is rational

(c) x + y is rational (missing from the question)

Using direct proofs.

Let x and y be

Such that:

x = \frac{1}{2}

y = \frac{2}{3}

The sum:

x + y = \frac{1}{2} + \frac{2}{3}

Take LCM

x + y = \frac{3+4}{6}

x + y = \frac{7}{6}

Proved, because 7/6 is rational

<em>The above proof works for all values of A, B, x and y; as long as they are rational values</em>

You might be interested in
canning operation is designed to fill cans with 14.5 oz of ingredients, on average, with a standard deviation of 0.1 oz. Nine ca
Pavlova-9 [17]

Answer:

SE = 0.025

Step-by-step explanation:

We are given;

Sample mean; x¯ = 14.52

Sample standard deviation; s = 0.075

Sample size; n = 9

Now,formula for standard error of sample mean is;

SE = s/√n

SE = 0.075/√9

SE = 0.075/3

SE = 0.025

3 0
3 years ago
Please help I have tried over and over and can't get it​
nirvana33 [79]
1) -3
2) 6
3) 4
4) 2
5) 5
6) 5
7) 7
8) -3
9) 9
10) 6
11) -5
12) 0

Here are your answers may I please have the brainliest
5 0
2 years ago
Aşağıda verilen şıklarda istenenleri bulunuz (NOT: sqrt( ): karekök, örneğin sqrt(4)=2 dir, R+: pozitif reel sayılar gösterimi).
Readme [11.4K]
Umm what’s the language
7 0
3 years ago
Convert 0.0000.489 to scientific notation
Volgvan
I do not understand why there are two decimal places.
But either ways if you are asking for :
0.0000489 then it is 4.89*10⁻⁵
0.489 then it is 4.89*10⁻¹
The trick is to count the zeroes to the first actual significant number you see and then write the number you counted with a negative sign for your power. 
I hope this helps!
4 0
3 years ago
Factor: 9t^2-16u^2 ?
liq [111]

Answer:

Step-by-step explanation:

9t²-16u² = 3²t²-4²u² = (3t)²-(4u)² = (3t+4u)(3t-4u)

8 0
3 years ago
Other questions:
  • Help with number 5....
    14·1 answer
  • Solve for x. 2x+5+6x-1=120​
    14·1 answer
  • 3. Select which ratios out of the following ratios are
    8·1 answer
  • Jen and Nikki are making bracelets to sell at the local market. They determined that each bracelet would have eight beads and tw
    15·1 answer
  • 25 POINTS!!! Tommy has $350 of his graduation gift money saved at home, and the amount is modeled by the function h(x) = 350. He
    14·1 answer
  • Help pls brainliest for whoever helps me ·ω·
    8·2 answers
  • Select the correct answer.
    9·2 answers
  • PLEASE ANSWER QUICK I NEED TO FINISH IN 50 MINUTES FOR MY TEST
    7·1 answer
  • Which is a possible solution for the inequality 42-J&lt;12<br> J=1<br> J=10<br> J=31
    8·2 answers
  • 0.3 × 0.7 = 0.21
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!