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
Pani-rosa [81]
3 years ago
14

Which axiom is used to prove that the product of two rational numbers is rational

Mathematics
1 answer:
aliina [53]3 years ago
5 0

Answer:

First, a rational number is defined as the quotient between two integer numbers, such that:

N = a/b

where a and b are integers.

Now, the axiom that we need to use is:

"The integers are closed under the multiplication".

this says that if we have two integers, x and y, their product is also an integer:

if x, y ∈ Z ⇒ x*y ∈ Z

So, if now we have two rational numbers:

a/b and c/d

where a, b, c, and d ∈ Z

then the product of those two can be written as:

(a/b)*(c/d) = (a*c)/(b*d)

And by the previous axiom, we know that a*c is an integer and b*d is also an integer, then:

(a*c)/(b*d)

is the quotient between two integers, then this is a rational number.

You might be interested in
7. CHALLENGE: Use the digits 0 to 9 to make the equation true. You don't need to use all thedigits you can only use each digit o
labwork [276]

9514 1404 393

Answer:

  20 = 2 + (7 -4) × 6

Step-by-step explanation:

The Order of Operations requires the parentheses be evaluated first, then the multiplication performed. Finally, the addition is performed.

If each of the blanks is filled with a single digit, the result of the multiplication must be a composite number greater than 10. Those are 12, 14, 15, 16, 18, 20. For the expression shown above, we have chosen to make the product be 18. That means the first blank is filled with 2 and the remaining blanks must evaluate to one of the products 2×9 or 3×6.

We have chosen 6 for the last blank, so the two blanks in parentheses must have a difference of 3. The digits 2 and 6 cannot be used, leaving possible choices as (3-0), (4-1), (7-4), (8-5).

Our final expression is chosen to be ...

  20 = 2 +(7 -4)×6

3 0
2 years ago
PLS HELP ME WITH THIS EQUATION! Find X<br><img src="https://tex.z-dn.net/?f=%7B3%7D%5E%7B2%7Dx%20-%2032%20%3D%20%20%7B2%7D%5E%7B
Vesnalui [34]

Answer:

3x^{2} -32=2x^{2} -4x\\3x^{2} -2x^{2} +4x-32=0\\x^{2} +4x-32=0\\x^{2} -4x+8x-32=0\\x(x-4)+8(x-4)=0\\(x-4)(x+8)=0\\x-4=0 \ or\ x+8=0\\x=4\ or\ x=-8

5 0
3 years ago
A glacier moves 152 ft a year how many inches a day does it move (hint 356 days in a year)
matrenka [14]
It moves roughly 5 inches a day. (p.s you made a mistake, there is 365 days in a year not 356)
6 0
3 years ago
Read 2 more answers
the ratio of girls to boys in mrs tuners class is 3:4. there 9 girls in mrs tuners class. how many boys are in mrs tuners class
Aleonysh [2.5K]

Answer:

12

Step-by-step explanation:

You set up cross multiplication 3/4 x  9/x, you go 4x9=36 divided by 3 equals 12

7 0
2 years ago
Find the perimeter and area of each figure.​
ASHA 777 [7]

Answer:

Perimeter = 89mm

area= 528 or 220

Step-by-step explanation:

hope this is useful

3 0
3 years ago
Read 2 more answers
Other questions:
  • Create a real-life situation that can be describe with the unit rate 9:1. Describe how quantities are related.
    12·1 answer
  • No.14<br> Please help me
    7·1 answer
  • Which expression is equivalent to 9(9m+3t)
    5·2 answers
  • 3 3/10 - 7/10 please help
    13·2 answers
  • What is the ratio of dogs to cats? <br><br><br>What is the ratio of cats to dogs?
    6·1 answer
  • Subtract 52 - 2 from -37 +4<br><br>​
    5·1 answer
  • Quadratic Functions in Standard Form
    12·1 answer
  • What is the amplitude of 1-sin 2πx/3? Please explain.
    6·1 answer
  • Which is the best explanation for why − √ 10 is irrational?
    10·1 answer
  • An x-method chart shows the product a c at the top of x and b at the bottom of x. Above the chart is the expression a x squared
    8·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!