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
motikmotik
3 years ago
13

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

ing step in the proof.
Mathematics
1 answer:
mario62 [17]3 years ago
3 0

Answer:

We conclude that the sum of two rational numbers is rational.

Hence, the fraction will be a rational number. i.e.

  • \frac{ad+cb}{bd}       ∵ b≠0, d≠0, so bd≠0

Step-by-step explanation:

Let a, b, c, and d are integers.

Let a/b and c/d are two rational numbers and b≠0, d≠0

Proving that the sum of two rational numbers is rational.

\frac{a}{b}+\frac{c}{d}

As the least common multiplier of b, d: bd

Adjusting fractions based on the LCM

\frac{a}{b}+\frac{c}{d}=\frac{ad}{bd}+\frac{cb}{db}

\mathrm{Since\:the\:denominators\:are\:equal,\:combine\:the\:fractions}:\quad \frac{a}{c}\pm \frac{b}{c}=\frac{a\pm \:b}{c}

          =\frac{ad+cb}{bd}

As b≠0, d≠0, so bd≠0

Therefore, we conclude that the sum of two rational numbers is rational.

Hence, the fraction will be a rational number. i.e.

  • \frac{ad+cb}{bd}       ∵ b≠0, d≠0, so bd≠0
You might be interested in
Multiply————-(b+12)^2
Talja [164]

Use Square of Sum: (a + b)^2 = a^2 + 2ab + b^2

b^2 + 2b * 12 + 12^2

Simplify 12^2 to 144

b^2 + 2b * 12 + 144

Simplify 2b * 12 to 24b

b^2 + 24b + 144

5 0
2 years ago
.   Multiply (x + 3)(x – 3).
konstantin123 [22]
X × x = x^2
x × -3 = -3x
3 × x = 3x
3 × -3 = -9

x^2 + 3x - 3x - 9
So I would agree with C because the -3x and the 3x cancel each other out. I hope this helps!
8 0
3 years ago
Helpppp I cannot figure this problem out ;-;
Yuliya22 [10]
A. -12, -7, -2, 3, 8
B. 3, 2, 1, 0, -1
6 0
2 years ago
How do you use the vertical line test?
Triss [41]
First let you know what to do. OK. Going to drag a ruler. Across the paper. Vertically. And if it touches 2 points on the grid. Then it fails the test.
5 0
3 years ago
I need help with 21 22 23.
olasank [31]
Find the square root of the area and yiull get the answer
8 0
2 years ago
Read 2 more answers
Other questions:
  • Replace the a,b,c,and d with the digits 2,4,6,8 to form the greatest product.each digit can only be used once.explain your subst
    12·2 answers
  • Kofi is 3 years older than Ama.If Ama is now x years old, what is kofi age​
    6·2 answers
  • Six cell phones weigh 46.2 ounces. Fourteen cell phones weigh 107.8 ounces. This relationship is an example of a proportional re
    13·1 answer
  • What is the order of the numbers from least to greatest?
    15·2 answers
  • Help me please I have to do a test!
    13·1 answer
  • How many solutions does 5(x -3) + 6 = 5x - 9 have?<br><br><br> Will mark brainlest
    13·2 answers
  • What is the area of these shapes
    5·1 answer
  • Full explanation: how do you find slope when your given two points
    11·1 answer
  • I REALLY NEED HELP PLEASEE!!!
    6·2 answers
  • MONEY Dinner and admission tickets to the aquarium costs $180 for three ladults. If two people each pay $70, how much will the t
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!