If a and b are two distinct rational numbers, then which of the following statements is true?

Mathematics

1 answer:

n200080 [17]3 years ago

6 0

Answer:

Both are rational.

Step-by-step explanation:

As a rational number can be written in the form p/q where p,q are co-prime integers, let a=p1/q1 b=p2/q2.

And we know the product of two integers is an integer

p1q2, p2q1 are integers. And the sum or difference of two integers is rational, rather being specific, it is an integer.

Thus a+b and a-b is rational.

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Can someone please help me with b and C questions

andre [41]

Answer:

(b) 33919

Step-by-step explanation:

⇒ 317 × 107 = (300 + 10 + 7)(100 + 7)

= 300(100 + 7) + 10(100 + 7) + 7(100 + 7)

= 30000 + 2100 + 1000 + 70 + 700 + 49

= 30000 + 2000 + 100 + 1000 + 70 + 700 + 40 + 9

= 30000 + 2000 + 1000+ 700 + 100 + 70 + 40 + 9

= 30000 + 3000 + 800 + 110 + 9

= 30000 + 3000 + 800 + 100 + 10 + 9

= 30000 + 3000 + 900 + 10 + 9

= 33919

$\begin{aligned} 5\frac{2}{3}+3\frac{1}{2}-\frac{5}{6}&=\dfrac{5 \times3+2}{3}+\dfrac{3 \times 2+1}{2}-\dfrac{5}{6}\\\\&=\dfrac{17}{3}+\dfrac{7}{2}-\dfrac{5}{6}\\\\& =\dfrac{17 \times 2}{3\times 2}+\dfrac{7\times 3}{2\times 3}-\dfrac{5}{6}\\\\ & = \dfrac{34}{6}+\dfrac{21}{6}-\dfrac{5}{6}\\\\ & = \dfrac{34+21-5}{6}\\\\ & = \dfrac{50}{6}\\\\&=8\frac{1}{3}\end{aligned}$