If a/b is a rational number and m any integer, then a/b=am/bm

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Solution

Given Statement is true

We know m/m = 1

(a/b)1 = (a/b)

replace 1 with (m/m)

(a/b) (m/m) = (a/b)

(am)/(bm) = (a/b)

Hence (a/b) = am/bm

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Similar questions

Q. In each of the following state if the statement is true (T) or false (F):
(i) The quotient of two integers is always an integer.
(ii) Every integer is a rational number.
(iii) Every rational number is an integer.
(iv) Every fraction is a rational number.
(v) Every rational number is a fraction
(vi) If

\frac{a}{b}

is a rational number and m any integer, then

\frac{a}{b} = \frac{a \times m}{b \times m}

(vii) Two rational numbers with different numerators cannot be equal.
(viii) 8 can be written as a rational number with any integer as denominator.
(ix) 8 can be written as a rational number with any integer as numerator.
(x)

\frac{2}{3} is equal to \frac{4}{6} .

Q. If

a

and

b

are non-zero integers,

m

and

n

are any integers, then which of the following are true?

If a is an integer and b is a rational number, then the number of rational numbers between a and b is

Which one of the following is correct and which one is not correct? Give reasons.

1) If 'a' is a rational number and 'b' is irrational, then a+b is irrational.

2) The product of a non-profit rational number with an irrational number is always irrational.

3) Addition of any two irrational numbers can be rational.

4) Division of any two integers is an integer.

Question 54

State whether the given statement is True or False.

If $\frac{p}{q}$ is a rational number and m is a non-zero integer, then $\frac{p \times m}{q \times m}$ is a rational number not equivalent to $\frac{p}{q}$ .

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If a/b is a rational number and m any integer, then a/b=a*m/b*m

Given Statement is true We know m/m = 1 (a/b)*1 = (a/b) replace 1 with (m/m) (a/b) * (m/m) = (a/b) (a*m)/(b*m) = (a/b) Hence (a/b) = a*m/b*m

If a/b is a rational number and m any integer, then a/b=am/bm

Given Statement is true

We know m/m = 1

(a/b)1 = (a/b)

replace 1 with (m/m)

(a/b) (m/m) = (a/b)

(am)/(bm) = (a/b)

Hence (a/b) = am/bm