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Q.

State true or false.

Insert three rational numbers between $\frac{1}{3} and \frac{4}{5}$ . And arranged in descending order is $\frac{5}{15}, \frac{6}{15}, \frac{7}{15}, \frac{8}{15}$ .

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a

True

b

False

answer is A.

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Detailed Solution

The given statement is true.
Concept: Insert three rational numbers between

\frac{1}{3} and \frac{4}{5}

. And arranged in descending order is

\frac{5}{15}, \frac{6}{15}, \frac{7}{15}, \frac{8}{15}

. Irrational number Rational numbers (q cannot equal 0) are those that can be expressed in the

\frac{p}{q}

form, where p and q are integers and there is no common factor between p and q.
Irrational numbers are those that are not based on reason (irrational numbers are those that lack reason ) . In order to compare quantities, we must first make both denominators equal in order to put three numbers between them.Take LCM of denominators. Now, Divide LCM by each numerator then multiply and divide by the following quantity to fractions.
Multiply first quantity by 5555 and second quantity by 3333 in order to make both denominators equal.

\frac{1}{3} = \frac{1}{3} \times \frac{5}{5} = \frac{5}{15}

\frac{4}{5} = \frac{4}{5} \times \frac{3}{3} = \frac{12}{15}

5 + \frac{1}{15} = \frac{6}{15}, 5 + \frac{2}{15} = \frac{7}{15}, 5 + \frac{3}{15} = \frac{8}{15}

Now, we have three numbers that can be inserted between

\frac{1}{3} and \frac{4}{5}

\frac{1}{3} = \frac{5}{15}, \frac{6}{15}, \frac{7}{15}, \frac{8}{15}, \frac{4}{5} = \frac{12}{15}

So, the answer is

\frac{5}{15}, \frac{6}{15}, \frac{7}{15}, \frac{8}{15}

.
Hence, the answer is option 1) true.

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