List of top Mathematics Questions on Need For Rational Numbers

The points P, Q, R, S, T, U, A and B on the number line are such that, TR = RS = SU and AP = PQ = QB. Name the rational numbers represented by P, Q, R and S.

Give four rational numbers equivalent to:
(i)\(\frac{-2}{7}\)
(ii) \(\frac{5}{-3}\)
(iii) \(\frac{4}{9}\)

Write the following rational numbers in ascending order:
(i) -\(\frac{3}{5}\),-\(\frac{2}{5}\),-\(\frac{1}{5}\)
(ii) -\(\frac{1}{3}\),-\(\frac{2}{9}\),-\(\frac{4}{3}\)
(iii) -\(\frac{3}{7}\),-\(\frac{3}{2}\),-\(\frac{3}{4}\)

Find : 
(i)\(\frac{7}{24}\)-\(\frac{17}{36}\)
(ii) \(\frac{5}{63}\)-(\(-\frac{6}{21}\))
(iii) -\(\frac{6}{13}\)-(-\(\frac{7}{15}\))
(iv) -\(\frac{3}{8}\)-\(\frac{7}{11}\)
(v)\(-\frac{21}{9}\)-6

Draw the number line and represent the following rational numbers on it:
(i) \(\frac{3}{4}\)(ii) \(\frac{-5}{8}\) (iii) \(\frac{-7}{4}\) (iv) \(\frac{7}{8}\)

Find the sum:
(i) \(\frac{5}{4}\)+(-\(\frac{11}{4}\))
(ii) \(\frac{5}{3}\)+\(\frac{3}{5}\)
(iii) -\(\frac{9}{10}\)+\(\frac{22}{15}\)
(iv) \(\frac{-3}{-11}\)+\(\frac{5}{9}\)
(v)\(-\frac{8}{19}\)+\(\frac{(-2)}{57}\)
(vi) \(-\frac{2}{3}\)+0
(vii) \(-\frac{21}{3}\)+\(\frac{43}{5}\)

Which is greater in each of the following:
(i) \(\frac{2}{3}\),\(\frac{5}{2}\) (ii) -\(\frac{5}{6}\),-\(\frac{4}{3}\) (iii) -\(\frac{3}{4}\),\(\frac{2}{-3}\) (iv) \(-\frac{1}{4}\),\(\frac{1}{4}\) (v) \(-\frac{32}{7}\),\(-\frac{34}{5}\)

Fill in the boxes with the correct symbol out of >, <, and =.
(i) -\(\frac{5}{7}\)__ \(\frac{2}{3}\) (ii) -\(\frac{4}{5}\)__-\(\frac{5}{7}\) (iii) -\(\frac{7}{8}\) __\(\frac{14}{-16}\) (iv) \(\frac{-8}{5}\) __\(\frac{-7}{4}\)(v) \(\frac{1}{-3}\) __\(\frac{-1}{4}\) (vi)\(\frac{5}{-11}\) __\(\frac{-5}{11}\) (vii) 0__ \(\frac{-7}{6}\)

Rewrite the following rational numbers in the simplest form:
(i) \(\frac{-8}{6}\) (ii) \(\frac{25}{45}\) (iii) \(\frac{-44}{72}\) (iv) \(\frac{-8}{10}\)

Which of the following pairs represent the same rational number?
(i) \(\frac{-7}{21} \space and \frac{3}{9}\)

(ii) \(\frac{-16}{20}\space and\space  \frac{20}{-25}\)

(iii) \(\frac{-2}{-3}\space and \space \frac{2}{3}\)

(iv) \(\frac{-3}{5} \space and \space \frac{-12}{20}\)

(v) \(\frac{8}{-5}\space and \space \frac{-24}{15}\)

(vi) \(\frac{1}{3}\space and\space  \frac{-1}{9}\)

(vii) \(\frac{-5}{-9}\space and \space \frac{5}{-9}\)

Write four more rational numbers in each of the following patterns:
(i) \(\frac{-3}{5},\frac{-6}{10},\frac{-9}{15},\frac{-12}{20}\)...

(ii) \(\frac{-1}{4},\frac{-2}{8},\frac{-3}{12},\)...

(iii) \(\frac{-1}{6},\frac{2}{-12},\frac{3}{-18},\frac{4}{-24}\),....

(iv)\(\frac{-2}{3},\frac{2}{-3},\frac{4}{-6},\frac{6}{-9}\),...

List five rational numbers between:
(i) –1 and 0
(ii) –2 and –1
(iii)\(\frac{-4}{5} \space and \frac{-2}{3}\)

(iv) \(\frac{-1}{2}\space and \frac{2}{3}\)