Ncert solutions mathematics class 8 Solutions for Chapter 1 rational numbers

Which of the following is the multiplicative inverse of \frac{1}{5}?

State whether the given mathematical statement is TRUE or FALSE:

-(-x) = x for x = \frac{11}{15}

Which of the following is the multiplicative inverse of -\frac{13}{19}?

Fill in the blanks.

The reciprocal of − 5 is __________.

Which of the following is the multiplicative inverse of -1?

Name the property/identity used in:

\frac{-19}{29}\times\frac{29}{-19}=1

Which of the following is the multiplicative inverse of \frac{-5}{8}\times\frac{-3}{7}?

Which of the following is the multiplicative inverse of -1\times\frac{-2}{5}?

Which property allows you to compute

\frac{1}{3}\times\left(6\times\frac{4}{3})\right)as\ \left(\frac{1}{3}\times6\right)\times\frac{4}{3}?

Name the property/identity used in:

-\frac{13}{17}\times\frac{-2}{7}=\frac{-2}{7}\times\frac{-13}{17}

Name the property/identity used in:

\frac{-4}{5}\times1=1\times\frac{-4}{5}=-\frac{4}{5}

State whether the following statement is TRUE or FALSE:

\frac{8}{9} the multiplication inverse of -1\ \frac{1}{8}

Multiply \frac{6}{13} by the reciprocal of -\frac{7}{16} and select the correct option.

State whether the following statement is TRUE or FALSE:

0.3 the multiplicative inverse of 3\ \frac{1}{3}

Which of the following are rational numbers that are equal to their reciprocals?

Fill in the blanks.

Zero has __________ reciprocal.

Which of the following rational number is equal to its negative counterpart?

Which of the following is a rational number that does not have a reciprocal?

Fill in the blanks.

The reciprocal of a positive rational number is __________.

Fill in the blanks.

The product of two rational numbers is always a __________.

Fill in the blanks.

The numbers __________ and __________ are their own reciprocals.

Fill in the blanks:

Reciprocal of \frac{1}{x}, where x ≠ 0 is _________.

Q1) Using appropriate properties find.

(i) -\frac{2}{3}\ \times\ \frac{3}{5}\ +\ \frac{5}{2}-\frac{3}{5}\times\frac{1}{6}

(ii) \frac{2}{5}\times\left(-\frac{3}{7}\right)-\frac{1}{6}\times\frac{3}{2}+\frac{1}{14}\times\frac{2}{5}

\begin{aligned} &\text { Using appropriate properties find. }\\ &\text { (i) }-\frac{2}{3} \times \frac{3}{5}+\frac{5}{2}-\frac{3}{5} \times \frac{1}{6} \end{aligned}

\text { (ii) } \frac{2}{5} \times\left(-\frac{3}{7}\right)-\frac{1}{6} \times \frac{3}{2}+\frac{1}{14} \times \frac{2}{5}

Write the additive inverse of each of the following.

\frac{2}{8}

\frac{-5}{9}

\frac{-6}{-5}

\frac{2}{-9}

Using appropriate properties find the value of:

\frac{2}{5} \times\left(-\frac{3}{7}\right)-\frac{1}{6} \times \frac{3}{2}+\frac{1}{14} \times \frac{2}{5}

Which of the following is the additive inverse of \frac{-6}{-5}?

Using appropriate properties find the value of -\frac{2}{3}\times\frac{3}{5}+\frac{5}{2}-\frac{3}{5}\times\frac{1}{6}

Which of the following is the multiplicative inverse of -13?

Which of the following is the additive inverse of -\frac{5}{9}?

Which of the following is the additive inverse of \frac{2}{-9}?

Which of the following is the additive inverse of \frac{2}{8}?

Which of the following is the additive inverse of \frac{19}{-16}?

State whether the given mathematical statement is TRUE or FALSE:

-(-x) = x for x = -\frac{13}{17}

Q2) Write the additive inverse of each of the following.

(i)\frac{2}{8}

(ii)\frac{-5}{9}

(iii)\frac{-6}{-5}

(iv)\frac{2}{-9}

(v)\frac{19}{-6}

Using appropriate properties find.

\text { (i) }-\frac{2}{3} \times \frac{3}{5}+\frac{5}{2}-\frac{3}{5} \times \frac{1}{6}

\text { (ii) } \frac{2}{5} \times\left(-\frac{3}{7}\right)-\frac{1}{6} \times \frac{3}{2}+\frac{1}{14} \times \frac{2}{5}

Write the additive inverse of each of the following.

(i) \frac{2}{8} (iv) \frac{2}{-9} (ii) \frac{-5}{9} (iii) \frac{-6}{-5} (v) \frac{19}{-6}

Q3) Verify that – (– x) = x for

(i) x= \frac{11}{15}

(ii) x= – \frac{13}{17}

Verify that : -(-x) = x for.

(i) x=\frac{11}{15} (ii) x=-\frac{13}{17}

Q4) Find the multiplicative inverse of the following.

(i) – 13

(ii)\frac{-13}{19}

(iii) \frac{1}{5}

(iv) \frac{-5}{8}\times\ \frac{-3}{7}

(v) -1 \times\frac{-2}{5}

(vi) -1

Q5) Name the property under multiplication used in each of the following.

(i) \frac{-4}{5}\times1=1\times\frac{-4}{5}=\ \frac{-4}{5}

(ii) \frac{-13}{17}\times\frac{-2}{7}=\ \frac{-2}{7}\times\ \frac{-13}{17}

(iii) \frac{-19}{29}\ \times\ \frac{29}{-19}=\ 1

Find the multiplicative inverse of the following.

(i) -13 (ii) \frac{-13}{19} (iii) \frac{1}{5} (iv) \frac{-5}{8} \times \frac{-3}{7} \quad(v)-1 \times \frac{-2}{5} \quad(v i)-1

Name the property under multiplication used in each of the following

(i) \frac{-4}{5} \times 1=1 \times \frac{-4}{5}=\frac{-4}{5} (ii) \frac{-13}{17} \times \frac{-2}{7}=\frac{-2}{7} \times \frac{-13}{17} (iii) \frac{-19}{29} \times \frac{29}{-19}=1

Q6) Multiply \frac{6}{13} by the reciprocal of \frac{-7}{16}

Q7) Tell what property allows you to compute \frac{1}{3}\times\left(6\times\frac{4}{3}\right)\ as\ \left(\frac{1}{3}\ \times6\right)\ \times\frac{4}{3}

\text { Multiply } \frac{b}{13} \text { by the reciprocal of } \frac{-7}{16}

Q8) Is \frac{8}{9} the multiplicative inverse of -1\frac{1}{8}? Why or why not?

\text { Tell what property allows you to compute } \frac{1}{3} \times\left(6 \times \frac{4}{3}\right) \text { as }\left(\frac{1}{3} \times 6\right) \times \frac{4}{3}

\text { Is } \frac{8}{9} \text { the multiplicative inverse of }-1 \frac{1}{8} ? \text { Why or why not? }

Q9) Is 0.3 the multiplicative inverse of 3\frac{1}{3}? Why or Why not?

\text { Is } 0.3 \text { the multiplicative inverse of } 3 \frac{1}{3} ? \text { Why or why not? }

Q10) Write.

(i) The rational number that does not have a reciprocal.

(ii) The rational numbers that are equal to their reciprocals.

(iii) The rational number that is equal to its negative.

Write.

(i) The rational number that does not have a reciprocal.

(ii) The rational numbers that are equal to their reciprocal.

(iii) The rational number that is equal to its negative.

Q11)Fill in the blanks.

(i) Zero has ________ reciprocal.

(ii) The numbers ________ and ________ are their own reciprocals.

(iii) The reciprocal of – 5 is ______.

(iv) Reciprocal of \frac{1}{x}, where x\ne 0 is __________.

(v) The product of two rational numbers is always a _______.

(vi) The reciprocal of a positive rational number is ________.

Fill in the blanks.

(i) Zero has ________ reciprocal.

(ii) The numbers ________ and ________ are their own reciprocal

(iii) The reciprocal of – 5 is ________.

(iv) Reciprocal of ?/?, where x ≠ 0 is ________.

(v) The product of two rational numbers is always a _______.

(vi) The reciprocal of a positive rational number is ________.

Which is the rational number between -\frac{2}{5}\ and\ \frac{1}{2}?

Which is the rational number between \frac{2}{3}\ and\ \frac{4}{5}?

Which are the rational numbers greater than -2?

Which of the followig rational number is smaller than 2?

Observe the following number line. Which point corresponds to -\frac{5}{6}?

Observe the following number line. Which point corresponds to \frac{7}{4}?

Observe the following number line. Which point corresponds to -\frac{9}{11}?

Observe the following number line. Which point corresponds to -\frac{5}{11} ?

Which is the rational number between \frac{3}{5}\ and\ \frac{3}{4}?

Which is the rational number between \frac{1}{4}\ and\ \frac{1}{2}?

Which is the rational number between -\frac{3}{2}\ and\ \frac{5}{3}?

Represent these numbers on the number line. (i) \frac{7}{4} (ii) \frac{-5}{6}

\text { Represent } \frac{-2}{11}, \frac{-5}{11}, \frac{-9}{11} \text { on the number line. }

Write five rational numbers which are smaller than 2.

Find ten rational numbers between \frac{-2}{5} \text { and } \frac{1}{2}

Find five rational numbers between. (i) \frac{2}{3} and \frac{4}{5} (ii) \frac{-3}{2} and \frac{5}{3} (iii) \frac{1}{4} and \frac{1}{2}

Write five rational numbers greater than -2.

\text { Find ten rational numbers between } \frac{3}{5} \text { and } \frac{3}{4}

Q1)Represent these numbers on the number line.

(i) \frac{7}{4}

(ii) \frac{-5}{6}

Q2) Represent \frac{-2}{11},\ \frac{-5}{11},\ \frac{-9}{11} on the number line.

Q3)Write five rational numbers which are smaller than 2.

Q4) Find ten rational numbers between, \frac{-2}{5}\ \&\ \frac{1}{2}

Q5) Find five rational numbers between.

(i)\frac{2}{3}\ \&\ \frac{4}{5}

(ii)\frac{-3}{2}\ \&\ \frac{5}{3}

(iii)\frac{1}{4}\ \&\ \frac{1}{2}

Q6) Write five rational numbers greater than –2.

Q7) Find ten rational numbers between \frac{3}{5}\ and\ \frac{3}{4}