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Exercise 1.1 - Chapter 1 Rational Numbers class 8 ncert solutions Maths - SaraNextGen [2024]


Question 1:

Using appropriate properties find:

(i) https://img-nm.mnimgs.com/img/study_content/curr/1/8/5/64/2798/Chapter%201_html_m1b6f8b3b.gif

(ii) https://img-nm.mnimgs.com/img/study_content/curr/1/8/5/64/2798/Chapter%201_html_364d7381.gif

Answer:

(i)

https://img-nm.mnimgs.com/img/study_content/curr/1/8/5/64/2798/Chapter%201_html_m6613a9a7.gif

https://img-nm.mnimgs.com/img/study_content/curr/1/8/5/64/2798/Chapter%201_html_41d442ba.gif

(ii)

https://img-nm.mnimgs.com/img/study_content/curr/1/8/5/64/2798/Chapter%201_html_m47c381d7.gif  (By commutativity)

https://img-nm.mnimgs.com/img/study_content/curr/1/8/5/64/2798/Chapter%201_html_8a8611e.gif

Question 2:

Write the additive inverse of each of the following:

(i) https://img-nm.mnimgs.com/img/study_content/curr/1/8/5/64/2799/Chapter%201_html_73c3baf7.gif  (ii) https://img-nm.mnimgs.com/img/study_content/curr/1/8/5/64/2799/Chapter%201_html_m4e4b5636.gif  (iii) https://img-nm.mnimgs.com/img/study_content/curr/1/8/5/64/2799/Chapter%201_html_m34deb755.gif  (iv) https://img-nm.mnimgs.com/img/study_content/curr/1/8/5/64/2799/Chapter%201_html_m2254bb1c.gif  (v) https://img-nm.mnimgs.com/img/study_content/curr/1/8/5/64/2799/Chapter%201_html_m2c2a0d26.gif

Answer:

(i) https://img-nm.mnimgs.com/img/study_content/curr/1/8/5/64/2799/Chapter%201_html_73c3baf7.gif

Additive inverse = https://img-nm.mnimgs.com/img/study_content/curr/1/8/5/64/2799/Chapter%201_html_7644ccca.gif

(ii) https://img-nm.mnimgs.com/img/study_content/curr/1/8/5/64/2799/Chapter%201_html_m5aa03f3f.gif

Additive inverse = https://img-nm.mnimgs.com/img/study_content/curr/1/8/5/64/2799/Chapter%201_html_m51d632db.gif

(iii) https://img-nm.mnimgs.com/img/study_content/curr/1/8/5/64/2799/Chapter%201_html_m2efa74a1.gif

Additive inverse = https://img-nm.mnimgs.com/img/study_content/curr/1/8/5/64/2799/Chapter%201_html_291cec5c.gif

(iv) https://img-nm.mnimgs.com/img/study_content/curr/1/8/5/64/2799/Chapter%201_html_m6f643572.gif

Additive inverse https://img-nm.mnimgs.com/img/study_content/curr/1/8/5/64/2799/Chapter%201_html_7224356d.gif

(v) https://img-nm.mnimgs.com/img/study_content/curr/1/8/5/64/2799/Chapter%201_html_c8cbe51.gif

Additive inverse https://img-nm.mnimgs.com/img/study_content/curr/1/8/5/64/2799/Chapter%201_html_38a112a5.gif

Question 3:

Verify that −(−x) = x for.

(i) https://img-nm.mnimgs.com/img/study_content/curr/1/8/5/64/2801/Chapter%201_html_11353762.gif  (ii) https://img-nm.mnimgs.com/img/study_content/curr/1/8/5/64/2801/Chapter%201_html_md7f3530.gif

Answer:

(i) https://img-nm.mnimgs.com/img/study_content/curr/1/8/5/64/2801/Chapter%201_html_11353762.gif

The additive inverse of https://img-nm.mnimgs.com/img/study_content/curr/1/8/5/64/2801/Chapter%201_html_11353762.gif  is https://img-nm.mnimgs.com/img/study_content/curr/1/8/5/64/2801/Chapter%201_html_d6d28c8.gif  as https://img-nm.mnimgs.com/img/study_content/curr/1/8/5/64/2801/Chapter%201_html_m7fcbcc1b.gif

This equality https://img-nm.mnimgs.com/img/study_content/curr/1/8/5/64/2801/Chapter%201_html_m7fcbcc1b.gif  represents that the additive inverse of https://img-nm.mnimgs.com/img/study_content/curr/1/8/5/64/2801/Chapter%201_html_m70bdd54.gif  is https://img-nm.mnimgs.com/img/study_content/curr/1/8/5/64/2801/Chapter%201_html_31126b37.gif  or it can be said that https://img-nm.mnimgs.com/img/study_content/curr/1/8/5/64/2801/Chapter%201_html_441ea089.gif  i.e., −(−x) = x

(ii) https://img-nm.mnimgs.com/img/study_content/curr/1/8/5/64/2801/Chapter%201_html_md7f3530.gif

The additive inverse of https://img-nm.mnimgs.com/img/study_content/curr/1/8/5/64/2801/Chapter%201_html_md7f3530.gif  is https://img-nm.mnimgs.com/img/study_content/curr/1/8/5/64/2801/Chapter%201_html_359629cc.gif  as https://img-nm.mnimgs.com/img/study_content/curr/1/8/5/64/2801/Chapter%201_html_m7dbeb038.gif

This equality https://img-nm.mnimgs.com/img/study_content/curr/1/8/5/64/2801/Chapter%201_html_m7dbeb038.gif  represents that the additive inverse of https://img-nm.mnimgs.com/img/study_content/curr/1/8/5/64/2801/Chapter%201_html_4b000ed6.gif  is −https://img-nm.mnimgs.com/img/study_content/curr/1/8/5/64/2801/Chapter%201_html_4b000ed6.gif  i.e., −(−x) = x

Question 4:

Find the multiplicative inverse of the following.

(i) https://img-nm.mnimgs.com/img/study_content/curr/1/8/5/64/2804/Chapter%201_html_m3a7dae92.gif  (ii) https://img-nm.mnimgs.com/img/study_content/curr/1/8/5/64/2804/Chapter%201_html_2aac05ed.gif  (iii) https://img-nm.mnimgs.com/img/study_content/curr/1/8/5/64/2804/Chapter%201_html_m1ebe579d.gif

(iv) https://img-nm.mnimgs.com/img/study_content/curr/1/8/5/64/2804/Chapter%201_html_mfe4dcf.gif  (v) https://img-nm.mnimgs.com/img/study_content/curr/1/8/5/64/2804/Chapter%201_html_65951097.gif  (vi) −1

Answer:

(i) −13

Multiplicative inverse = −https://img-nm.mnimgs.com/img/study_content/curr/1/8/5/64/2804/Chapter%201_html_517f2671.gif

(ii) https://img-nm.mnimgs.com/img/study_content/curr/1/8/5/64/2804/Chapter%201_html_7e58f5bc.gif

Multiplicative inverse = https://img-nm.mnimgs.com/img/study_content/curr/1/8/5/64/2804/Chapter%201_html_m69f0fd28.gif

(iii) https://img-nm.mnimgs.com/img/study_content/curr/1/8/5/64/2804/Chapter%201_html_m1ebe579d.gif

Multiplicative inverse = 5

(iv) https://img-nm.mnimgs.com/img/study_content/curr/1/8/5/64/2804/Chapter%201_html_6f5773e9.gif

Multiplicative inverse https://img-nm.mnimgs.com/img/study_content/curr/1/8/5/64/2804/Chapter%201_html_7ca71093.gif

(v) https://img-nm.mnimgs.com/img/study_content/curr/1/8/5/64/2804/Chapter%201_html_71e88f02.gif

Multiplicative inverse https://img-nm.mnimgs.com/img/study_content/curr/1/8/5/64/2804/Chapter%201_html_mc0a9782.gif

(vi) −1

Multiplicative inverse = −1

Question 5:

Name the property under multiplication used in each of the following:

(i) https://img-nm.mnimgs.com/img/study_content/curr/1/8/5/64/2807/Chapter%201_html_m25c44b92.gif

(ii) https://img-nm.mnimgs.com/img/study_content/curr/1/8/5/64/2807/Chapter%201_html_m5ae91133.gif

(iii) https://img-nm.mnimgs.com/img/study_content/curr/1/8/5/64/2807/Chapter%201_html_72df3216.gif

Answer:

(i) https://img-nm.mnimgs.com/img/study_content/curr/1/8/5/64/2807/Chapter%201_html_m59268500.gif

1 is the multiplicative identity.

(ii) Commutativity

(iii) Multiplicative inverse

Question 6:

Multiply https://img-nm.mnimgs.com/img/study_content/curr/1/8/5/64/2809/Chapter%201_html_150ef6f6.gif by the reciprocal ofhttps://img-nm.mnimgs.com/img/study_content/curr/1/8/5/64/2809/Chapter%201_html_68fae563.gif .

Answer:

https://img-nm.mnimgs.com/img/study_content/curr/1/8/5/64/2809/Chapter%201_html_276085ff.gif

Question 7:

Tell what property allows you to computehttps://img-nm.mnimgs.com/img/study_content/curr/1/8/5/64/2814/Chapter%201_html_m735c2a05.gif .

Answer:

Associativity

Question 8:

Is https://img-nm.mnimgs.com/img/study_content/curr/1/8/5/64/2818/Chapter%201_html_m7c9b0a1b.gif the multiplicative inverse ofhttps://img-nm.mnimgs.com/img/study_content/curr/1/8/5/64/2818/Chapter%201_html_435cff23.gif ? Why or why not?

Answer:

If it is the multiplicative inverse, then the product should be 1.

However, here, the product is not 1 as

https://img-nm.mnimgs.com/img/study_content/curr/1/8/5/64/2818/Chapter%201_html_61da99c0.gif

Question 9:

Is 0.3 the multiplicative inverse ofhttps://img-nm.mnimgs.com/img/study_content/curr/1/8/5/64/2820/Chapter%201_html_3c3ca36b.gif ? Why or why not?

Answer:

https://img-nm.mnimgs.com/img/study_content/curr/1/8/5/64/2820/Chapter%201_html_m62097530.gif

0.3 × https://img-nm.mnimgs.com/img/study_content/curr/1/8/5/64/2820/Chapter%201_html_3c3ca36b.gif  = 0.3 × https://img-nm.mnimgs.com/img/study_content/curr/1/8/5/64/2820/Chapter%201_html_1a8b1efb.gif

Here, the product is 1. Hence, 0.3 is the multiplicative inverse ofhttps://img-nm.mnimgs.com/img/study_content/curr/1/8/5/64/2820/Chapter%201_html_3c3ca36b.gif .

Question 10:

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.

Answer:

(i) 0 is a rational number but its reciprocal is not defined.

(ii) 1 and −1 are the rational numbers that are equal to their reciprocals.

(iii) 0 is the rational number that is equal to its negative.

Question 11:

Fill in the blanks.

(i) Zero has __________ reciprocal.

(ii) The numbers __________ and __________ are their own reciprocals

(iii) The reciprocal of − 5 is __________.

(iv) Reciprocal ofhttps://img-nm.mnimgs.com/img/study_content/curr/1/8/5/64/2822/Chapter%201_html_5d52ab13.gif , where https://img-nm.mnimgs.com/img/study_content/curr/1/8/5/64/2822/Chapter%201_html_m3112d4d6.gif is __________.

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

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

Answer:

(i) No

(ii) 1, −1

(iii) https://img-nm.mnimgs.com/img/study_content/curr/1/8/5/64/2822/Chapter%201_html_m2ebf8685.gif

(iv) x

(v) Rational number

(vi) Positive rational number

Also Read : Exercise-1.2-Chapter-1-Rational-Numbers-class-8-ncert-solutions-Maths

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