NCERT MATHS CLASS 7 गणित कक्षा 7
Rational Numbers परिमेय संख्या
LINK TO SOLUTIONS OF ALL QUESTIONS IS GIVEN BELOW
सभी प्रश्नों के समाधान का लिंक नीचे दिया गया है
1. A number that can be expressed in the form p /q , where p and q are integers and q ≠ 0, is called a rational number. The numbers -2/7, 3/8, 3 – etc are rational numbers.
2. All integers and fractions are rational numbers.
3. If the numerator and denominator of a rational number are multiplied or divided by a non-zero integer, we get a rational number which is said to be equivalent to the given rational number. For example -3/7 = -3×2/7×2 = -6/14. So, we say -6/14 is the equivalent form of -3/7 − . Also note that -6/14 = -6 ÷ 2/14÷2 =-3/7
4. Rational numbers are classified as Positive and Negative rational numbers. When the numerator and denominator, both, are positive integers, it is a positive rational number. When either the numerator or the denominator is a negative integer, it is a negative rational number. For example, 3/8 is a positive rational number whereas- 8/ 9 is a negative rational number.
5. The number 0 is neither a positive nor a negative rational number.
6. A rational number is said to be in the standard form if its denominator is a positive integer and the numerator and denominator have no common factor other than 1. The numbers 1/3, 2/ 7 − etc. are in standard form.
7. There are unlimited numbers of rational numbers between two rational numbers.
8. Two rational numbers with the same denominator can be added by adding their numerators, keeping the denominator same. Two rational numbers with different denominators are added by first taking the LCM of the two denominators and then converting both the rational numbers to their equivalent forms having the LCM as the denominator. For example, -2/ 3 + 3/8 = -16+9/24 = -7/24. Here, LCM of 3 and 8 is 24.
9. While subtracting two rational numbers, we add the additive inverse of the rational number to be subtracted to the other rational number. Thus, 7/8 – 2/3 = 7/8 + additive inverse of 2/3 = 7/8 + (-2/3)/3 = 21+(-16)/24 = 5/24.
10. To multiply two rational numbers, we multiply their numerators and denominators separately, and write the product as product of numerators/product of denominators
11. To divide one rational number by the other non-zero rational number, we multiply the rational number by the reciprocal of the other. Thus, -7/2 ÷ 4/3 = -7/2 × (reciprocal of 4/3) = 7/2 × ¾ = 21/8
EXERCISE 9.1
1. List five rational numbers between:
(i) –1 and 0
(ii) –2 and –1
(iii) -4/5 and -2/3
(iv) -1/2 and 2/3
2. Write four more rational numbers in each of the following patterns:
(i)-3/5, -6/10, -9/15, -12/20……….
(ii) -1/4, -2/8, -3/12 ……..
(iii) -1/6, 2/-12, 3/-18, 4/-24………
(iv) -2/3, 2/-3, 4/-6, 6/-9……..
3. Give four rational numbers equivalent to:
(i) -2/7
(ii) 5/-3
(iii) 4/9
4. Draw the number line and represent the following rational numbers on it:
(i) ¾
(ii) -5/8
(iii) -7/4 = -13/4
(iv) 7/8
5. 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 The points by P, Q, R and S.
6. Which of the following pairs represent the same rational number?
(i) (-7/21) and (3/9)
(ii) (-16/20) and (20/-25)
(iii) (-2/-3) and (2/3)
(iv) (-3/5) and (-12/20)
(v) (8/-5) and (-24/15)
(vi) (1/3) and (-1/9)
(vii) (-5/-9) and (5/-9)
7. Rewrite the following rational numbers in the simplest form:
(i) -8/6
(ii) 25/45
(iii) -44/72
(iv) -8/10
8. Fill in the boxes with the correct symbol out of >,< and =.
(i) -5/7 [ ] 2/3
(ii) -4/5 [ ] -5/7
(iii) -7/8 [ ] 14/-16
(iv) -8/5 [ ] -7/4
(v) 1/-3 [ ] -1/4
(vi) 5/-11 [ ] -5/11
(vii) 0 [ ] -7/6
9. Which is greater in each of the following?
(i) 2/3, 5/2
(ii) -5/6, -4/3
(iii) -3/4, 2/-3
(iv) -1/4, ¼
(v) -32/7, -3⅘
10. Write the following rational numbers in ascending order:
(i) -3/5, -2/5, -1/5
(ii) -1/3, -2/9, -4/3
(iii) -3/7, -3/2, -3/4
OPERATIONS ON RATIONAL NUMBERS परिमेय संख्याओं पर संक्रियाएँ
EXERCISE 9.2
1. Find the sum:
(i) (5/4) + (-11/4)
(ii) (5/3) + (3/5)
(iii) (-9/10) + (22/15)
(iv) (-3/-11) + (5/9)
(v) (-8/19) + (-2/57)
(vi) -2/3 + 0
(vii) 2⅓ +4⅗
2. Find
(i) 7/24 – 17/36
(ii) 5/63 – (-6/21)
(iii) -6/13 – (-7/15)
(iv) -3/8 – 7/11
(v) -21/9 - 6
3. Find the product:
(i) (9/2) × (-7/4)
(ii) (3/10) × (-9)
(iii) (-6/5) × (9/11)
(iv) (3/7) × (-2/5)
(v) (3/11) × (2/5)
(vi) (3/-5) × (-5/3)
4. Find the value of:
(i) (-4) ÷ (2/3)
(ii) (-3/5) ÷ 2
(iii) (-4/5) ÷ (-3)
(iv) (-1/8) ÷ ¾
(v) (-2/13) ÷ 1/7
(vi) (-7/12) ÷ (-2/13)
(vii) (3/13) ÷ (-4/65)
अभ्यास 9.1
1. इनमें से पाँच परिमेय संख्याओं की सूची बनाइए:
(i) -1 और 0
(ii) -2 और -1
(iii) -4/5 और -2/3
(iv) -1/2 और 2/3
2. निम्नलिखित में से प्रत्येक पैटर्न में चार और परिमेय संख्याएँ लिखिए:
(i)-3/5, -6/10, -9/15, -12/20 ……….
(ii) -1/4, -2/8, -3/12 …… ..
(iii) -1/6, 2/-12, 3/-18, 4/-24 ………
(iv) -2/3, 2/-3, 4/-6, 6/-9 ……..
3. तुल्य चार परिमेय संख्याएँ दीजिए:
(i) -2/7
(ii) 5/-3
(iii) 4/9
4. संख्या रेखा खींचिए और उस पर निम्नलिखित परिमेय संख्याओं को निरूपित कीजिए:
(i)
(ii) -5/8
(iii) -7/4 = -13/4
(iv) 7/8
5. संख्या रेखा पर P, Q, R, S, T, U, A और B इस प्रकार हैं कि TR = RS = SU और AP = PQ = QB। P, Q, R और S द्वारा दर्शाई गई परिमेय संख्याओं के नाम लिखिए।
6. निम्नलिखित में से कौन सा युग्म एक ही परिमेय संख्या का प्रतिनिधित्व करता है?
(i) (-7/21) और (3/9)
(ii) (-16/20) और (20/-25)
(iii) (-2/-3) और (2/3)
(iv) (-3/5) और (-12/20)
(v) (8/-5) और (-24/15)
(vi) (1/3) और (-1/9)
(vii) (-5/-9) और (5/-9)
7. निम्नलिखित परिमेय संख्याओं को सरलतम रूप में फिर से लिखिए:
(i) -8/6
(ii) 25/45
(iii) -44/72
(iv) -8/10
8. >,< और = में से सही चिह्न वाले बक्सों को भरें।
(i) -5/7 [ ] 2/3
(ii) -4/5 [ ] -5/7
(iii) -7/8 [ ] 14/-16
(iv) -8/5 [ ] -7/4
(v) १/-३ [ ] -1/4
(vi) 5/-11 [ ] -5/11
(vii) ० [ ] -7/6
9. निम्नलिखित में से प्रत्येक में कौन सा बड़ा है?
(i) 2/3, 5/2
(ii) -5/6, -4/3
(iii) -3/4, 2/-3
(iv) -1/4,
(v) -32/7, -3⅘
10. निम्नलिखित परिमेय संख्याओं को आरोही क्रम में लिखिए:
(i) -3/5, -2/5, -1/5
(ii) -1/3, -2/9, -4/3
(iii) -3/7, -3/2, -3/4
परिमेय संख्याओं पर क्रियाएँ परिमेय क्रियाएँ क्रियाएँ
अभ्यास 9.2
1. योग ज्ञात कीजिए:
(i) (5/4) + (-11/4)
(ii) (5/3) + (3/5)
(iii) (-9/10) + (22/15)
(iv) (-3/-11) + (5/9)
(v) (-8/19) + (-2/57)
(vi) -2/3 + 0
(vii) 2⅓ +4⅗
2. खोजें
(i) 7/24 - 17/36
(ii) 5/63 - (-6/21)
(iii) -6/13 - (-7/15)
(iv) -3/8 - 7/11
(v) -21/9 - 6
3. उत्पाद खोजें:
(i) (9/2) × (-7/4)
(ii) (3/10) × (-9)
(iii) (-6/5) × (9/11)
(iv) (3/7) × (-2/5)
(v) (3/11) × (2/5)
(vi) (3/-5) × (-5/3)
4. का मान ज्ञात कीजिए:
(i) (-4) (2/3)
(ii) (-3/5) 2
(iii) (-4/5) (-3)
(iv) (-1/8)
(v) (-2/13) 1/7
(vi) (-7/12) (-2/13)
(vii) (3/13) (-4/65)
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