Andhra Pradesh SCERT Class 7 Maths Rational Numbers Question and Answers Solutions
Andhra Pradesh SCERT 7th Class Maths Solutions Chapter 8 Rational Numbers Question and answers. Students who are searching for Andhra Pradesh Class 7 Maths Chapter 8 can find here Solution of this chapter.
Board |
Andhra Pradesh (AP Board) |
Class |
7th |
Subject |
Maths |
Topic |
Solution |
EXERCISE 8.1
1.) List five rational numbers between:
(i) –1 and 0
ANSWER:
We have to find five rational numbers between –1 and 0
We first covert –1 and 0 to rational numbers with the same denominators.
We make denominator 7.
–1 = -7/7 and 0 = 0/7
Five rational numbers between –1 and 0 are -1/7,-2/7,-3/7,-4/7 and -5/7
(ii) –2 and –1
ANSWER:
We have to find five rational numbers between –2 and –1
(iii) − 4/5 and −2/3
ANSWER:
We have to find five rational numbers between − 4/5 and −2/3
We first covert − 4/5 and −2/3 to rational numbers with the same denominators.
We make denominator 45.
− 4 x 9 /5 x 9 =-36/45 and −2 x 15 /3 x 15 = -30/45
Five rational numbers between − 4/5 and −2/3 are -31/45,-32/45,-33/45,-34/45 and -35/45
(iv) –1/2 and 2/3
ANSWER:
We have to find five rational numbers between –1/2 and 2/3
We first covert –1/2 and 2/3 to rational numbers with the same denominators.
We make denominator 24.
− 1 x 12 /2 x 12 =-12/24 and 2 x 8 /3 x 8 = 16/24
Five rational numbers between –1/2 and 2/3 are -5/24,-3/24,-1/24, 5/24 and 11/24
2.) Write four more rational numbers in each of the following patterns:
(i) -3/5, -6/10, -9/15, -12/20…
ANSWER:
We have to write four more rational numbers in given pattern of rational numbers.
We first observe given pattern.
-6/10 = -3 x 2 /5 x 2
-9/15 = -3 x 3 /5 x 3
-12/20 = -3 x 4 /5 x 4
From observing given pattern,
Four more rational numbers are,
-3 x 5 /5 x 5 = -15/25
-3 x 6 /5 x 6 = -18/30
-3 x 7 /5 x 7 = -21/35
-3 x 8 /5 x 8 = -24/40
(ii) -1/4,-2/8,-3/12…..
ANSWER:
We have to write four more rational numbers in given pattern of rational numbers.
We first observe given pattern.
-2/8 = -1 x 2 /4 x 2
-3/12 = -1 x 3 /4 x 3
From observing given pattern,
Four more rational numbers are,
-1 x 4 /4 x 4 = -4/16
-1 x 5 /4 x 5 = -5/20
-1 x 6 /4 x 6 = -6/24
-1 x 7 /4 x 7 = -7/28
(iii) -1/6, 2/-12, 3/-18, 4/-24…..
ANSWER:
We have to write four more rational numbers in given pattern of rational numbers.
We first observe given pattern.
2/-12 = -1 x 2 /6 x 2
3/-18 = -1 x 3 /6 x 3
4/-24 = -1 x 4 /6 x 4
From observing given pattern,
Four more rational numbers are,
-1 x 5 /6 x 5 = -5/30
-1 x 6 /6 x 6 = -6/36
-1 x 7 /6 x 7 = -7/42
-1 x 8 /6 x 8 = -8/48
3.) Give four rational numbers equivalent to:
(i)−2/7
ANSWER:
We have to give four rational numbers equivalent to −2/7
We multiply given rational number by 2,3,4,5 for equivalent rational numbers.
Equivalent rational numbers are
−2x 2 /7 x 2 = −4/14
−2 x 3/7 x 3 = −6/21
−2 x 4/7 x 4 = −8/28
−2 x 5/7 x 5 = −10/35
(ii) 5/−3
ANSWER:
We have to give four rational numbers equivalent to 5/−3
We multiply given rational number by 2,3,4,5 for equivalent rational numbers.
Equivalent rational numbers are
5 x 2 /−3 x 2 = 10/-6
5 x 3/−3 x 3 = 15/-9
5 x 4/−3 x 4 = 20/-12
5 x 5/−3 x 5 =25/ -15
(iii) 4/9
ANSWER:
We have to give four rational numbers equivalent to 4/9
We multiply given rational number by 2,3,4,5 for equivalent rational numbers.
Equivalent rational numbers are
4 x 2 /9 x 2 =8/18
4 x 3/9 x 3 =12/27
4 x 4/9 x 4 = 16/36
4 x 5/9 x 5 = 20/45
4.) Draw the number line and represent the following rational numbers on it:
(i) 3/4
ANSWER:
Wehave to draw the number line and we represent rational number on it.
We have to show 3/4 on number line.
(ii) −5/8
ANSWER:
We have to draw the number line and we represent rational number on it.
We have to show −5/8 on number line.
(iii)−7/4
ANSWER:
We have to draw the number line and we represent rational number on it.
We have to show −7/4 on number line.
(iv) 7/8
ANSWER:
We have to draw the number line and we represent rational number on it.
We have to show 7/8 on number line.
5.) 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.
ANSWER:
Given that,
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.
We have to find the rational numbers represented by P, Q, R and S.
From number line, we observe that,
Each Unit is divided in 3 parts.
Point P represents 7/3
Point Q represents 8/3
Point R represents -4/3
Point S represents -5/3
6.) Which of the following pairs represent the same rational number?
(i)−7/ 21 and 3/9
ANSWER:
We have find which pair represent the same rational number.
−7/ 21 Dividing by 7 we get = -1/3
3/9 = Dividing by 3 we get = 1/3
– 1/3 and 1/3 are not equal.
−7/ 21 and 3/9 has not same rational number.
(ii) -16/20 and 20/-25
ANSWER:
We have find which pair represent the same rational number.
-16/20 Dividing by 4 we get = -4/5
20/-25 = Dividing by 5 we get = 4/-5
-4/5 and 4/-5 are equal.
-16/20 and 20/-25 has same rational number.
(iii) -2/-3 and 2/3
ANSWER:
We have find which pair represent the same rational number.
-2/-3 we cancel negative sign. We get,
-2/-3 = 2/3
2/3
-2/-3 and 2/3 has same rational number.
(iv) – 3/ 5 and −12/20
ANSWER:
We have find which pair represent the same rational number.
– 3/ 5 Dividing by 1 we get = – 3/ 5
−12/20 = Dividing by 4 we get = -3/5
– 3/ 5 and −12/20 has same rational number.
(v) 8/-5 and −24/15
ANSWER:
We have find which pair represent the same rational number.
8/-5 Dividing by 1 we get = 8/-5
8/-5 we multiply by 3 to numerator and denominator we get,
8 x 3 /-5 x 3 = 24/-15 which is equivalent to 8/-5
8/-5 and −24/15 has same rational number.
(vi) 1/3and -1/9
ANSWER:
We have find which pair represent the same rational number.
1/3 Dividing by 1 we get = 1/3
1/3 we multiply by 3 numerator and denominator we get,
1 x 3 /3 x 3 = 3/9 which is not equivalent to 1/3
1/3 and -1/9 has same rational number.
(vii)−5/9 and 5/-9
ANSWER:
We have find which pair represent the same rational number.
−5/9 Dividing by 1 we get = −5/9
5/-9 Dividing by 1 we get = 5/-9
−5/9 and 5/-9 has same rational number.
7.) Rewrite the following rational numbers in the simplest form:
(i) −8/6
ANSWER:
We have to write given rational number in the simplest form.
−8/6
We divide both numerator and denominator by 2 we get,
(−8/2)/(6/2) = -4/3
The simplest form of −8/6 is -4/3
(ii) 25/45
ANSWER:
We have to write given rational number in the simplest form.
25/45
We divide both numerator and denominator by 5 we get,
(25/5)/(45/5) = 5/9
The simplest form of 25/45 is 5/9
(iii)− 44/72
ANSWER:
We have to write given rational number in the simplest form.
− 44/72
We divide both numerator and denominator by 4 we get,
(-44/4)/(72/4) = -11/18
The simplest form of − 44/72 is -11/18
(iv) −8/10
ANSWER:
We have to write given rational number in the simplest form.
−8/10
We divide both numerator and denominator by 2 we get,
(−8/2)/(10/2) = -4/5
The simplest form of −8/10 is -4/5
8.) Fill in the boxes with the correct symbol out of >, <, and =.
(i) −5/7 ____ 2/3
ANSWER:
We have to compare given rational number.
−5/7 and 2/3
We do cross multiplication of numerator of 1st rational number to denominator of 2nd rational number.
-5 x 3 < 7 x 2
-15 < 14
Hence,
−5/7 < 2/3
(ii)− 4/5 ____ −5/7
ANSWER:
We have to compare given rational number.
− 4/5 and −5/7
We do cross multiplication of numerator of 1st rational number to denominator of 2nd rational number.
-4 x 7 < 5 x -5
-28 < -25
Hence,
− 4/5 < −5/7
(iii) −7/ 8 ____ 14/−16
ANSWER:
We have to compare given rational number.
−7/ 8 and 14/−16
We do cross multiplication of numerator of 1st rational number to denominator of 2nd rational number.
-7 x -16 < 8 x 14
112 = 112
Hence,
−7/ 8 = 14/−16
(iv)− 8/ 5 ____ −7/4
ANSWER:
We have to compare given rational number.
− 8/ 5 and −7/4
We do cross multiplication of numerator of 1st rational number to denominator of 2nd rational number.
-8 x 4 < 5 x -7
-32 > -35
Hence,
− 8/ 5 > −7/4
(v) 1/−3 ____ −1/ 4
ANSWER:
We have to compare given rational number.
1/−3 and −1/ 4
We do cross multiplication of numerator of 1st rational number to denominator of 2nd rational number.
1 x 4 < -3 x -1
4 > 3
Hence,
1/−3 > −1/ 4
(vi) 5/−11____ −5/11
ANSWER:
We have to compare given rational number.
5/−11 and −5/11
We do cross multiplication of numerator of 1st rational number to denominator of 2nd rational number.
5 x 11 < -11 x -5
55 = 55
Hence,
5/−11 = −5/11
(vii) 0 ____ −7/6
ANSWER:
We have to compare given rational number.
0/1 and −7/6
We do cross multiplication of numerator of 1st rational number to denominator of 2nd rational number.
0 x 6 > 1 x -7
0 > -7
Hence,
0 > −7/6
9.) Which is greater in each of the following:
(i)2/3, 5/2
ANSWER:
We have to compare given rational number.
2/3 and 5/2
We do cross multiplication of numerator of 1st rational number to denominator of 2nd rational number.
2 x 2 < 3 x 5
4 < 15
Hence,
2/3 < 5/2
(ii) −5/6, −4/3
ANSWER:
We have to compare given rational number.
−5/6 and −4/3
We do cross multiplication of numerator of 1st rational number to denominator of 2nd rational number.
-5 x 3 < 6 x -4
-15 > -24
Hence,
−5/6 > −4/3
(iii)−3/4, 2/−3
ANSWER:
We have to compare given rational number.
−3/4 and 2/−3
We do cross multiplication of numerator of 1st rational number to denominator of 2nd rational number.
-3 x -3 > 4 x 2
9 > 8
Hence,
−3/4 > 2/−3
(iv) −1/4, 1/4
ANSWER:
We have to compare given rational number.
−1/4 and 1/4
We do cross multiplication of numerator of 1st rational number to denominator of 2nd rational number.
-1 x 4 > 4 x 1
-4 < 4
Hence,
−1/4 < 1/4
(v) − 3(2/7), -3(4/5)
ANSWER:
We first convert mixed fraction into simple fraction.
− 3(2/7) = -19/7
-3(4/5) = -11/5
We have to compare given rational number.
-19/7 and -11/5
We do cross multiplication of numerator of 1st rational number to denominator of 2nd rational number.
-19 x 5 > 7 x -11
-95 < -77
Hence,
− 3(2/7) < -3(4/5)
10.) Write the following rational numbers in ascending order:
(i)− 3/5,-2/5,-1/5
ANSWER:
We have to write given rational numbers in ascending order.
− 3/5,-2/5,-1/5 here denominator is same.
We know,
When denominator is same, numerator of those fraction is greater that fraction is greater.
− 3/5 < -2/5 < -1/5
The ascending order is − 3/5,-2/5,-1/5.
(ii) – 1/3,-2/9,-4/3
ANSWER:
We have to write given rational numbers in ascending order.
– 1/3,-2/9,-4/3
We find LCM of denominator 3, 9, 3
LCM of denominator is 9.
– 1x 3/3 x 3,-2 x 1 /9 x 1,-4 x 3 /3 x 3
= -3/9,-2/9,-12/9 here denominator is same.
We know,
When denominator is same, numerator of those fraction is greater that fraction is greater.
-4/3 < – 1/3 < -2/9
The ascending order is -4/3, – 1/3, 2/9.
(iii) -3/7,-3/2,-3/4
ANSWER:
We have to write given rational numbers in ascending order.
-3/7,-3/2,-3/4
We find LCM of denominator 7,2,4
LCM of denominator is 28.
– 3x 4/7 x 4,-3 x 14 /2 x 14,-3 x 7 /4 x 7
= -12/28,-42/28,-21/28 here denominator is same.
We know,
When denominator is same, numerator of those fraction is greater that fraction is greater.
-3/2 <-3/4 < -3/7
The ascending order is -3/2,-3/4, -3/7
EXERCISE 8.2
1.) Find the sum:
(i) 5/4 + (11/4)
ANSWER:
Here we have to do addition of rational numbers.
5/4 + (11/4)
Here denominator is same.
We know,
When we adding rational numbers with same denominators, we add the numerators keeping the denominators same.
5/4 + (11/4) = (5 + 11) / 4
= 16/4
5/4 + (11/4) = 4
(ii) 5/3 + 3/5
ANSWER:
Here we have to do addition of rational numbers.
5/3 + 3/5
Here denominator is not same.
We make denominator is same.
We take LCM of denominator 3 and 5
LCM of denominator 3 and 5 is 15.
5 x 5 /3 x 5 + 3 x 3 /5 x 3
= 25/15 + 9/15
We know,
When we adding rational numbers with same denominators, we add the numerators keeping the denominators same.
= (25 + 9) /15
5/3 + 3/5 = 34/25 = 2(4/15)
(iii)−9/10 + 22/15
ANSWER:
Here we have to do addition of rational numbers.
−9/10 + 22/15
Here denominator is not same.
We make denominator is same.
We take LCM of denominator 10 and 15
LCM of denominator 10 and 15 is 30.
-9 x 3 /10 x 3 + 22 x 2 /15 x 2
= -27/30 + 44/30
We know,
When we adding rational numbers with same denominators, we add the numerators keeping the denominators same.
= (-27 + 44) /30
−9/10 + 22/15 = 17/30
(iv)−3/− 11+ 5/9
ANSWER:
Here we have to do addition of rational numbers.
−3/− 11 + 5/9
= 3/ 11 + 5/9
Here denominator is not same.
We make denominator is same.
We take LCM of denominator 11 and 9
LCM of denominator 11 and 9 is 99.
3 x 9 /11 x 9 + 5 x 11 /9 x 11
= 27/99 + 55/99
We know,
When we adding rational numbers with same denominators, we add the numerators keeping the denominators same.
= (27 + 55) /99
−3/− 11 + 5/9 = 82/99
(v)−8/19 +(−2)/57
ANSWER:
Here we have to do addition of rational numbers.
−8/19 + (−2)/57
Here denominator is not same.
We make denominator is same.
We take LCM of denominator 19 and 57
LCM of denominator 19 and 57 is 57.
-8 x 3 /19 x 3 + (−2)/57
= -24/57 + (−2)/57
We know,
When we adding rational numbers with same denominators, we add the numerators keeping the denominators same.
= (-24 + (-2)) /57
−8/19 + (−2)/57 = -26/57
(vi)−2/3 + 0
ANSWER:
Here we have to do addition of rational numbers.
−2/3 + 0
We know,
Sum of any number with 0 is the number itself.
−2/3 + 0 = -2/3
(vii) – 2(1/3) + 4 (3/5)
ANSWER:
Here we have to do addition of rational numbers.
We 1st convert mixed fraction into simple fraction.
– 2(1/3) = -5/3
4 (3/5) = 23/5
-5/3 + 23/5
Here denominator is not same.
We make denominator is same.
We take LCM of denominator 3 and 5
LCM of denominator 3 and 5 is 15.
-5 x 5 /3 x 5 + 23 x 3 /5 x 3
= -25/15 + 69/15
= (-25 + 69)/15
– 2(1/3) + 4 (3/5) = 44/15
2.) Find
(i) 7/24 – 17/36
ANSWER:
Here we have to do subtraction of rational numbers.
7/24 – 17/36
Here denominator is not same.
We make denominator is same.
We take LCM of denominator 24 and 36
LCM of denominator 24 and 36 is 72.
7 x 3 /24 x 3 – 17 x 2 /36 x 2
= 21/72 – 34/72
= (21 – 34)/72
7/24 – 17/36 = -13/72
ii) 5/63 – (-6/21)
ANSWER:
Here we have to do subtraction of rational numbers.
5/63 – (-6/21)
Here denominator is not same.
We make denominator is same.
We take LCM of denominator 63 and 21
LCM of denominator 63 and 21is 63.
5/63 – (-6) x 3 /21 x 3
= 5/63 + 18/63
= (5 + 18)/63
5/63 – (-6/21) = 23/63
(iii)− 6/13 – (-7/15)
ANSWER:
Here we have to do subtraction of rational numbers.
− 6/13 – (-7/15)
Here denominator is not same.
We make denominator is same.
We take LCM of denominator 13 and 15
LCM of denominator 13 and 15is 195.
-6 x 15 /13 x 15– (-7) x 13 /15 x 13
= -90/195 – (-91)/195
= (-90 + 91)/195
− 6/13 – (-7/15) = 1/195
(iv) − 3/8 – 7/11
ANSWER:
Here we have to do subtraction of rational numbers.
− 3/8 – 7/11
Here denominator is not same.
We make denominator is same.
We take LCM of denominator 8 and 11
LCM of denominator 8 and 11 is 88.
-3 x 11 /8 x 11 – (7) x 8 /11 x 8
= -33/88 – 56/88
= (-33 – 56)/88
− 3/8 – 7/11 = − 89/88
(v) − 2 (1/9) – 6
ANSWER:
Here we have to do subtraction of rational numbers.
− 2 (1/9) – 6
− 2 (1/9) = -17/9
-17/9 – 6
Here denominator is not same.
We make denominator is same.
We take LCM of denominator 9 and 1
LCM of denominator 9 and 11 is 9.
-17/9 – 6 x 9 /1 x 9
= -17/9 – 54/9
= (-17 – 54)/9
− 2 (1/9) – 6 = − 71/9
3.) Find the product:
(i) 9/2 × (−7/4)
ANSWER:
We have to find product of given rational numbers.
9/2 × (−7/4)
We directly do,
Multiply the numerators of the two rational numbers / multiply the denominators of the two rational numbers.
9 x -7 / 2 x 4
9/2 × (−7/4) = -63/8
ii) 3/10 × (−9)
ANSWER:
We have to find product of given rational numbers.
3/10 × (−9)
We know,
When we multiplying a rational number by a positive integer, wemultiply the numerator by that integer, keeping the denominator unchanged.
3/10 × (−9) = (3 x -9) / 10
3/10 × (−9) = -27/10
(iii)−6/5 × 9/11
ANSWER:
We have to find product of given rational numbers.
−6/5 × 9/11
We directly do,
Multiply the numerators of the two rational numbers / multiply the denominators of the two rational numbers.
−6 x 9 /5 ×11
−6/5 × 9/11 = -54/55
(iv) 3/7 x (-2/5)
ANSWER:
We have to find product of given rational numbers.
3/7 x (-2/5)
We directly do,
Multiply the numerators of the two rational numbers / multiply the denominators of the two rational numbers.
3 x -2 /7 x 5
3/7 x (-2/5) = −6/35
(v) 3/11 × 2/5
ANSWER:
We have to find product of given rational numbers.
3/11 × 2/5
We directly do,
Multiply the numerators of the two rational numbers / multiply the denominators of the two rational numbers.
3 x 2 /11 x 5
3/11 × 2/5 = 6/55
(vi) 3/-5 x -5/3
ANSWER:
We have to find product of given rational numbers.
3/-5 x -5/3
We directly do,
Multiply the numerators of the two rational numbers / multiply the denominators of the two rational numbers.
3 x -5 /-5 x 3
-15/-15 = 1
3/-5 x -5/3 = 1
4.) Find the value of:
(i) (−4) ÷ 2/3
ANSWER:
We have to find division of given rational numbers.
(−4) ÷ 2/3
We know,
When we divide one rational number by the other non-zero rational numberwe multiply the rational number by the reciprocal of the other.
(−4) x 3/2
-12/2
(−4) ÷ 2/3 = -6
(ii)−3/5 ÷2
ANSWER:
We have to find division of given rational numbers.
−3/5 ÷2
We know,
When we divide one rational number by the other non-zero rational number we multiply the rational number by the reciprocal of the other.
−3/5 x 1/2
We directly do,
Multiply the numerators of the two rational numbers / multiply the denominators of the two rational numbers.
-3 x 1/ 5 x 2
−3/5 ÷2 = -3/10
(iii)−4/5 ÷ (−3)
ANSWER:
We have to find division of given rational numbers.
−4/5 ÷ (−3)
We know,
When we divide one rational number by the other non-zero rational number we multiply the rational number by the reciprocal of the other.
−4/5 x (1/−3)
We directly do,
Multiply the numerators of the two rational numbers / multiply the denominators of the two rational numbers.
-4 x 1/ 5 x -3
−4/5 ÷ (−3) = 4/15
(iv) − 1/8 ÷ 3/4
ANSWER:
We have to find division of given rational numbers.
− 1/8 ÷ 3/4
We know,
When we divide one rational number by the other non-zero rational number we multiply the rational number by the reciprocal of the other.
− 1/8 x 4/3
We directly do,
Multiply the numerators of the two rational numbers / multiply the denominators of the two rational numbers.
-1 x 4/ 8 x 3
−4/24 = -1/6
− 1/8 ÷ 3/4= -1/6
(v) −2/13 ÷ 1/7
ANSWER:
We have to find division of given rational numbers.
−2/13 ÷ 1/7
We know,
When we divide one rational number by the other non-zero rational number we multiply the rational number by the reciprocal of the other.
−2/13 x 7/1
We directly do,
Multiply the numerators of the two rational numbers / multiply the denominators of the two rational numbers.
-2 x 7/ 13 x 1
−2/13 ÷ 1/7 = −14/13
(vi) – 7/12 ÷ (−2/13)
ANSWER:
We have to find division of given rational numbers.
– 7/12 ÷ (−2/13)
We know,
When we divide one rational number by the other non-zero rational number we multiply the rational number by the reciprocal of the other.
– 7/12 x (−13/2)
We directly do,
Multiply the numerators of the two rational numbers / multiply the denominators of the two rational numbers.
-7 x -13/ 12 x 2
– 7/12 ÷ (−2/13) = 91/24
(vii) 3/13 ÷ (-4/65)
ANSWER:
We have to find division of given rational numbers.
3/13 ÷ (-4/65)
We know,
When we divide one rational number by the other non-zero rational number we multiply the rational number by the reciprocal of the other.
3/13 x (-65/4)
We directly do,
Multiply the numerators of the two rational numbers / multiply the denominators of the two rational numbers.
3 x -65/ 13 x 4
3/13 ÷ (-4/65) = -195/52 = -15/4