What is the value of 32 ÷ 4 of 2 x 3 + [5 of 6-{7 of 8 (10 + 6 of (5/ 6) ÷5-1) ÷80}]-7×3+2
Answers
Step-by-step explanation:
2 – 3/5 (ii) 4 + 7/8 (iii) 3/5 + 2/7 (iv) 9/11 – 4/15 (v) 7/10 + 2/5 + 3/2
(vi) 2 + 3 (vii) 8 - 3
Answer:
(i) 2 – 3/5 = 2/1 – 3/5
= (2 * 5 – 3 * 1)/5 [LCM (1, 5) = 5]
= (10 - 3)/5
= 7/5
= 1
(ii) 4 + 7/8 = 4/1 + 7/8
= (4 * 8 + 7)/8 [LCM (1, 8) = 8]
= (32 + 7)/8
= 39/8
= 4
(iii) 3/5 + 2/7 = (3 * 7 + 2 * 5)/35 [LCM (7, 5) = 35]
= (21 + 10)/35
= 31/35
(iv) 9/11 – 4/15 = (9 * 15 – 4 * 11)/165 [LCM (11, 15) = 165]
= (135 - 44)/165
= 91/165
(v) 7/10 + 2/5 + 3/2 = (7 * 1 + 2 * 2 + 3 * 5)/10
= (7 + 4 + 15)/10
= 26/10 [26 and 10 are divided by 2]
= 13/5
= 2
(vi) 2 + 3 = 8/3 + 7/2
= (8 * 2 + 7 * 3)/6 [LCM (2, 3) = 6]
= (16 + 21)/6
= 37/6
= 6
(vii) 8 - 3 = 17/2 – 29/8
= (17 * 4 – 29 * 1)/8 [LCM (2, 8) = 8]
= (68 - 19)/8
= 39/8
= 4
Question 2:
Arrange the following in descending order:
(i) 2/9, 2/3, 8/21 (ii) 1/5, 3/7, 7/10
Answer:
(i) 2/9, 2/3, 8/21 = (2 * 7, 2 * 21, 8 * 3)/63 [LCM (9, 3, 21) = 63]
= (14, 42, 24)/63
= 14/63, 42/63, 24/63
Now, 42/63, 24/63, 14/63 [Arrange in descending order]
So, 2/3, 8/21, 2/9
(ii) 1/5, 3/7, 7/10 = (1 * 14, 3 * 10, 7 * 7)/70
= (14, 30, 49)/70
= 14/70, 30/70, 49/70
Now, 49/70, 30/70, 14/70 [Arrange in descending order]
So, 7/10, 3/7, 1/5
Question 3:
In a “magic square”, the sum of the numbers in each row, in each column and along the diagonals is the same. Is this a magic square?
Class_7_Maths_Fraction_&_Decimals_Representing_Fractions
(Along the first row 4/11 + 9/11 + 2/11 = 15/11)
Answer:
Sum of first row: 4/11 + 9/11 + 2/11 = 15/11 (Given)
Sum of second row: 3/11 + 5/11 + 7/11 = (3 + 5 + 7)/11 = 15/11
Sum of third row: 8/11 + 1/11 + 6/11 = (8 + 1 + 6)/11 = 15/11
Sum of first column: 4/11 + 3/11 + 8/11 = (4 + 3 + 8)/11 = 15/11
Sum of second column: 9/11 + 5/11 + 1/11 = (9 + 5 + 1)/11 = 15/11
Sum of third column: 2/11 + 7/11 + 6/11 = (2 + 7 + 6)/11 = 15/11
Sum of first diagonal (left to right): 4/11 + 5/11 + 6/11 = (4 + 5 + 6)/11 = 15/11
Sum of second diagonal (left to right): 2/11 + 5/11 + /11 = (2 + 5 + 8)/11 = 15/11
Answer:
Step-by-step explanation:(i) 2 – 3/5 = 2/1 – 3/5
= (2 * 5 – 3 * 1)/5 [LCM (1, 5) = 5]
= (10 - 3)/5
= 7/5
= 1
(ii) 4 + 7/8 = 4/1 + 7/8
= (4 * 8 + 7)/8 [LCM (1, 8) = 8]
= (32 + 7)/8
= 39/8
= 4
(iii) 3/5 + 2/7 = (3 * 7 + 2 * 5)/35 [LCM (7, 5) = 35]
= (21 + 10)/35
= 31/35
(iv) 9/11 – 4/15 = (9 * 15 – 4 * 11)/165 [LCM (11, 15) = 165]
= (135 - 44)/165
= 91/165
(v) 7/10 + 2/5 + 3/2 = (7 * 1 + 2 * 2 + 3 * 5)/10
= (7 + 4 + 15)/10
= 26/10 [26 and 10 are divided by 2]
= 13/5
= 2
(vi) 2 + 3 = 8/3 + 7/2
= (8 * 2 + 7 * 3)/6 [LCM (2, 3) = 6]
= (16 + 21)/6
= 37/6
= 6
(vii) 8 - 3 = 17/2 – 29/8
= (17 * 4 – 29 * 1)/8 [LCM (2, 8) = 8]
= (68 - 19)/8
= 39/8
= 4
Question 2:
Arrange the following in descending order:
(i) 2/9, 2/3, 8/21 (ii) 1/5, 3/7, 7/10
Answer:
(i) 2/9, 2/3, 8/21 = (2 * 7, 2 * 21, 8 * 3)/63 [LCM (9, 3, 21) = 63]
= (14, 42, 24)/63
= 14/63, 42/63, 24/63
Now, 42/63, 24/63, 14/63 [Arrange in descending order]
So, 2/3, 8/21, 2/9
(ii) 1/5, 3/7, 7/10 = (1 * 14, 3 * 10, 7 * 7)/70
= (14, 30, 49)/70
= 14/70, 30/70, 49/70
Now, 49/70, 30/70, 14/70 [Arrange in descending order]
So, 7/10, 3/7, 1/5
Question 3:
In a “magic square”, the sum of the numbers in each row, in each column and along the diagonals is the same. Is this a magic square?
Class_7_Maths_Fraction_&_Decimals_Representing_Fractions
(Along the first row 4/11 + 9/11 + 2/11 = 15/11)
Answer:
Sum of first row: 4/11 + 9/11 + 2/11 = 15/11 (Given)
Sum of second row: 3/11 + 5/11 + 7/11 = (3 + 5 + 7)/11 = 15/11
Sum of third row: 8/11 + 1/11 + 6/11 = (8 + 1 + 6)/11 = 15/11
Sum of first column: 4/11 + 3/11 + 8/11 = (4 + 3 + 8)/11 = 15/11
Sum of second column: 9/11 + 5/11 + 1/11 = (9 + 5 + 1)/11 = 15/11
Sum of third column: 2/11 + 7/11 + 6/11 = (2 + 7 + 6)/11 = 15/11
Sum of first diagonal (left to right): 4/11 + 5/11 + 6/11 = (4 + 5 + 6)/11 = 15/11
Sum of second diagonal (left to right): 2/11 + 5/11 + /11 = (2 + 5 + 8)/11 = 15/11