Page 110 - Math_Genius_V1.0_C7_Flipbook

D:\Surender Prajapati\CBSE_ICSE_Book_New\CBSE\Grade-7\Math_Genius-7\Open_File\05_Chapter\05_Chapter
\ 15-Nov-2024 Surender Prajapati Proof-5 Reader’s Sign _______________________ Date __________

5
Solution: (a) x × x × x × x × x = x
10
(b) y × y × y × y × y × … 10 times = y
2 3 2
2
3
2
(c) a × a × b × b × b × c × c = a × b × c = a b c
2
2 2 2
2
(d) p × p × q × q × r × r = p × q × r = p q r
2
(e) 2 × 2 × (x × x × x × … 7 times) = 2 × x = 4x 7
2
7
7
(f) 2 × 3 × 3 × (m × m × m × … 5 times) × (n × n × n × … 7 times) = 18 × m × n = 18 m n
5
5
7
2
2
(g) 3 × 3 × p × p × 5 × q × q × 7 × r × r × r = 3 × p × 5 × q × 7 × r 3
2
= 9 × 5 × 7 × p × q × r = 315p q r
2
2
3
2 2 3
Example 8: Write the expanded form of the following:
3 2
2 3
3 2
(a) a b (b) x y z (c) 4m 2 (d) 27pq r
3
2 2 3
2 3
(e) 16l m n (f) 15a b c
Solution: (a) a b = a × a × a × b × b Quick Check
3 2
3 2
(b) x y z = x × x × x × y × y × z There are x y mango saplings in a row
2 2
2
2
(c) 4m = 2 × 2 × m × m of a field. If there are y z rows in the field.
How many mango saplings are in the field?
2 3
(d) 27pq r = 3 × 3 × 3 × p × q × q × r × r × r
2 3
(e) 16l m n = 2 × 2 × 2 × 2 × l × l × l × m × m × n × n × n
3
(f) 15a b c = 3 × 5 × a × a × b × b × c × c × c
2 2 3
2 3
Example 9: The cost of one table fan is `a b . Find the cost of such type of ab table fans.

Solution: The cost of 1 table fan = `a b
2 3
3 4
2 3
\ The total cost of ab table fans = `(a b × ab) = `a b
3 4
Thus, the cost of ab table fans is `a b .
Practice Time 5B
1. Identify the constants and the variables in the following.
1
(a) – (b) 0x (c) –4 (d) 11xz
2 1
(e) 11a 2 (f) xyz (g) 29pq 2 (h) 3 a
2. Express the following in exponential form.
(a) p × p × q × q × q (b) x × x × x × y × y × y
(c) 3 × a × a × b × b × c (d) 2 × 2 × 2 × m × m × m
(e) 2 × 2 × 2 × m × m × 3 × n × n × 5 × l × l × l (f) 2 × 2 × x × x × x × y × y × y × 7 × z × z
(g) 7 × 7 × (a × a × a × … 9 times) × 6 × 6 × 6 × (b × b × b × … 11 times)
3. Write the expanded form of the following.
3
2 2 3
(a) x y (b) x y z (c) 14p q (d) 9pqr
2 3
2 2
2
3 2
2 3
3
2
(e) 12m n (f) 15a b (g) 2x × y × 8z 3 (h) 8m × n × 4p
2
3
4. Ravi has x y bananas. The cost of each banana is `xy. Find the total cost of all bananas.
2 3
2 2
2
5. There are a b students in a class. `c is collected from each student for annual day function.
How many rupees has been collected from the class?
Mathematics-7 108