Ex 12.4 Q1 Algebraic Expression Solution- NCERT Maths Class 7
Question
Observe the patterns of digits made from line segments of equal length. You will find such segmented digits on the display of electronic watches or calculators.
(a)
(b)
(c)
If the number of digits formed is taken to be n, the number of segments required to form n digits is given by the algebraic expression appearing on the right of each pattern. How many segments are required to form \(5, 10, 100\) digits of the kind,
Text Solution
What is known?
The patterns of digits made from line segments of equal length
What is unknown?
Number of segments required to form \(5, 10, 100\) digits of the kind, ,
Reasoning:
This question is very easy like simply put the value of n in the pattern formulae and you can easily find out the number of segments.
Steps:
Putting value of \( n=5, 10\) and \(100\) in the pattern formulae.
\(({\rm{i}})\quad 5n + 1\) \[\begin{align}5 \times 5 + 1 & = 25 + 1\\& = 26\\5 \times 10 + 1 & = 50 + 1\\& = 51\\5 \times 100 + 1 & = 500 + 1\\& = 501\end{align}\]
\({\rm{(ii)}}\quad 3n + 1\) \[\begin{align}3 \times 5 + 1 & = 15 + 1\\& = 16\\3 \times 10 + 1 &= 30 + 1\\& = 31\\3 \times 100 + 1 & = 300 + 1\\& = 301\\\end{align}\]
\(( {{\rm{iii}}}) \quad 5n + 2 \) \[\begin{align}\\5 \times 5 + 2 & = 25 + 2\\&= 27\\5 \times 10 + 2 & = 50 + 2\\& = 52\\5 \times 100 + 2 & = 500 + 2\\& = 502\\\end{align}\]
S. No. | Symbol | Digit’s Number | Pattern’s Formulae | No. of. Segments |
(i) | \(5\) | \({\rm{5 n + 1}}\) | 26 | |
\(10\) | 51 | |||
\(100\) | 501 | |||
(ii) |
\(5\) | \({\rm{3}}\,{\rm{n + 1}}\) |
16 | |
\(10\) | 31 | |||
\(100\) | 301 | |||
(iii) |
\(5\) | \({\rm{5 n + 2}}\) |
27 | |
\(10\) | 52 | |||
\(100\) | 502 |