CBSE Class 9 Maths Lab Manual – Division of a Paper Strip in Equal Parts

Objective
To divide a thin strip of paper into equal parts (7 equal parts).

Prerequisite Knowledge
Intercept Theorem: If there are three (or more) parallel lines and intercepts made by them on any transversal are equal, then intercepts made by them on any other transversal are also equal.

Materials Required
Tracing sheet, colours, ruled sheet of paper, geometry box.

Procedure

  1. Cut a rectangular strip of paper from a tracing sheet which is to be divided into 7 equal parts. Name it as ABCD.
    CBSE Class 9 Maths Lab Manual – Division of a Paper Strip in Equal Parts 1
  2. Now, take a ruled sheet, and mark the lines as 0, 1, 2, 3, 4 from top to bottom.
  3. Place the paper strip on the ruled sheet such as the point A coincides with line marked 0 and the point D coincides with line marked 7 as shown in the fig. (ii).
    CBSE Class 9 Maths Lab Manual – Division of a Paper Strip in Equal Parts 2
  4. Mark the points on the strip where parallel lines of ruled sheet cuts the strip as X1, X2, X3, X4, X5, X6 on line AD and Y1, Y2, Y3, Y4, Y5, Y6 on line BC.
  5. Now draw the lines X1Y1, X2Y2, X3Y3, X4Y4, X5Y5, X6Y6, parallel to AB and colour them as shown in fig. (iii).
    CBSE Class 9 Maths Lab Manual – Division of a Paper Strip in Equal Parts 3

Observation
X1Y1, X2Y2, X3Y3, X4Y4, X5Y5, X6Y6 divide the paper strip into seven equal parts.

Result
We obtain equally divided strip as AX1Y1B = X1X2Y2Y1 = X2X3Y3Y2 = X3X4Y4Y3 = X4X5Y5Y4 = X5X6Y6Y5 = X6DCY6.

Learning Outcome
Students can divide any rectangular strip in equal parts.

Activity Time
To make fraction chart.

  1. Take 9 strips of same size and colour them with different colours.
  2. Now by using ruled sheet, divide these strips into 1, 2, 3, 4, 5, 6,……9 equal parts.
  3. Paste these divided strips on a chart paper one below the other. See fig. (iv).
  4. A beautiful fraction chart is formed.
    Students may use different colour glazed papers to make it attractive and to identify clearly.
    CBSE Class 9 Maths Lab Manual – Division of a Paper Strip in Equal Parts 4

Viva Voce

Question 1.
How many equal parts of a strip can be done ?
Answer:
Infinite equal parts.

Question 2.
If a strip is divided in 8 equal parts what will be the value of 6 parts ?
Answer:
\(\frac { 6 }{ 8 }\)

Question 3.
What do you mean by intercept theorem ?
Answer:
If there are three (or more) parallel lines and intercepts made by them on one transversal are equal, the intercept on any other transversal are equal.

Question 4.
What is \(\frac { 1 }{ 6 }\) th of a rectangular strip ?
Answer:
A strip is divided into six equal parts, each part is one-sixth.

Question 5.
Can you divide a strip of 7 cm, into 6 equal parts by using ruler ?
Answer:
No.

Question 6.
Why is it necessary to use ruled sheet ?
Answer:
To get a collection of parallel lines at equal distances.

Question 7.
Which theorem is used in the activity ‘Division of a paper strip in equal parts’ ?
Answer:
Intercept theorem.

Question 8.
How many folds are required to divide a rope into 10 equal parts ?
Answer:
9 folds.

Multiple Choice Questions

Question 1.
What is the length of one part of the strip of 7 cm, if it is divided into two equal parts ?
(i) 3.5 cm
(ii) \(\frac { 2 }{ 7 }\) cm
(iii) 4 cm
(iv) none of these

Question 2.
What will be the value of 7 parts of a strip if it is divided into 9 equal parts ?
(i) \(\frac { 1 }{ 9 }\)
(ii) \(\frac { 3 }{ 9 }\)
(iii) \(\frac { 7 }{ 9 }\)
(iv) none of these

Question 3.
If a rectangular strip of 8 cm is divided into 8 equal parts, what will be length of each part ?
(i) 2 cm
(ii) 1 cm
(iii) 3 cm
(iv) none of these

Question 4.
What is the equivalent fraction of \(\frac { 2 }{ 3 }\) ?
(i) \(\frac { 8 }{ 12 }\)
(ii) \(\frac { 1 }{ 3 }\)
(iii) \(\frac { 3 }{ 2 }\)
(iv) none of these

Question 5.
Write two equivalent fractions of \(\frac { 5 }{ 6 }\) ?
(i) \(\frac { 10 }{ 12 } ,\frac { 15 }{ 18 }\)
(ii) \(\frac { 5 }{ 6 } ,\frac { 6 }{ 5 }\)
(iii) \(\frac { 6 }{ 5 } ,\frac { 10 }{ 12 }\)
(iv) none of these

Question 6.
To divide a thread into 11 equal parts, how many successive folds will you give ?
(i) 8
(ii) 10
(iii) 7
(iv) none of these

Question 7.
Which is greater (\(\frac { 23 }{ 25 }\)) or (\(\frac { 12 }{ 5 }\)) ?
(i) \(\frac { 23 }{ 25 }\)
(ii) \(\frac { 12 }{ 5 }\)
(iii) \(\frac { 36 }{ 25 }\)
(iv) none of these

Question 8.
Write two fractions which is equal to 1.
(i) \(\frac { 4 }{ 4 } ,\frac { 6 }{ 6 }\)
(ii) \(\frac { 4 }{ 4 } ,\frac { 2 }{ 3 }\)
(iii) \(\frac { 18 }{ 9 } ,\frac { 24 }{ 12 }\)
(iv) none of these

Question 9.
Add: \(3\frac { 3 }{ 5 } +8\frac { 2 }{ 3 }\)
(i) \(\frac { 184 }{ 15 }\)
(ii) \(\frac { 148 }{ 15 }\)
(iii) \(11\frac { 5 }{ 8 }\)
(iv) none of these

Question 10.
Simplify: \(\frac { 4 }{ 9 } +\frac { 5 }{ 6 } -\frac { 2 }{ 3 }\)
(i) \(\frac { 11 }{ 18 }\)
(ii) \(\frac { 18 }{ 11 }\)
(iii) \(\frac { 15 }{ 9 }\)
(iv) none of these

Answers

  1. (i)
  2. (iii)
  3. (ii)
  4. (i)
  5. (i)
  6. (ii)
  7. (ii)
  8. (i)
  9. (i)
  10. (i)

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