**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**

- Cut a rectangular strip of paper from a tracing sheet which is to be divided into 7 equal parts. Name it as ABCD.

- Now, take a ruled sheet, and mark the lines as 0, 1, 2, 3, 4 from top to bottom.
- 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).

- Mark the points on the strip where parallel lines of ruled sheet cuts the strip as X
_{1}, X_{2}, X_{3}, X_{4}, X_{5}, X_{6}on line AD and Y_{1}, Y_{2}, Y_{3}, Y_{4}, Y_{5}, Y_{6}on line BC. - Now draw the lines X
_{1}Y_{1}, X_{2}Y_{2}, X_{3}Y_{3}, X_{4}Y_{4}, X_{5}Y_{5}, X_{6}Y_{6}, parallel to AB and colour them as shown in fig. (iii).

**Observation**

X_{1}Y_{1}, X_{2}Y_{2}, X_{3}Y_{3}, X_{4}Y_{4}, X_{5}Y_{5}, X_{6}Y_{6} divide the paper strip into seven equal parts.

**Result**

We obtain equally divided strip as AX_{1}Y_{1}B = X_{1}X_{2}Y_{2}Y_{1} = X_{2}X_{3}Y_{3}Y_{2} = X_{3}X_{4}Y_{4}Y_{3} = X_{4}X_{5}Y_{5}Y_{4} = X_{5}X_{6}Y_{6}Y_{5} = X_{6}DCY_{6}.

**Learning Outcome**

Students can divide any rectangular strip in equal parts.

**Activity Time**

To make fraction chart.

- Take 9 strips of same size and colour them with different colours.
- Now by using ruled sheet, divide these strips into 1, 2, 3, 4, 5, 6,……9 equal parts.
- Paste these divided strips on a chart paper one below the other. See fig. (iv).
- A beautiful fraction chart is formed.

Students may use different colour glazed papers to make it attractive and to identify clearly.

**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**

- (i)
- (iii)
- (ii)
- (i)
- (i)
- (ii)
- (ii)
- (i)
- (i)
- (i)

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