Math Labs with Activity – Divide a Thin Strip of Paper into Number of Equal Parts

Math Labs with Activity – Divide a Thin Strip of Paper into Number of Equal Parts

OBJECTIVE

To divide a thin strip of paper into a given number of equal parts (say into 8 equal parts)

Materials Required

1. A sheet of ruled paper in which all the lines are parallel and equidistant
2. Given rectangular strip of paper
3. A geometry box

Theory
The Intercept theorem used in Activity 1 may also be applied to divide a thin strip of paper into a given number of equal parts.

Procedure
Step 1: Take the rectangular strip of paper which has to be divided into a given number of equal parts (say into 8 equal parts). Label it as ABCD as shown in Figure 2.1.

Step 2: Mark the lines of the ruled paper as 0,1,2,3,…, sequentially from top to bottom. Place the strip over the ruled paper such that the point A lies over the line marked 0 and the point B lies over the line marked 8 as shown in Figure 2.2.
Step 3: Mark the points of intersection of the side AB of the rectangular strip with the parallel lines of the ruled paper as X₁, X₂, X₃, X₄, X₅, X₆ and X₇ as shown in Figure 2.2.

Step 4: Remove the paper strip from the ruled paper and draw the lines X₁Y₁,  X₂Y₂, X₃Y₃, X₄Y₄ , X₅Y₅, X₆Y₆ and X₇Y₇ parallel to the side BC passing through the points X₁, X₂, X₃, X₄, X₅, X₆ and X₇.

Observations
The lines X₁Y₁,  X₂Y₂, X₃Y₃, X₄Y₄ , X₅Y₅, X₆Y₆ and X₇Y₇ divide the strip ABCD into 8 equal parts.

Result
The strip of paper is divided into 8 equal parts.

Remarks: The above method of division of a strip of paper into a desired number of equal parts can be used to compare fractions. A number of paper strips of equal length can be divided into different numbers of equal parts as shown below (in Figure 2.4).

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