## 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**

- A sheet of ruled paper in which all the lines are parallel and equidistant
- Given rectangular strip of paper
- 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 X_{1}, X_{2}, X_{3}, X_{4}, X_{5}, X_{6} and X_{7} as shown in Figure 2.2.

**Step 4:** Remove the paper strip from the ruled paper and 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} and X_{7}Y_{7} parallel to the side BC passing through the points X_{1}, X_{2}, X_{3}, X_{4}, X_{5}, X_{6} and X_{7}.

**Observations**

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} and X_{7}Y_{7} 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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