Question

Show that rational numbers are commutative under addition and multiplication using paper cutting and pasting.

Answer 1

Verification of commutative law under Addition and Multiplication using the graph sheet through cutting and pasting is as follows:

The commutative law under Addition

• Cut out 2 strips of length 3 units from a graph/grid paper and colour them green.
• Similarly, cut out 2 strips of length 4 units from a graph/grid paper and colour them pink.
• i) For representing 3 + 4, paste one strip of length 3 units along with one strip of length 4 units.
• ii) For representing 4 + 3, paste one strip of length 4 units along with one strip of length 3 units.
• Now compare the length of strips obtained in step (i) and (ii)

The commutative law under Multiplication

• (i) Cut out 3 strips each of 4 boxes from a graph/grid paper and colour them pink.
• (ii) Similarly, cut out 4 strips each of 3 boxes from a graph/grid paper and colour them green.
• Place them on a graph/grip paper to form a rectangle as shown.
• Now compare the number of boxes obtained in step (i) and (ii)