Represent 2 × 1 5 diagrammatically.

Given, 2 × 1 5 It is given in the format: 1 m × 1 n = 1 m × n or a b × c d = a × c b × d Therefore, 2 1 × 1 5 = 2 × 1 1 × 5 = 2 5 We can represent it pictorially as,

Write 4 rational numbers equivalent to 2 7 .

Given rational number is 2 7 . We can get equivalent rational numbers by multiplying the numerator and denominator by the same integer number. So, other four rational numbers, equivalent to given rational numbers are: 2 × 2 7 × 2 = 4 14 2 × 3 7 × 3 = 6 21 2 × 4 7 × 4 = 8 28 2 × 5 7 × 5 = 10 35 Therefore, four equivalent rational numbers are 4 14 , 6 21 , 8 28 , 10 35 .

Simplify 2 3 × 5 4 × t 9 10 3 × t 3 .

Given, 2 3 × 5 4 × t 9 10 3 × t 3 We know that, a m ÷ a n = a m - n By solving this, we get = 2 3 × 5 4 × t 9 10 3 × t 3 = 2 3 × 5 4 × t 9 ( 2 × 5 ) 3 × t 3 = 2 3 × 5 4 × t 9 5 3 × 2 3 × t 3 = 5 4 - 3 × t 9 - 3 = 5 t 6 Therefore, the solution is 5 t 6 .