Question

Instructions:Drag the tiles to the correct boxes to complete the pairs.

Answer 1

Answer:

1st Tile = 144m²n³

2nd tile = $72m^{4}n^{4}$

3rd tile = $36m^{3}n$

4th tile = $48m^{4}n^{4}$

Step-by-step explanation:

In this question we have to find out the least common multiple of the denominators and pair them with the rational expressions.

LCM of 9m²n and 16mn²

prime factors of 9m²n = 3×3×m×m×n

prime factors of 16mn³ = 2×2×2×2×m×n×n×n

So LCM of both = 2×2×2×2×3×3×m×m×n×n×n = 144 m²n³

LCM of $8m^{4}n^{2}, 18m^{2}n^{4}$

prime factors of $8m^{4}n^{2}$ = 2×2×2×m×m×m×m×n×n

prime factors of $18m^{2}n^{4}$ = 2×3×3×m×m×n×n×n×n

LCM of both = 2×2×2×3×3×m×m×m×m×n×n×n×n = $72m^{4}n^{4}$

Similarly LCM of $12mn, 18m^{3}n$ will be $36m^{3}n$

LCM of $24mn^{4}, 16m^{4}n$ will be $48m^{4}n^{4}$

Answer 2

The least common denominator has the highest degree of each of the variables and the LCM of the constants as factors.