Question

Instructions:Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used.

Answer 1

Answer:

The mapping is as follows:

      Gcd                              Tile

1)    $4p^2q^5$                 $8p^3q^6\ and\ 4p^2q^5$

2)   $4p^3q^2$                 $4p^4q^5\ and\ 8p^3q^2$

3)    $8p^2q$                    $16p^3q^2\ and\ 24p^2q$

4)    $8pq^5$                    $24pq^6\ and\ 16p^3q^5$

Step-by-step explanation:

We know that gcd(or greatest common divisor) of two numbers is greatest possible  factors that is common to both the numbers.

• First tile is:

$4p^4q^5\ and\ 8p^3q^2$

The gcd of these two monomials is: $4p^3q^2$

• Second tile is:

$24pq^6\ and\ 16p^3q^5$

The gcd of these two monomials is: $8pq^5$

• Third tile is:

$8p^3q^6\ and\ 4p^2q^5$

The gcd of these two monomials is: $4p^2q^5$

• Fourth tile is:

$16p^3q^2\ and\ 24p^2q$

The gcd of these two monomials is: $8p^2q$

• Fifth tile is:

$12p^3q\ and\ 4p^2q^5$

The gcd of these two monomials is: $4p^2q$

Answer 2

The GCF of the first two is 4p³q².
The GCF of the second two is 8pq⁵.
The GCF of the third two is 4p²q⁵.
The GCF of the fourth two is 8p²q.
The GCF of the fifth two is 4p²q.

To find the GCF of each pair, find the greatest number that will divide into each coefficient.  As for the variable portions, choose the variable that has the smallest exponent from each pair.