Question

45 + 54 = 99 times ( ) + ( )

Answer 1

a) You have to find the greatest common factor for the values 45 and 54

To do so you have to determine the factors for each value and determine the highest value both numbers are divisible for.

Factors of 45 are

1, 3, 5, 9, 15, 45

Factors of 54 are

1, 2, 3, 6, 9, 18, 27, 54

The greatest common factor is 9, this means that you can divide both numbers by 9 and the result will be an integer:

$\frac{45}{9}=5$$\frac{54}{9}=6$

b) Given the addition

$45+54$

You have to factorize the adition using the common factor.

That is to "take out" the 9 of the addition, i.e. divide 45 and 54 by 9 and you get the result (5+6) but for this result to be equvalent to the original calculation, you have to multiply it by 9

$45+54=9(5+6)$