Writing Expressions Using the G.C.F
Learn: How can you use the greatest common factor?
Dina is making packs for a group of her friends going on a trip. Each pack should have the same number of sandwiches and the same number of bottles of water. What is the greatest number of snack packs that she can make with no any left over?
To solve this problem, you need to find the numbers that are factors of both 60 and 90 which are the common factors of 60 and 90.
The number of snack packs is the greatest number that is a factor of both 60 and 90.
The greatest number of snack packs she can make is 30.
We can represent this scenario by the relation
30 bags each pack contains 2 sandwiches and 3 bottles of water.
Example 1
Nada has 12 red flowers and 20 yellow flowers.
She wants to make bouquets with the same number of each color flower in each bouquet.
What is the greatest number of bouquets she can make?
Write the expression that represent this situation.
Solution
Note
Let r stand for a red flower and y stand for a yellow flower. You can represent this information with an expression.
Example 2
Use the distributive property and G.C.F to write the expression of the following addition problems.
a. 7 + 56
b. 8 + 10
c. 15 + 45
d. 60 + 20
Solution
