Rewrite addition problems using greatest common factors and the distributive
property to create equivalent expressions.
Practice Set B
Name:
Date:
1. Brendan has 25 basketball cards and 20 baseball cards. He would like to make
packages to sell that include each type of card using all of the cards. Each package
must have the same amount of each type of card. What is the greatest amount of
packages Brendan could create and how many basketball and baseball cards are in
each package? Explain your reasoning.
a. Use the distributive property to express the sum of the two sports cards (that
have a common factor) as a multiple of the sum of the sports cards with no
common factor.
2. There are 30 violinists and 45 cellists at an orchestra camp. The orchestra director
would like to make groups of musicians that include every violinist and cellist. Each
group must have the same amount of each type of musician. What is the greatest
amount of groups the orchestra conductor can create and how many violinists and
cellists are in each group? Explain your reasoning.
a. Use the distributive property to express the sum of the two types of
musicians (that have a common factor) as a multiple of the sum of the musicians
with no common factor.
Rewrite addition problems using greatest common factors and the distributive
property to create equivalent expressions.
Practice Set B Answer Key
1. Brendan has 25 basketball cards and 20 baseball cards. He would like to make
packages to sell that include each type of card using all of the cards. Each package
must have the same amount of each type of card. What is the greatest amount of
packages Brendan could create and how many basketball and baseball cards are in
each package? Explain your reasoning.
The greatest amount of packages Brendan could make with the sports cards is 5
packages. Each package would have 5 basketball cards and 4 baseball cards.
Explanation will vary. Any method for determining the greatest amount of packages and
the amount of basketball and baseball cards that are in each package are acceptable as
long as explanation is included.
a. Use the distributive property to express the sum of the two sports cards (that
have a common factor) as a multiple of the sum of the sports cards with no
common factor.
20 + 25 = 5 (5+4)
2. There are 30 violinists and 45 cellists at an orchestra camp. The orchestra director
would like to make groups of musicians that include every violinist and cellist. Each
group must have the same amount of each type of musician. What is the greatest
amount of groups the orchestra conductor can create and how many violinists and
cellists are in each group? Explain your reasoning.
The greatest amount of groups that the orchestra director can create is 15 groups.
Each group would have 2 violinists and 3 cellists.
Explanation will vary. Any method for determining the greatest amount of groups and
the amount of violinists and cellists that are in each group are acceptable as long as
explanation is included.
a. Use the distributive property to express the sum of the two types of
musicians (that have a common factor) as a multiple of the sum of the musicians
with no common factor.
30+45 = 15(2+3)