In the year 123 B. C. King Pompasus was looking for a way to guarantee that all the guests at his parties would get the same amount of food. He decided to have them all line up and have the servants pass out each piece of food to the guests. Thus, he invented the Distributive Property of Mathematics!
Each team in the Tour de France has a sponsor. The sponsor for Victor de Velo's team is the French national lottery, La Française des Jeux.

As part of their sponsorship, La Française des Jeux equips each team member with a team jersey and helmet. A team jersey costs the lottery
180 francs and a helmet with the logo costs 135 francs.


There are 9 team members so the lottery must purchase 9 helmets and 9 jerseys. There are two ways to figure out the cost of these items. The first way is to multiply the cost of a jersey times 9 people and add it to the cost of a helmet times 9 people.

(180 × 9) + (135 × 9)
(Note: The parentheses are not necessary due to order of operations.)
1620 + 1215
2835 francs

The second way La Française des Jeux can figure the cost in by adding the cost of a jersey and helmet to find the cost per person and then multiply by 9 people.

(180 + 135) × 9
(Note: Using this method, the parentheses are necessary.)
315 × 9
2835 francs

Either way, the lottery will arrive at a total cost of 2835 francs.


 In mathematics, this is called the Distributive Property. The Distributive Property states that ax + bx = (a + b)x.

This can make solving problems simpler.

Example 1:
5 × 19 + 5 × 6 can be done mentally if thought of as

5 × (9 + 16) or 5 × 25

Example 2:
(12 + 0.5) × 20 can be done mentally if thought of as

12 × 20 + 0.5 × 20 or 240 + 10

In addition to the jersey and helmets, La Française des Jeux also provided each of the 9 team members with a water bottle at the cost of 38 francs each and a bicycle decal at a cost of 12 francs apiece.

Use the distributive property to find the total cost of these two items for the whole team.

 Find the cost of the water bottle and the decal.

Number Theory Main | Properties of One

Copyright 2020 Tower 23