6th Grade Math Textbook, Fundamentals

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6-5

Votes for Leo

Votes for Bob

Total Votes

Ratio Equivalent Ratios

5

3 

5 • 2

3 • 2

10

6 

5 • 3

3 • 3

15

9 

5 • 4

3 • 4

20

12

816 24 32

20 votes for Leo 12 votes for Bob  32

So the table shows that Leo received 20 votes and

Bob received 12 votes.

Proportion by Parts

Objective To model solutions of proportions

• To solve proportions using part-to-whole ratios

Bob and Leo were running for the position of
team captain. For every 5 votes Leo received
from his teammates, Bob got 3 votes. If each
one of the 32 players voted once, how many votes did
each boy receive?

To find the number of votes each boy received,
use a 5 to 3 ratio.

You can use a model, a table, or proportions

to solve the problem.

Method 1 Use a Model

• Use 32 counters. Make two sets based
  on the ratio of the parts.

Ratio: 5 votes for Leo to 3 votes for Bob

9RWHVIRU/HR 9RWHVIRU%RE

Votes for LeoVotes for BobTotal

20  12  32

• Add the counters to both sets according
  to the ratio 5 : 3 until you reach a total
  of 32 counters.

So the model shows that Leo received 20 votes

and Bob received 12 votes.

Method 2 Make a Table

• Use the ratio 5 : 3.


• Multiply each term to find equivalent
  ratios until you reach a total of 32 votes.