Grade 5 Bar Models: Ratio Bar Models

Worked examples

Real problems from the practice worksheets, solved one step at a time.

1. Example 1

   The ratio of Lisa's pencils to Sam's pencils is 5 : 6. Lisa has 50 pencils. How many pencils does Sam have?

   1. Draw Lisa's bar as 5 units and Sam's bar as 6 units of the same size.
   2. 5 units = 50, so 1 unit = 50 ÷ 5. 50 ÷ 5: take away 5 × 10 = 50 (0 left). 50 ÷ 5 = 10.
   3. Sam has 6 units: 6 × 10 = 60.
   4. Sam has 60 pencils.

   Answer: 60

2. Example 2

   Amy and Mia share 48 apples in the ratio 1 : 7. How many apples does Mia get?

   1. Draw Amy's bar as 1 unit and Mia's bar as 7 units. Together that is 1 + 7 = 8 units.
   2. 8 units = 48, so 1 unit = 48 ÷ 8. 48 ÷ 8 = 6, because 8 × 6 = 48.
   3. Mia gets 7 units: 7 × 6 = 42.
   4. Mia gets 42 apples.

   Answer: 42

3. Example 3

   The ratio of Tom's pencils to Max's pencils is 3 : 7. Max has 76 more pencils than Tom. How many pencils does Tom have?

   1. Draw Tom's bar as 3 units and Max's bar as 7 units. Max's bar is longer by 7 − 3 = 4 units.
   2. 4 units = 76, so 1 unit = 76 ÷ 4. 76 ÷ 4: take away 4 × 10 = 40 (36 left), 4 × 9 = 36 (0 left). 10 + 9 = 19, so 76 ÷ 4 = 19.
   3. Tom has 3 units: 3 × 19 = 10 × 3 + 9 × 3 = 30 + 27 = 57.
   4. Tom has 57 pencils.

   Answer: 57