Grade 5 Bar Models: Fraction Bar Models

Worked examples

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

1. Example 1

   4/11 of Max's books are red. Max has 32 red books. How many books does Max have in all?

   1. Cut Max's bar into 11 equal units. The red books are 4 of those units.
   2. 4 units = 32, so 1 unit = 32 ÷ 4. 32 ÷ 4 = 8, because 4 × 8 = 32.
   3. All 11 units: 11 × 8 = 88.
   4. Max has 88 books in all.

   Answer: 88

2. Example 2

   Jack had 40 books. Jack gave away 1/4 of them and then used 1/2 of the rest. How many books does Jack have left?

   1. Draw a bar for all 40 books and cut it into 4 equal units: 1 unit = 40 ÷ 4 = 10.
   2. Jack gave away 1 unit, so 4 − 1 = 3 units are left: 3 × 10 = 30. That is the rest.
   3. Cut the rest (30) into 2 equal units: 1 unit = 30 ÷ 2 = 15.
   4. Jack used 1 unit, so 2 − 1 = 1 unit is left: 1 × 15 = 15.
   5. Jack has 15 books left.

   Answer: 15

3. Example 3

   Emma has 105 pencils. 2/5 of them are red and the rest are blue. How many more blue pencils than red pencils are there?

   1. Cut the bar for all 105 pencils into 5 equal units: 1 unit = 105 ÷ 5 = 21.
   2. Red is 2 units and blue is the rest: 5 − 2 = 3 units.
   3. Blue has 3 − 2 = 1 more unit than red: 1 × 21 = 21.
   4. There are 21 more blue pencils than red pencils.

   Answer: 21