The purpose of this note is to encourage problem solving using bar diagrams. it is a supplement to the article U Teach Your Child Fractions 5: Equivalent Fractions.
So, what is a bar diagram?
A bar diagram is a rectangle that is partitioned(divided) into equal sized rectangles called cells.
Example of a bar diagram.
Using diagrams to solving problems can be an effective problem solving technique. Properly drawn diagrams that reflect problem data often aid comprehension and they can lead to a solution. However it is the case that diagrams can lead one astray. But with practice, one can master drawing a diagram that reflects the problem situation. Thus, I encourage drawing diagrams in problem solving situations. This skill can nudge one towards a solution. This note provides an opportunity to solve equivalent fractions problems via drawing bar diagrams.
Let’s illustrate with an example.
An elderly gentleman had 5 children. He uses three methods state the conditions to follow to settle the affairs of his estate:
- A bar diagram,
- By fractional notation,
- By equivalent fractions.
The Conditions of the will: Each child gets an equal portion.
1. A bar diagram Approach
Solution: Draw a rectangle to represent the estate. Divide it into five subdivisions: each subdivision represents a heir’s share. Each heirs must get an equal share, so each subdivision is a cell.
The bar diagram showing an equal share for the heirs is :
The bar diagram is divided into five equal parts, so each part represents the fraction represents, 1 / 5.
2. Fractional Notation for the heirs: 1 / 5, 1 / 5, 1 / 5, 1 / 5, 1 / 5.
3. An equivalent fraction representation: 3 /15, 4 /20, 5 /25, 6 /30, 7 /35.
Solve the following problems using the three methods.
1. The first four siblings get equal amounts. The second sibling gets 4/16 of the wealth. How much must the youngest heir get?
2.The oldest and the youngest heirs’ shares is one half of the estate. The remaining siblings get equal shares.
A Possible Hint: The first two colors represent the oldest and youngest shares.
3. The oldest inherits twice as much as the each of his siblings.
4. The oldest inherits five times as much as the others siblings.
5. The sum of the oldest and the youngest is ¾ of the inheritance. The others are awarded an equal share.
6. The combined inheritance of the oldest and the youngest heirs is ¾ of the inheritance. The second sibling receives three times as much as the fourth sibling, while third gets twice as much as the fourth.
7. The oldest gets three times the amount of the youngest, but the sum of the oldest and the youngest is ¾ of the inheritance. The second receives three times as much as the fourth sibling, while the third child gets twice as much as the fourth child.
8. The oldest and the youngest get an equal share. The remaining three siblings get equal shares. Hint: There is more than one what to solve this problem.9. After one hour 1/8 of the disembarked passengers returned to the cruise ship. There are now 3/8 of the ship’s passengers on board. Using fractions, express the number of passengers that left the ship during the first hour if 1/16 never left. This is a problem for discussion.