Problem solving methods1. Comparing the fractions

You use this method when the question states that a fraction (ratio/decimal) of something is equal to a fraction of another thing.

Convert both fractions with a common numerator.

Using this method allows you to understand how many unit to assign to each thing.

Example: of Javier’s allowance is equal to of Joanna’s allowance. a) Find the ratio of Javier’s allowance to Joanna’s allowance. b) Joanna’s allowance is increased by $15; the ratio of Javier’s allowance to Joanna’s

allowance will be 3:2. How much is Javier’s allowance now?

(a) = (This meant that Javier has 9 units and Joanna has 5 units.)

Ratio: 9:5

Think about this question:of Hilary’s money is $8 less than of Randy’s money. They have a total of $132. How much money does Randy have?

2. Table method

This method is like modelling. To use this method, you need to have:1) Starting units/algebra * note that you can only use 1 algebra letter2) A change to the units (should use addition and subtraction) 3) Ending ratioAfter constructing the table you need to cross multiply to calculate what is the unit.

Example

(b) Javier Joanna

9u × 2 = 5u ×3 + $15 × 318u = 15u + $453u = $45

1u = $15

Javier’s allowance: $150

3. Elimination Method

9u 5u +0 +15 3 2

This method is used for questions that give many unknown variables.We manipulate the information given in the question and use it to remove one of the variable.

Example: 3 files and 2 books cost $60. 2 files and 3 books cost $70. Find the cost of 1 file.

3F 2B $60 2F 3B $79

9F 6B $180 4F 6B $158

5F $221F $5.50

4. Working backwards Method

This method is used for questions take you through many steps and tells you what you have in the end.

Things to take note

Percentage, Decimal and Fraction

They are related. 100% = 1 50% = 0.5 =

Percentage: Know what it is referring toExample: Karen had 80 beads. Shannon had 15% more beads than Karen. During a game, Shannon lost 25% of her beads to Karen. How many more beads had Karen than Shannon in the end?

1) Sharon: Karen 115: 100

2) Sharon did not lose 25u to Karen She lost 115u ÷ 4 = 28.75u

Remainder Concept

Remainder concept problem sums often contain the word “remainder” or ask about the total amount of something given the remainder. Most of the time, remainder concept questions test the knowledge of fractions.

Example: Mrs Lee read 40% of the pages of a book on Monday. On Tuesday, she read 20% of the remaining pages of the book. She then had 180 pages left unread. How many pages are there in the book?

A different type of speed questionExample: How long does it take for the 2 painters to paint the room if painter A take 3 hour to paint the room and painter B takes 4 hours to paint the room?You need find out how much of the room the painters can paint in 1 hour. Then, you can find out how much of the room, the painters can paint in 1 hour.Finally, you find out your answer by dividing the rate.

A room/h B room/h A+B room/hTime taken: 1 ÷ = h