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Grade 9

Problem solving with fractions


As with all problem solving situations, one of the trickiest things is 'mathematising' the question.  Mathematising is finding the mathematics within the words.  

Unfortunately I can't give you any shortcuts or rules to make this easy for you, (my first suggestion is for you to practice a lot), but there are a few clues you can often find in the questions. 

I'm just going to show you some questions, and circle the words where the mathematics is hiding!

Question 1

Shared equally is a clue to DIVISION. Mathematising this question gives you $\frac{3}{5}\div4$35÷​4.

Question 2

Full price would be $\frac{7}{7}$77, so to find the full price we would find $\frac{1}{7}\times384$17×384 and then get $\frac{7}{7}$77 by multiplying by $7$7.  

Question 3

If $\frac{1}{2}$12 are boys, then the remaining class are assumed to be girls.  So $1-\frac{1}{2}$112are girls, which equals $\frac{1}{2}$12. Therefore, because $10$10 boys represents half the class, then there must also be $10$10 girls (the other half of the class).



In a hockey tournament, Adam's team won $1$1 out of $3$3 games, and did not tie any games.

  1. How many games did Adam's team lose?

  2. What fraction of the games did Adam's team lose?


In a survey of $270$270 people, $\frac{1}{10}$110 said their favourite sport was soccer, and $\frac{1}{9}$19 said their favourite sport was tennis.

  1. What is the total fraction of people who said their favourite sport was soccer or tennis?

  2. What is the fraction of people who did not put soccer or tennis as their favourite sport?

  3. How many people did not put soccer or tennis as their favourite sport?


A bottle is $\frac{2}{7}$27 full of cordial. If $230$230 millilitres of cordial is added to it, the bottle is $\frac{5}{6}$56 full. How many millilitres does the bottle hold when full?



Simplify numerical expressions involving integers and rational numbers, with and without the use of technology

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