# Direct Inverse Proportion (Percentage Change)

Ask any secondary 2 student in Singapore which is the toughest math topic and most of them will tell you it is **Direct/Inverse Proportion**. Overall, this is actually a very easy chapter, except for a particular kind of question: **Questions with percentage increase and proportions**.

So why do students find this kind of question difficult? The biggest hurdle is to get over the fact that each algebra alphabet (x or y) can represent more than 1 value. In secondary 1, they have been drilled to solve for x and each x would give a specific value for each question. Now, they have to abandon that understanding and accept the fact that the values of x and y can both change in a single question. Once students are able to get over this fact, understanding direct/inverse proportions would become a whole lot easier.

For students who find it difficult to understand percentage change questions, do read on. I have broken down a typical proportion/percentage change question into 4 steps to make it more digestible for my beloved students.

Here is a typical Proportion question with percentage change:

**Example 1:**

Given that y is directly proportional to the square of x. When x is increased by 200%, calculate the percentage increase in y.

**Step 1: **Always write down the relationship as per given in the question:

**Step 2: **Convert the percentage change into a numerical multiplier:

**Step 3**: Derive the corresponding change in y, given the relationship and the change in x:

Step 4: Calculate percentage change in y.

**Practice Questions:**

1) It is given that y is directly proportional to square of x. When x is increased by 150%, calculate the percentage increase in y.

(Ans: 525%)

2) it is given that y is inversely proportional to square root of x. When x is increased by 200%, calculate the percentage change in y.

(Ans:-42.3%)

3) it is given that y is inversely proportional to cube of x. When x is reduced by 50%, calculate the percentage change in y.

(Ans: 700%)

4) it is given that G is directly proportional to cube of M. When M is reduced by 20%, calculate the percentage change in G.

(Ans: -48.8%)

*"Expect problems and eat them for breakfast" ~ Alfred A. Montapert*

**Specialist Math Tutor**