Transposing and Solving Worded Questions

Sometimes the hardest part in a mathematics question is not the actual solving of the formula or calculation. It's figuring out what the question is and what needs to be calculated in the first place is. These worded problems require you to:

• Translate from English to Math.
• Then work out the calculation.

Here are some key words and their symbols.

• Plus Sign – sum, plus, added together, combined, increased by.
• Subtraction Sign – minus, less, difference, decreased by
• Division Sign – over, divided by, quotient, out of
• Multiplication Sign – product, multiplied by, twice (x2), thrice (x3)
• Equals Sign – equals, the same as, totals, equivalent to

If there is an unknown number, you can denote it/represent it with x, y, z or any other symbol you feel comfortable with, even "?"

Often, you have to change the worded question into a formula and then solve.

Other ways to solve these questions are to:

• Substitute in the 'answer' option numbers to your formulas e.g. start with the easy and small numbers and then solve.

Venn diagrams

Venn diagrams are used to illustrate reasoning and they can be very useful when dealing with worded problems.

Note that with Venn diagrams:

• The population is in the box.
• There is usually one attribute/thing represented by 1 circle and another by the other circle (and there could be more than 2 circles).
• If something isn’t in any of the circles but in the box, it means that it is still part of the population but doesn’t have any of the attributes.

Let’s discuss the following Venn diagrams below. Note in particular the Venn diagram that has ¬A ∧ ¬B (not A and not B)—the red shaded part means that there is part of the population that doesn’t have A and that doesn't have B. For example, A is that you have black hair and B is that you have red hair. There may be people in the population (in the box) that won’t be represented in any of the circles at all, and these people won’t have red hair and they won't have black hair (they may have hair that is another colour).

Example Question/s

Watch video for explanation of the following question/s:

Annie has a discount card at the mall. For every $25 cost she buys, she only pays $23. How much she needs to pay if she buys a cost of $300?

A $276 B $298 C $288 D $245 E None of these

The third of a number is decreased by itself and the result is -8. An equation to find the value of x would be:

A 3x – x = -8 B 3/x – x = -8 C x – 3x = -8 D [x/3] - x = -8 E [x / (3 – x)] = -8

The following Venn diagram below shows the total of number of students in a classroom and the subjects they study.

Answer the following questions:

• How many students are in the classroom in total?
• How many students do art?
• How many students do English?
• How many students do at least 2 subjects?
• How many students do not do any of the 4 subjects listed?

Key Rules to remember

Translate from English to formulas – find out what the question asking you to do exactly by:

• Highlighting key figures. Remember that:
• “Plus” sign – sum, plus, added together, combined, increased by
• Subtraction Sign – minus, less, difference, decreased by
• Division Sign – over, divided by, quotient, out of
• Multiplication Sign – product, multiplied by, twice (x2), thrice (x3)
• Equals Sign – equals, the same as, totals, equivalent to.

Venn diagrams:

• Show total population of a group that:
• Have certain attributes shown in circles or overlapping attributes (shown by overlap in circles)
• Do not have certain attributes by space outside of circle but within the box.

Practice time!

Now, it's your turn to practice.

Click on the button below and start your practice questions. We recommend doing untimed mode first, and then, when you're ready, do timed mode.

Every question has two solutions videos after you complete the question. The first is a quick 60 second video that shows you how our expert answers the question quickly. The second video is a more in-depth 5-steps or less explainer video that shows you the steps to take to answer the question. It's really important that you review the second video because that's where you'll learn additional tips and tricks.

Once you're done with the practice questions, move on to the next checkpoint.

Now, let's get started on your practice questions.

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