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Learning Portal -Math: Word Problems

Word Problems

Have you ever looked at a math question and had no idea what it was asking you to do? Maybe you understand mathematical equations and algebraic expressions, but when a question is phrased as a sentence, you don’t know where to start. Maybe you just don’t understand the terms being used, or can’t remember what they mean. This module will help you understand the language of math so that you can apply your knowledge when solving math problems

Top Tips 

✓ Read carefully. Read the entire question before writing anything down or doing any math. You may need to read the question more than once before starting.

✓ Determine what the question is asking. Write down what it is the question wants you to find. Assign a variable to this unknown and clearly define what the variable represents.

✓ Write down all the given information. Clearly write down all the information that is provided to you in the question. Make sure to include any units

✓ Look for keywords. Pick out the keywords that will help you translate the word problem into math. Highlight or underline these words.

✓ Sketch a picture or a diagram. A picture or a diagram can help you to visualize the problem. Clearly label your picture or diagram with all the given information and the unknown information you are trying to find.

✓ Choose the correct formula(s). Look for formulas that include the given and unknown information provided in your problem. You may need to use more than one equation or formula to get to your final answer.

✓  Check your answer. Look at your final answer, and think about if it makes sense. Ask yourself if the value is around what you would expect, and does the sign make sense?

Solving Word Problems

What are Math keywords and why are they important?

Word problems show the real-world application of math concepts, so they are an essential part of learning math. However, many people find solving word problems difficult or intimidating. You may be comfortable with the math concepts, but how do you convert the words into a math problem? To help you translate words into math, there are specific keywords you can look for in a question. These keywords indicate the math operation(s) you should use to solve the problem.

This is a list of commonly used keywords that are used to identify each math operation. Look for these keywords when solving word problems to help you translate the words into math.

Addition

add, sum, more, more than, increase, increased by, together, combined, total of, in total, plus, added to, also, in all, join, both, gain, and

Example:

Tan weighs 71 kilograms. Minh weighs 9 kilograms more than Tan. How much does Minh weigh?

Solution:

  • The words more than indicate this is an addition problem.
  • To get Minh’s weight we must add 9 to Tan’s weight.
  • 70 + 9 = 79

Therefore, Minh weighs 79 kilograms.

Subtraction

subtract, difference, difference between, less, less than, decrease, decreased by, minus, fewer, fewer than, reduce, deduct, left over, remaining, remove, take away, fell

Example:

Marcella has 6 fewer male cousins than female cousins. Let ƒ represent the number of female cousins. Write an expression for the number of male cousins.

Solution:

  • The word fewer indicates this is a subtraction problem.

  • To get the number of male cousins, we need to subtract 6 from the number of female cousins.

  • If we substitute ƒ for the number of female cousins, the expression for the number of male cousins is: ƒ - 6

Multiplication

multiplied by, of, by, times, product, product of, factor of, double, triple, twice, rate

Example:

Kailey is putting in a flower garden. She wants to have eight times as many tulips as sunflowers. Let s represent the number of sunflowers. Write an expression for the number of tulips.

Solution:

  • The word times indicates this is a multiplication problem.

  • To get the number of tulips, we need to multiply the number of sunflowers by 8.

  • If we substitute s as the number of sunflowers, the expression for the number of tulips is: 8

Division

divide, per, out of, ratio, rate, quotient of, percent, split, equal parts/groups, evenly, average, share, shared between, shared equally

Example:

Three friends went out to dinner and agreed to split the bill evenly. The bill was $79.35. How much should each person pay?

Solution:

  • The words split evenly indicate this is a division problem.

  • To determine how much each friend paid we need to divide the total cost by 3.

  • 79.35 ÷ 3 = 26.45

  • Therefore, each friend paid $26.45.

Equals

is, are, was, were, will be, gives, yields, answer, equates to, makes, produces, results, same as

Example:

Jeannette has $5 and $10 bills in her wallet. The number of fives is three more than six times the number of tens. Let t represent the number of tens and ƒ represent the number of fives. Write an equation to represent the number of fives.

Solution:

  • The word is indicates the equals sign.

  • We need to translate the rest of the words to determine the final equation.

  • The words more than indicate addition, and the word times indicates multiplication.

number of fives

is

3 more than

6 times the number of tens

ƒ

=

3 +

6t

Therefore, the final equation for the number of fives is: ƒ = 3 + 6t

 

Examples are derivatives from: Prealgebra by Lynn Marecek & Mary Anne Anthony-Smith is licensed under CC BY 4.0 / A derivative from the original work

Steps to solve word problems

Do you have difficulty solving mathematical word problems? Do you need a strategy to tackle word problems? You’re not alone. Many students have difficulty with this area of math.

This strategy can be utilized for all math word problems as well as math-related word problems in other courses such as chemistry or physics. After practicing the step-by-step method, you will find solving math problems less daunting.

The GRASS Method

  • Step 1 – GIVEN Read the question slowly and carefully. Reread the question. Write down or highlight/underline the GIVEN values.
  • Step 2 – REQUIREDWrite down what the problem is asking you to find. This is the information that is REQUIRED.
  • Step 3 – APPLYIdentify key words that will help you APPLY the correct math operation or formula.
  • Step 4 – SOLVE(and check!) Perform the calculations by plugging in given values to SOLVE the problem. Think about your answer - does it make sense?
  • Step 5 - STATEMENTWrite a STATEMENT that answers the question asked. Make sure to include units!

Attribution 

Unless otherwise stated, the material in this guide is from the Learning Portal created by College Libraries Ontario. Content has been adapted for the GPRC Learning Commons in June 2021. This work is licensed under a Creative Commons BY NC SA 4.0 International License.

All icons on these pages are from The Noun Project. See individual icons for creator attribution. 

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