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Learning Math : Word Problems
Word Problems: sub-module 2 of 2 of math hub
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
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?
Read the entire question before writing anything down or doing any math. You may need to read the question more than once before starting.
Write down what it is the question wants you to find. Assign a variable to this unknown and clearly define what the variable represents. 
Clearly write down all the information that is provided to you in the question. Make sure to include any units.
Pick out the keywords that will help you translate the word problem into math. Highlight or underline these words.
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.
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.
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.
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.
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
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: 8s
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.
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 - opens in a new window by Lynn Marecek & Mary Anne Anthony-Smith is licensed under CC BY 4.0 - opens in a new window / A derivative from the original work - opens in a new window
Test Yourself!
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 – REQUIRED Write down what the problem is asking you to find. This is the information that is REQUIRED.
- Step 3 – APPLY Identify 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 - STATEMENT Write a STATEMENT that answers the question asked. Make sure to include units!