Conquer ASVAB Math Word Problems

Conquer ASVAB Math Word Problems: Proven Strategies

Conquering ASVAB Math word problems involves mastering both strategy and practice. Here are some proven strategies to help you confidently approach and solve word problems on the ASVAB Math section

Break It Down Step-by-Step

• Don’t try to solve everything in one go. Break the problem into manageable pieces:
  1. Identify what the problem is asking for.
  2. Highlight or underline the key information.
  3. Translate that into an equation or relationship.

Breaking the problem down makes it easier to understand and solve systematically.

Translate Words into Math

• As mentioned earlier, word problems are often coded with specific phrases that point to certain operations. These keywords are your guide:
  • Addition: sum, total, in all, together, combined
  • Subtraction: difference, fewer, minus, left, decrease
  • Multiplication: product, of, times, multiplied by
  • Division: per, each, ratio, out of, divided by

When you see these keywords, translate them into the appropriate mathematical symbols.

Use a Variable for Unknowns

If the problem involves an unknown quantity, assign a variable (like $x$ or $\mathrm{y)\; to\; represent\; it.}\mathrm{<br>}\mathrm{<br>}\mathrm{<br>}\mathrm{<br>}$

For example: "The total cost of 5 pencils is $15. What is the price of one pencil?" You can let $x$ represent the price of one pencil. $$5x = 15 \quad \Rightarrow \quad x = \frac{15}{5} = 3$$So, the price of one pencil is $3.

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Set Up Equations

For many word problems, you need to write one or more equations to represent the relationships between the different parts of the problem.

Example: “A train travels 40 miles per hour for 3 hours. How far does it travel?”

• Set up an equation for distance: $\text{Distance} = \text{Rate} \times \text{Time}$
• So, $\text{Distance} = 40 \times 3 = 120$ miles.

Eliminate Unnecessary Information

Word problems can sometimes include extra information meant to throw you off track. Focus on the key numbers and relationships needed to solve the problem.
Example: If a problem talks about a person's age, but you're only asked to find the total cost of something, don't let the age distract you.

Double-Check Your Work

After solving a problem, re-read the question to make sure you’re answering exactly what’s being asked. Also, check your math to avoid careless errors.

It helps to look at the units as well to ensure they match up correctly with the answer.

Use Logical Reasoning

Sometimes, word problems involve logical relationships that you can deduce, even if there’s no explicit math involved. Use your reasoning skills to understand the problem better.

For example, if the problem says, "Sarah has twice as many apples as John," you can use this relationship to form an equation, such as: $$\text{Sarah’s apples} = 2 \times \text{John’s apples}$$  and solve based on any additional information.

The more you practice word problems, the more you’ll start to recognize patterns and relationships that appear in similar questions. Regular practice will build confidence and improve your speed.

Example Problem with Solution:

Problem: A store sells pencils at 5 for $2. How much will it cost to buy 12 pencils?

Steps:

1. Identify the cost per pencil:

   \text{Cost per pencil} = \frac{2}{5} = 0.40 \quad (\text{since 5 pencils cost $2})

2. Find the cost for 12 pencils:

   $$\text{Cost for 12 pencils}=12\times 0.40=4.80$$

Answer: It will cost $4.80 for 12 pencils. (Get more practice lesson and study materials 👈).

Bonus Tips for Time Management:

• Don’t linger on hard problems: If you encounter a difficult word problem, move on and come back to it if you have time. Spend no more than 2-3 minutes per question on average.
• Use estimation: For some problems, rounding numbers or estimating can help you quickly eliminate obviously wrong answer choices.

With these strategies, you'll feel much more confident tackling word problems on the ASVAB Math section.