Section I Word Knowledge
Section II Paragraph Comprehension
Section III Mathematics
Section IV General Science
Section V Technical Sciences
Section VI Full Length Practice Exams

Solving Real-World Mathematical Problems

Solving Real-World Mathematical Problems

This lesson introduces solving real-world mathematical problems by using estimation and mental computation. This lesson also includes real-world applications involving integers, fractions, and decimals.


Estimating


Estimations are rough calculations of a solution to a problem. The most common use for estimation is completing calculations without a calculator or other tool. There are many estimation techniques, but this lesson focuses on integers, decimals, and fractions.

To round a whole number, round the value to the nearest ten or hundred. The number 142 rounds to 140 for the nearest ten and to 100 for the nearest hundred. The context of the problem determines the place value to which to round.


Keep In Mind

An estimation is an educated guess at the solution to a problem.


In most problems with fractions and decimals, the context of the problem requires rounding to the nearest whole number. Rounding these values makes calculation easier and provides an accurate estimation to the solution of the problem.

Other estimation strategies include the following:

  • Using friendly or compatible numbers
  • Using numbers that are easy to compute
  • Adjusting numbers after rounding

Estimating Review


Real-World Integer Problems


The following five steps can make solving word problems easier:

1. Read the problem for understanding.

2. Visualize the problem by drawing a picture or diagram.

3. Make a plan by writing an expression to represent the problem.

4. Solve the problem by applying mathematical techniques.

5. Check the answer to make sure it answers the question asked.


BE CAREFUL!

Make sure that you read the problem fully before visualizing and making a plan.


In basic problems, the solution may be evident, but make sure to demonstrate knowledge of writing the expression. In multi-step problems, first make a plan with the correct expression. Then, apply the correct calculation.

Real-World Integer Problems Review


Real-World Fraction and Decimal Problems


The five steps in the previous section are applicable to solving real-world fraction and decimal problems. The expressions with one step require only one calculation: addition, subtraction, multiplication, or division. The problems with multiple steps require writing out the expressions and performing the correct calculations.


Keep In Mind

Estimating the solution first can help determine if a calculation is completed correctly.


Real-World Fraction and Decimal Problems Review


Let’s Review!


  • Using estimation is beneficial to determine an approximate solution to the problem when the numbers are complex.
  • When solving a word problem with integers, fractions, or decimals, first read and visualize the problem. Then, make a plan, solve, and check the answer.

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