Section 1.8 Problem-Solving Strategies 71 Problem-Solving Strategies Section 1.8 1. Problem-Solving Strategies In this section, we offer additional practice with applications of whole numbers. Keep in mind that all word problems are different and that there is no magic “trick” to solve an application problem. However, we can offer the following guidelines. Guidelines for Problem Solving Step 1 Read the problem carefully and familiarize yourself with the situation. If possible, draw a diagram or write down an appropriate formula. Sometimes you may be able to estimate a reasonable answer. Step 2 Write down what information is given and what must be found. Step 3 Form a strategy. Identify what mathematical operation applies (addition, subtraction, multiplication, or division). Sometimes a combination of operations is necessary. Step 4 Perform the mathematical operations to solve for the unknown. Step 5 Check the answer. If the answer is reasonable and checks, state the answer in words. 2. Applications Involving One Operation We illustrate these guidelines with a variety of examples.To assist with step 3 where we must identify an appropriate mathematical operation, we summarize some of our key words and phrases. See Table 1-5. Table 1-5 Operation Key Word or Phrase Addition Sum, added to, increased by, more than, plus, total of Subtraction Difference, minus, decreased by, less, subtract Multiplication Product, times, multiply Division Quotient, divide, per, shared equally Solving a Travel Application Example 1 Kent travels from Columbus, Ohio, to Indianapolis, Indiana, and then on to Springfield, Illinois. The total distance he drives is 351 mi. The distance between Columbus and Indianapolis is 168 mi. Find the distance between Indianapolis and Springfield. Solution: Familiarize and draw a picture. Springfield Indianapolis Columbus ? 168 mi 351 mi Given: In this case, we know the total distance and one of the parts. Find: Find the second distance (between Indianapolis and Springfield). Concepts 1. Problem-Solving Strategies 2. Applications Involving One Operation 3. Applications Involving Multiple Operations Skill Practice 1. The odometer of a car read 24,316 mi last year. This year the reading is 37,134. How many miles was the car driven during the year? Answer 1. 12,818 mi
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