Lesson 6: Multi-Step Decimal Problems

Property

To add or subtract decimals, align the numbers by their decimal points. Add or subtract as you would with whole numbers, starting from the rightmost digit. Place the decimal point in the answer directly below the decimal points in the numbers above.

Examples

• $145.78 + 92.3 = 238.08$
• $204.5 - 67.123 = 137.377$
• $89.654 + 11.47 = 101.124$

Explanation

When adding or subtracting larger decimal numbers, the process remains the same. The key is to carefully align the decimal points to ensure you are adding or subtracting corresponding place values. You can add trailing zeros to numbers to make them the same length after the decimal point, which can help with alignment. Then, simply perform the operation as if they were whole numbers and bring the decimal point straight down into your answer.

Property

Solving multi-step word problems involves identifying the necessary operations (addition, subtraction, multiplication, division) based on the context and performing them in the correct sequence to find the solution. There is no single formula; instead, you must build a plan from the information given.

Examples

• Jasmine buys a book for 14.95 dollars and a pen for 2.75 dollars. She pays with a 20 dollar bill. How much change does she get?

First, find the total cost: $\$14.95 + \$2.75 = \$17.70$.
Then, find the change: $\$20.00 - \$17.70 = \$2.30$.

• A runner is training for a marathon. On Monday, they ran $5.5$ km. On Tuesday, they ran $1.25$ km farther than on Monday. How many kilometers did they run in total over the two days?

First, find Tuesday''s distance: $5.5 + 1.25 = 6.75$ km.
Then, find the total distance: $5.5 + 6.75 = 12.25$ km.

Explanation

Real-world problems often require more than one calculation to solve. To tackle these, first read the problem carefully to understand what is being asked. Next, identify the different pieces of information given and plan the steps needed to reach the final answer. Finally, perform the calculations in order, paying close attention to decimal placement, to solve the problem.