How to Perform Operations of Decimals in Word Problems
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To kick things off, let's get a handle on decimals. A decimal represents a number that's smaller than one, or a mix of a whole number and a fraction. The rules for dealing with decimals are much like those for whole numbers, but the decimal point is the star of the show.
There are four primary operations you can perform with decimals:
- Addition
- Subtraction
- Multiplication
- Division
Now, let's dig into some word problems that involve decimal operations.
Systematic Approach to Solve Word Problems with Decimal Operations
Stage 1: Grasp the Problem To start with, read the problem attentively. Figure out what you already know and what you're trying to find.
Stage 2: Plan Your Strategy Now, determine which operation (addition, subtraction, multiplication, or division) will get you to your solution. This will be dictated by the question posed in the problem.
Stage 3: Execute the Operation Carry out the decided operation on the decimals. Don't forget to line up the decimal points when you're adding or subtracting, and ensure to follow the correct rules for decimal multiplication and division.
Stage 4: Validate Your Solution Lastly, verify if your answer fits logically within the problem's context.
Exercises for Operations of Decimals
1) Addition: If Lucy buys a pencil that costs \(\$0.50\) and an eraser that costs \(\$0.35\), how much does she spend in total?
2) Subtraction: Jake has \(\$5.00\) in his wallet. He spent \(\$1.25\) on a snack. How much money does he have left?
3) Multiplication: A car can travel \(35.5\) miles with \(1\) gallon of gas. How far can the car travel with \(10\) gallons of gas?
4) Division: Emily baked a \(2.5\) lb cake and wants to divide it equally among \(5\) friends. How much cake does each friend get?
5) Addition: At a school fair, John spent \(\$2.75\) on games and \(\$1.50\) on food. How much did he spend in total?
6) Subtraction: Maria has \(\$10.00\). She wants to buy a book that costs \(\$4.95\). How much money will she have left after buying the book?
7) Multiplication: If a pack of \(12\) pencils costs \(\$1.44\), what is the cost of one pencil?
8) Division: A rope of length \(2.4\) meters is to be cut into \(4\) equal pieces. What will be the length of each piece?
9) Addition/Subtraction: Tom found \(\$20.50\) under his bed and his sister gave him another \(\$15.25\). He then bought a toy for \(\$18.00\). How much money does he have left now?
10) Multiplication/Division: A car travels \(27.5\) miles on a gallon of gas. How many miles can it travel on \(5\) gallons of gas and if it traveled \(137.5\) miles, how many gallons of gas did it consume?
1) Addition: \( \$0.50 \) (pencil) + \( \$0.35 \) (eraser) = \( \$0.85 \). Lucy spends \( \$0.85 \) in total.
2) Subtraction: \( \$5.00 \) (initial amount) - \( \$1.25 \) (snack) = \( \$3.75 \). Jake has \( \$3.75 \) left.
3) Multiplication: \( 35.5 \) miles/gallon \( \times 10 \) gallons = \( 355 \) miles. The car can travel \( 355 \) miles with \( 10 \) gallons of gas
4) Division: \( 2.5 \) lb / \( 5 \) friends = \( 0.5 \) lb/friend. Each friend gets \( 0.5 \) lb of cake
5) Addition: \( \$2.75 \) (games) + \( \$1.50 \) (food) = \( \$4.25 \). John spent \( \$4.25 \) in total
6) Subtraction: \( \$10.00 \) (initial amount) - \( \$4.95 \) (book) = \( \$5.05 \). Maria will have \( \$5.05 \) left after buying the book
7) Multiplication: \( \$1.44/\text{pack} \div 12 \) pencils/pack = \( \$0.12/\text{pencil} \). One pencil costs \( \$0.12 \).
8) Division: \( 2.4 \) meters / \( 4 \) pieces = \( 0.6 \) meter/piece. Each piece will be \( 0.6 \) meter long.
9) Addition/Subtraction: \( \$20.50 \) (found) + \( \$15.25 \) (gift) - \( \$18.00 \) (toy) = \( \$17.75 \). Tom has \( \$17.75 \) left now.
10) Multiplication/Division: \( 27.5 \) miles/gallon \( \times 5 \) gallons = \( 137.5 \) miles. The car can travel \( 137.5 \) miles with \( 5 \) gallons of gas.
\( 137.5 \) miles / \( 27.5 \) miles/gallon = \( 5 \) gallons. The car consumed \( 5 \) gallons of gas for \( 137.5 \) miles.
