Mathematics
Grade 7
15 min
Add, subtract, multiply, or divide two decimals: word problems
Add, subtract, multiply, or divide two decimals: word problems
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Introduction & Learning Objectives
Learning Objectives
Identify the correct mathematical operation (addition, subtraction, multiplication, or division) required to solve a decimal word problem.
Translate real-world scenarios involving decimals into mathematical expressions.
Accurately add and subtract decimals in word problem contexts.
Accurately multiply decimals in word problem contexts.
Accurately divide decimals in word problem contexts.
Interpret the solution of a decimal word problem in the context of the original problem.
Estimate answers to decimal word problems to check for reasonableness.
Ever wonder how stores calculate your total bill when you buy items with prices like $3.99 or $12.50? ๐ It all comes down to understanding decimals and operations!
In this lesson, you'll learn how to break...
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Key Concepts & Vocabulary
TermDefinitionExample
DecimalA number that includes a whole number part and a fractional part, separated by a decimal point.In the number 5.25, '5' is the whole number part and '.25' is the fractional part.
Word ProblemA mathematical problem presented in a narrative or descriptive form, requiring careful reading and interpretation to solve.If a recipe calls for 0.75 cups of sugar and you want to double it, how much sugar do you need?
Operation KeywordsWords or phrases within a word problem that often indicate which mathematical operation (addition, subtraction, multiplication, or division) should be used.Keywords like 'total,' 'sum,' 'altogether' often suggest addition, while 'difference,' 'left,' 'how much more�...
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Core Formulas
Adding and Subtracting Decimals
Align the decimal points vertically, then add or subtract as with whole numbers. Place the decimal point in the answer directly below the aligned decimal points.
Use this rule when combining quantities (addition) or finding the difference between quantities (subtraction). Remember to add zeros as placeholders if needed.
Multiplying Decimals
Multiply the numbers as if they were whole numbers. Count the total number of decimal places in both factors. Place the decimal point in the product so it has the same total number of decimal places.
Apply this rule when finding the total of multiple equal groups, calculating an area, or scaling a quantity by a decimal factor.
Dividing Decimals
If the divisor is a decimal, move its decimal point to th...
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Challenging
A car travels 351 miles on a full tank of 13.5 gallons of gas. The driver wants to know the cost to drive 100 miles if gas costs $3.90 per gallon. Which expression correctly calculates this cost?
A.(351 / 13.5) * 3.90
B.(13.5 * 3.90) / 100
C.(100 / 351) * 13.5 * 3.90
D.100 / (13.5 * 3.90)
Challenging
A chef buys 12.5 kg of potatoes at $1.98 per kg and 5.5 kg of carrots. The potatoes will be used to make 50 equal servings of mashed potatoes. What is the cost of the potatoes for one serving?
A.$24.75
B.$4.95
C.$0.25
D.$0.495
Challenging
A student was asked to solve: "A 12.5-meter roll of ribbon is cut into pieces that are 0.25 meters long. How many pieces can be cut?" The student's work is shown: 12.5 รท 0.25 = 0.05. Which pitfall does this answer demonstrate?
A.Incorrect decimal placement
B.Ignoring units and context
C.Misinterpreting operation keywords
D.Not checking for reasonableness
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