Mathematics
Grade 10
15 min
Add and subtract decimals: word problems
Add and subtract decimals: word problems
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1
Introduction & Learning Objectives
Learning Objectives
Deconstruct multi-step word problems to identify necessary decimal addition and subtraction operations.
Translate verbal and written scenarios involving decimals into precise mathematical expressions.
Accurately perform addition and subtraction with decimals of varying lengths, including whole numbers.
Apply estimation strategies to predict and verify the reasonableness of their answers in decimal-based word problems.
Solve real-world problems involving financial transactions, measurements, and data analysis using decimal arithmetic.
Clearly articulate their final answer, including the correct units (e.g., dollars, meters, kilograms).
You're the lead engineer on a project to build a new bridge. The total length is 1.25 km, and two sections measuring...
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Key Concepts & Vocabulary
TermDefinitionExample
Decimal AlignmentThe process of lining up the decimal points of numbers vertically before performing addition or subtraction. This ensures that digits with the same place value (tenths, hundredths, etc.) are correctly added or subtracted.To add 12.7 and 3.45, you align them as:
12.70
+ 3.45
Annexing ZerosAdding zeros to the end of a decimal number after the decimal point. This does not change the value of the number but helps in aligning place values for calculation.When subtracting 4.1 from 8.253, you annex two zeros to 4.1, making it 4.100, to align the thousandths place.
KeywordsSpecific words or phrases in a word problem that indicate which mathematical operation to perform.Addition keywords: 'total', 'sum', 'altogether', 'co...
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Core Formulas
Decimal Alignment Rule
a.bcd \pm e.f \rightarrow \begin{array}{@{}c@{\;}c@{}c@{}c@{}c} & a & . & b & c & d \\ \pm & & e & . & f & 0 \\ \hline \end{array}
When adding or subtracting decimals, always align the numbers vertically so that their decimal points are in the same column. Annex zeros as placeholders if necessary to ensure all numbers have the same number of decimal places.
Word Problem Translation Process
Text \rightarrow Identify \, Knowns/Unknowns \rightarrow Select \, Operation(s) \rightarrow Formulate \, Expression
A systematic approach to solving word problems. First, read and understand the problem. Second, identify the given values (knowns) and what you need to find (unknown). Third, use keywords to select the correct ope...
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Challenging
A business account has a starting balance of $4821.55 on Monday. On Tuesday, a payment of $1350.40 is received. On Wednesday, salaries of $2180.75 are paid. On Thursday, a supply order for $450.00 is paid. On Friday, a client makes a deposit of $885.50. What is the final account balance on Friday?
A.$6027.40
B.$1725.90
C.$2555.90
D.$9688.20
Challenging
A fabric store has two rolls of cloth. Roll A is 15.5 meters long and Roll B is 22.75 meters long. A customer needs three pieces cut: 8.8 meters, 12.25 meters, and 10.5 meters. After cutting all three pieces from the available rolls, what is the total length of cloth remaining?
A.6.70 meters
B.31.55 meters
C.38.25 meters
D.7.20 meters
Challenging
An experiment begins with a chemical solution weighing 180.00 g. First, 22.45 g of a reactant is added. Then, the mixture is heated, causing 8.12 g to evaporate. Finally, a precipitate is filtered out, removing 15.90 g. The lab technician records a final mass of 133.53 g. Is this recorded mass correct? If not, what is the difference between the calculated correct mass and the recorded mass?
A.Yes, the recorded mass is correct.
B.No, the recorded mass is 0.10 g too high.
C.No, the recorded mass is 0.10 g too low.
D.No, the recorded mass is 1.00 g too low.
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