Mathematics
Grade 8
15 min
Add and subtract rational numbers: word problems
Add and subtract rational numbers: word problems
Tutorial Preview
1
Introduction & Learning Objectives
Learning Objectives
Identify keywords in word problems that indicate addition or subtraction of rational numbers.
Translate real-world scenarios involving rational numbers into mathematical expressions.
Accurately add and subtract rational numbers (fractions, decimals, mixed numbers) in problem-solving contexts.
Convert between different forms of rational numbers (e.g., fractions to decimals) to facilitate calculations in word problems.
Solve multi-step word problems involving both addition and subtraction of rational numbers.
Interpret and state the final answer to a word problem in the context of the original problem.
Ever wonder how much pizza is left after your friends eat some, or how much money you save after a purchase? 🍕💰 These everyday questions often involve addi...
2
Key Concepts & Vocabulary
TermDefinitionExample
Rational NumberA number that can be expressed as a fraction $\frac{p}{q}$ where $p$ and $q$ are integers and $q \neq 0$. This includes integers, fractions, terminating decimals, and repeating decimals.$\frac{3}{4}$, $-0.5$, $2\frac{1}{3}$, $7$
Word ProblemA mathematical problem presented in a narrative or descriptive form, requiring interpretation to translate into numerical operations.If a recipe calls for $\frac{2}{3}$ cup of flour and you only have $\frac{1}{2}$ cup, how much more do you need?
Keywords for AdditionWords or phrases in a word problem that typically indicate the operation of addition.Keywords include 'sum', 'total', 'altogether', 'in all', 'combined', 'increase', 'plus'.
Keywords f...
3
Core Formulas
Adding/Subtracting Fractions
To add or subtract fractions, find a common denominator, then add or subtract the numerators. Keep the denominator the same: $\frac{a}{b} \pm \frac{c}{d} = \frac{ad \pm bc}{bd}$ (after finding common denominator).
Use this rule when your word problem involves fractions. Always simplify your answer to its lowest terms.
Adding/Subtracting Decimals
To add or subtract decimals, align the decimal points vertically, then add or subtract as you would with whole numbers. Place the decimal point in the answer directly below the aligned decimal points.
This rule is applied when your word problem involves decimal numbers, often related to money, measurements, or percentages.
Converting Mixed Numbers to Improper Fractions
To convert a mixed number $A\f...
5 more steps in this tutorial
Sign up free to access the complete tutorial with worked examples and practice.
Sign Up Free to ContinueSample Practice Questions
Challenging
A project requires cutting several pieces from a 12-foot wooden plank. The pieces needed are $3\frac{1}{2}$ feet, $2\frac{3}{4}$ feet, and $4\frac{1}{8}$ feet. Each time a cut is made with a saw, $\frac{1}{16}$ of a foot is turned into sawdust (this is called the 'kerf'). If all three pieces are cut from the plank, how much of the 12-foot plank is left?
A.$1\frac{9}{16}$ feet
B.$1\frac{5}{8}$ feet
C.$1\frac{1}{2}$ feet
D.$1\frac{3}{4}$ feet
Challenging
The sum of two rational numbers is $\frac{1}{2}$. If one of the numbers is $-\frac{3}{5}$, what is the other number?
A.$\frac{1}{10}$
B.$-\frac{1}{10}$
C.$1\frac{1}{10}$
D.$-1\frac{1}{10}$
Challenging
A student solved the following problem: 'A fish was at -8.2 meters. It swam up 3.5 meters. What is its new position?' The student's work is: 8.2 + 3.5 = 11.7, so the answer is -11.7 meters. Which error did the student make?
A.The student should have subtracted the absolute values because the signs were different.
B.The student misaligned the decimal points.
C.The student used the wrong sign for the final answer.
D.The student added the numbers instead of multiplying them.
Want to practice and check your answers?
Sign up to access all questions with instant feedback, explanations, and progress tracking.
Start Practicing Free