Mathematics
Grade 10
15 min
Add and subtract mixed numbers: word problems
Add and subtract mixed numbers: word problems
What you'll learn
- Represent complex numbers in the complex plane, including real and imaginary components, with 100% accuracy on a formative assessment.
- Apply the distance formula to calculate the modulus (absolute value) of a complex number graphed in the complex plane and express the result in simplified radical form in at least 4 out of 5 problems correctly.
- Convert complex numbers between rectangular (a + bi) and polar (r(cos θ + i sin θ)) forms, accurately plotting each form on the complex plane, in at least 3 out of 4 cases.
- Explain the geometric interpretation of complex number addition, subtraction, multiplication, and division in the complex plane, illustrating each operation with a labeled diagram in a written explanation.
Tutorial Preview
1
Introduction & Learning Objectives
Learning Objectives
Translate multi-step word problems involving mixed numbers into precise mathematical expressions.
Analyze a given scenario to determine whether addition or subtraction of mixed numbers is the required operation.
Accurately solve addition and subtraction problems with mixed numbers, including those requiring borrowing or regrouping.
Convert between improper fractions and mixed numbers as a strategic step in solving complex problems.
Simplify fractional results to their lowest terms and present the final answer in the context of the original word problem.
Verify the reasonableness of their solutions in real-world contexts, such as geometric perimeters or material measurements.
A triangular park has two sides measuring 8 1/4 km and 5 2/3 km. If the total per...
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Key Concepts & Vocabulary
TermDefinitionExample
Mixed NumberA number consisting of a whole number and a proper fraction.3 1/2 (three and one-half)
Improper FractionA fraction in which the numerator (top number) is greater than or equal to the denominator (bottom number).7/2 (seven-halves)
Least Common Denominator (LCD)The smallest common multiple of the denominators of two or more fractions. It is required to add or subtract fractions.For 1/3 and 1/4, the LCD is 12.
Regrouping (Borrowing)In subtraction of mixed numbers, the process of 'borrowing' 1 from the whole number part and converting it into a fraction with a common denominator to allow for subtraction of the fractional parts.To solve 5 1/4 - 2 3/4, you regroup 5 1/4 into 4 5/4.
Simplifying a FractionThe process of dividing both the numerator and t...
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Core Formulas
Converting a Mixed Number to an Improper Fraction
A \frac{b}{c} = \frac{(A \times c) + b}{c}
Use this to convert mixed numbers into a form that is often easier for calculations, especially in multi-step problems. Multiply the whole number (A) by the denominator (c), then add the numerator (b). Keep the original denominator (c).
Adding Mixed Numbers
A \frac{b}{d} + C \frac{e}{d} = (A+C) \frac{b+e}{d}
When denominators are the same, add the whole numbers and the numerators separately. If the resulting fraction is improper, convert it to a mixed number and add the whole part to the existing whole number.
Subtracting Mixed Numbers (with Regrouping)
If b < e in A \frac{b}{d} - C \frac{e}{d}, regroup as (A-1) \frac{b+d}{d} - C \frac{e}{d}
If the first fraction is smalle...
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Challenging
After a series of transactions, a company's stock ended the week at 132 1/2 dollars. This was a decrease of 4 7/8 dollars from its starting price at the beginning of the week. What was the stock's starting price?
A.137 3/8 dollars
B.127 5/8 dollars
C.136 3/8 dollars
D.137 1/4 dollars
Challenging
The perimeter of a rectangular field is 50 1/3 meters. The width of the field is 9 3/4 meters. What is the length of the field?
A.40 7/12 meters
B.15 5/12 meters
C.19 1/2 meters
D.20 1/6 meters
Challenging
A water tank's level starts at 12 1/2 feet. Due to evaporation, it loses 1 5/8 feet. Then, a valve is opened, and it loses another 2 1/4 feet. Finally, rainfall adds 3 1/6 feet. What is the final water level in the tank?
A.11 17/24 feet
B.12 1/24 feet
C.11 19/24 feet
D.12 5/24 feet
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Frequently asked questions
What grade level is "Add and subtract mixed numbers: word problems"?
Add and subtract mixed numbers: word problems is a Grade 10 Mathematics lesson on ExcelOS.
What will I learn in Add and subtract mixed numbers: word problems?
You'll be able to: Represent complex numbers in the complex plane, including real and imaginary components, with 100% accuracy on a formative assessment; Apply the distance formula to calculate the modulus (absolute value) of a complex number….
Is "Add and subtract mixed numbers: word problems" free to practice?
Yes. You can read the tutorial preview for free, and signing up for a free ExcelOS account unlocks the full tutorial and all practice questions with instant feedback.
How many practice questions are included with Add and subtract mixed numbers: word problems?
This lesson includes 25 practice questions across multiple difficulty levels, each with instant feedback and explanations.