Mathematics
Grade 10
15 min
Add and subtract fractions with unlike denominators: word problems
Add and subtract fractions with unlike denominators: word problems
What you'll learn
- Represent complex numbers graphically on the complex plane and accurately perform vector addition to visually determine the sum of two or more complex numbers with at least 80% accuracy on a summative assessment.
- Calculate the sum of two or more complex numbers in the form a + bi algebraically and express the result in the same form, demonstrating understanding by correctly solving at least 4 out of 5 problems on a problem set.
- Explain the geometric interpretation of complex number addition and how it relates to vector addition, justifying the connection with a clear and concise written explanation scoring at least 3 out of 4 points on a rubric assessing mathematical reasoning.
- Apply the properties of complex number addition (commutative, associative, additive identity, additive inverse) to simplify complex expressions and justify each step with appropriate mathematical reasoning in at least 3 out of 4 problems on a quiz.
Tutorial Preview
1
Introduction & Learning Objectives
Learning Objectives
Deconstruct complex word problems to identify the required fractional operations.
Accurately determine the least common denominator (LCD) for two or more fractions.
Convert fractions to equivalent forms with a common denominator to perform addition or subtraction.
Set up and solve multi-step problems involving both addition and subtraction of fractions.
Express the solution in its simplest form, including converting improper fractions to mixed numbers when appropriate.
Apply fractional arithmetic to solve problems in contexts such as geometry, resource allocation, and data analysis.
A team is building a robot. The chassis takes up 1/3 of the budget, and the electronics take up 2/5. Do they have enough left for a sensor package that costs 1/4 of the budget...
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Key Concepts & Vocabulary
TermDefinitionExample
Unlike DenominatorsDenominators of two or more fractions that are not equal. Direct addition or subtraction is not possible until a common denominator is found.In the fractions 1/3 and 3/5, the denominators 3 and 5 are unlike.
Least Common Denominator (LCD)The smallest positive integer that is a multiple of all the denominators of a set of fractions. It is the Least Common Multiple (LCM) of the denominators.For the fractions 1/6 and 3/8, the multiples of 6 are 6, 12, 18, 24... and the multiples of 8 are 8, 16, 24... The LCD is 24.
Equivalent FractionsFractions that represent the same value, even though they have different numerators and denominators. To create an equivalent fraction, multiply the numerator and denominator by the same non-zero number.1/2 is equivalent...
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Core Formulas
Addition of Fractions with Unlike Denominators
\frac{a}{b} + \frac{c}{d} = \frac{ad + bc}{bd}
This is the general formula for adding two fractions. To use it, you find a common denominator by multiplying the two denominators (b*d), then create equivalent numerators (a*d and b*c) and add them.
Subtraction of Fractions with Unlike Denominators
\frac{a}{b} - \frac{c}{d} = \frac{ad - bc}{bd}
This is the general formula for subtracting two fractions. It follows the same process as addition, but the equivalent numerators are subtracted.
Least Common Denominator (LCD) Method
\frac{a}{b} \pm \frac{c}{d} = \frac{a \cdot \frac{LCD(b,d)}{b} \pm c \cdot \frac{LCD(b,d)}{d}}{LCD(b,d)}
A more efficient method for complex fractions. Find the LCD of the denominators. For each fractio...
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Challenging
The perimeter of an isosceles triangle is 19/12 units. The base (the unequal side) has a length of 1/4 unit. What is the length of one of the two equal sides?
A.2/3
B.3/4
C.1/2
D.5/6
Challenging
A tank has two pipes. Pipe A can fill 1/5 of the tank in an hour. Pipe B can drain 1/8 of the tank in an hour. If the tank is initially 1/2 full and both pipes are opened simultaneously, what fraction of the tank will be full after one hour?
A.3/40
B.13/40
C.23/40
D.17/40
Challenging
A budget was allocated with 1/3 for salaries, 1/4 for materials, and the rest for overhead. Due to a price increase, the materials cost an extra amount equal to 1/12 of the total budget. This extra cost was deducted from the overhead allocation. What fraction of the total budget is now left for overhead?
A.1/3
B.5/12
C.1/4
D.1/6
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What grade level is "Add and subtract fractions with unlike denominators: word problems"?
Add and subtract fractions with unlike denominators: word problems is a Grade 10 Mathematics lesson on ExcelOS.
What will I learn in Add and subtract fractions with unlike denominators: word problems?
You'll be able to: Represent complex numbers graphically on the complex plane and accurately perform vector addition to visually determine the sum of two or more complex numbers with at least 80% accuracy on a summative assessment; Calculate the….
Is "Add and subtract fractions with unlike denominators: 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 fractions with unlike denominators: word problems?
This lesson includes 25 practice questions across multiple difficulty levels, each with instant feedback and explanations.