Mathematics
Grade 10
15 min
Add and subtract mixed numbers with like denominators
Add and subtract mixed numbers with like denominators
What you'll learn
- Identify the whole number and fractional parts of a mixed number with 100% accuracy.
- Solve 8 out of 10 addition problems involving mixed numbers with like denominators correctly, showing all steps.
- Solve 8 out of 10 subtraction problems involving mixed numbers with like denominators correctly, showing all steps, including regrouping when necessary.
- Explain in your own words how to add or subtract mixed numbers with like denominators in at least three clear steps.
Tutorial Preview
1
Introduction & Learning Objectives
Learning Objectives
Apply the rules of adding mixed numbers to calculate the perimeter of polygons in geometric proofs.
Utilize subtraction of mixed numbers to determine unknown side lengths of segments within congruent figures.
Convert mixed numbers to improper fractions as a primary strategy for verifying sums and differences.
Justify the steps in calculating segment lengths involving mixed numbers, mirroring the logical structure of a formal proof.
Analyze and solve geometric problems where side lengths of congruent figures are expressed as mixed numbers.
Solve for variables in geometric equations that require the addition or subtraction of mixed numbers with like denominators.
If two congruent triangular trusses in a bridge each have a side measuring 15 3/8 feet, how wou...
2
Key Concepts & Vocabulary
TermDefinitionExample
Mixed NumberA number consisting of a whole number and a proper fraction.The length of a segment is $5 \frac{3}{4}$ inches. Here, 5 is the whole number and $\frac{3}{4}$ is the fraction.
Improper FractionA fraction where the numerator is greater than or equal to the denominator.The mixed number $5 \frac{3}{4}$ is equivalent to the improper fraction $\frac{23}{4}$.
Like DenominatorsDenominators in two or more fractions that are the same value.In the fractions $\frac{5}{8}$ and $\frac{1}{8}$, the like denominator is 8.
Congruent FiguresFigures that have the exact same size and shape. All corresponding sides and corresponding angles are equal.If $\triangle ABC \cong \triangle DEF$, then the length of side $AB$ is equal to the length of side $DE$.
PerimeterThe total dista...
3
Core Formulas
Method 1: Add/Subtract Whole Numbers and Fractions Separately
(A \frac{b}{c}) \pm (B \frac{d}{c}) = (A \pm B) + (\frac{b \pm d}{c})
Add or subtract the whole number parts first, then add or subtract the fraction parts. Combine the results. This method may require regrouping (borrowing) for subtraction if the first fraction is smaller than the second.
Method 2: Convert to Improper Fractions
A \frac{b}{c} = \frac{A \times c + b}{c}, then perform \frac{X}{c} \pm \frac{Y}{c} = \frac{X \pm Y}{c}
Convert each mixed number into an improper fraction. Then, add or subtract the numerators, keeping the common denominator. This method avoids the complexity of regrouping in subtraction.
4 more steps in this tutorial
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Sign Up Free to ContinueSample Practice Questions
Easy
According to the definition provided in the tutorial, what must be true for two figures to be considered congruent?
A.They must have the same area and a different shape.
B.They must have the exact same size and shape.
C.They must have the same number of sides and proportional angles.
D.They must have the same perimeter but different side lengths.
Easy
A triangular piece of land has side lengths of $2 \frac{1}{5}$ miles, $4 \frac{2}{5}$ miles, and $5 \frac{1}{5}$ miles. What is the perimeter of the land?
A.$11 \frac{4}{5}$ miles
B.$11 \frac{4}{15}$ miles
C.$12 \frac{4}{5}$ miles
D.$11 \frac{3}{5}$ miles
Easy
Which of the following is the correct conversion of the mixed number $7 \frac{2}{5}$ into an improper fraction?
A.$\frac{14}{5}$
B.$\frac{35}{5}$
C.$\frac{37}{5}$
D.$\frac{72}{5}$
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Frequently asked questions
What grade level is "Add and subtract mixed numbers with like denominators"?
Add and subtract mixed numbers with like denominators is a Grade 10 Mathematics lesson on ExcelOS.
What will I learn in Add and subtract mixed numbers with like denominators?
You'll be able to: Identify the whole number and fractional parts of a mixed number with 100% accuracy; Solve 8 out of 10 addition problems involving mixed numbers with like denominators correctly, showing all steps; Solve 8 out of 10 subtraction….
Is "Add and subtract mixed numbers with like denominators" free to practice?
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How many practice questions are included with Add and subtract mixed numbers with like denominators?
This lesson includes 25 practice questions across multiple difficulty levels, each with instant feedback and explanations.