Mathematics
Grade 10
15 min
Subtract mixed numbers with unlike denominators
Subtract mixed numbers with unlike denominators
What you'll learn
- Identify the least common multiple (LCM) of two denominators in order to create equivalent fractions for subtraction problems with mixed numbers.
- Solve subtraction problems involving mixed numbers with unlike denominators, showing all steps, with at least 80% accuracy.
- Explain the process of borrowing from the whole number part of a mixed number when the fraction being subtracted is larger, using mathematical vocabulary.
- Apply the skill of subtracting mixed numbers with unlike denominators to solve real-world word problems.
Tutorial Preview
1
Introduction & Learning Objectives
Learning Objectives
Convert mixed numbers into improper fractions to facilitate subtraction.
Identify the least common denominator (LCD) for two or more fractions.
Subtract mixed numbers with unlike denominators, including problems that require regrouping (borrowing).
Apply the subtraction of mixed numbers to solve problems involving geometric lengths.
Verify if two line segments are congruent by calculating and comparing their lengths expressed as mixed numbers.
Simplify fractional results and convert improper fractions back to mixed numbers in the context of a final geometric measurement.
How can you prove two metal rods are congruent for a construction project if one is 10 1/4 feet long and the other is what's left after cutting 5 2/3 feet from a 16-foot rod? 🤔
In...
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Key Concepts & Vocabulary
TermDefinitionExample
Mixed NumberA number consisting of a whole number and a proper fraction.7 3/4, where 7 is the whole number and 3/4 is the fraction.
Improper FractionA fraction in which the numerator (top number) is greater than or equal to the denominator (bottom number).31/4 is the improper fraction equivalent of 7 3/4.
Least Common Denominator (LCD)The smallest positive integer that is a multiple of the denominators of a set of fractions. It's required to add or subtract fractions with unlike denominators.For 1/3 and 1/4, the LCD is 12.
Congruent SegmentsLine segments that have the exact same length. We use subtraction of lengths to verify if a calculated segment length is equal to a known segment length.If segment AB has a length of 5 1/2 units and segment CD also has a leng...
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Core Formulas
Converting Mixed Number to Improper Fraction
A \frac{b}{c} = \frac{(A \times c) + b}{c}
Use this formula to convert mixed numbers into improper fractions before performing subtraction. This method avoids the potential complexity of regrouping.
Subtraction with Unlike Denominators
\frac{a}{b} - \frac{c}{d} = \frac{ad - bc}{bd}
This is the general rule for subtracting two fractions. For mixed numbers, first convert them to improper fractions, then find a common denominator (ideally the LCD) before applying this principle.
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Challenging
The result of subtracting a mixed number from 20 1/4 is 13 5/6. What was the mixed number that was subtracted?
A.6 5/12
B.7 7/12
C.6 11/12
D.7 1/12
Challenging
Given a line segment AD. Point B is on AD such that AB = 5 1/3. Point C is on AD such that AC = 12 1/4. The entire segment AD has a length of 17 1/2. Which segment, BC or CD, is longer, and by how much?
A.BC is longer by 1/6
B.CD is longer by 1/4
C.BC is longer by 1/12
D.CD is longer by 1/12
Challenging
To prove that segment MN is congruent to segment PQ, a student needs to show their lengths are equal. The length of MN is the result of 22 1/5 - 14 3/4. The length of PQ is given as 7 9/20. Is the student's proof successful?
A.Yes, both segments are 7 9/20 units long.
B.No, the length of MN is 7 11/20 units.
C.No, the length of MN is 8 1/20 units.
D.No, the length of MN is 7 9/10 units.
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Frequently asked questions
What grade level is "Subtract mixed numbers with unlike denominators"?
Subtract mixed numbers with unlike denominators is a Grade 10 Mathematics lesson on ExcelOS.
What will I learn in Subtract mixed numbers with unlike denominators?
You'll be able to: Identify the least common multiple (LCM) of two denominators in order to create equivalent fractions for subtraction problems with mixed numbers; Solve subtraction problems involving mixed numbers with unlike denominators….
Is "Subtract mixed numbers with unlike denominators" 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 Subtract mixed numbers with unlike denominators?
This lesson includes 25 practice questions across multiple difficulty levels, each with instant feedback and explanations.