Mathematics
Grade 10
15 min
Subtract mixed numbers with unlike denominators
Subtract mixed numbers with unlike denominators
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...
2
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...
3
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.
4 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
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.
Want to practice and check your answers?
Sign up to access all questions with instant feedback, explanations, and progress tracking.
Start Practicing Free