Mathematics
Grade 10
15 min
Add mixed numbers with unlike denominators
Add mixed numbers with unlike denominators
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1
Introduction & Learning Objectives
Learning Objectives
Apply the properties of congruent figures to set up expressions involving the sum of side lengths.
Convert mixed numbers into improper fractions to prepare for addition.
Determine the least common denominator (LCD) for two or more fractions.
Accurately add two or more mixed numbers with unlike denominators.
Convert an improper fraction back into a simplified mixed number to represent a final geometric measurement.
Calculate the perimeter of a polygon with side lengths expressed as mixed numbers by leveraging the properties of a congruent figure.
Imagine two congruent, oddly-shaped garden plots. If you know the side lengths of one plot are 5 1/2 feet, 7 1/3 feet, and 4 3/4 feet, how would you calculate the exact amount of fencing needed for the second plot...
2
Key Concepts & Vocabulary
TermDefinitionExample
Congruent FiguresGeometric figures that have the exact same size and shape. All corresponding sides and corresponding angles are equal in measure.If Triangle ABC is congruent to Triangle XYZ (written as ∆ABC ≅ ∆XYZ), then the length of side AB is equal to the length of side XY.
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 is required to add or subtract fractions with unlike denominators....
3
Core Formulas
Converting a Mixed Number to an Improper Fraction
A \frac{b}{c} = \frac{(A \times c) + b}{c}
To convert a mixed number to an improper fraction, multiply the whole number by the denominator, add the numerator to the product, and place the result over the original denominator. This is the crucial first step for adding or multiplying mixed numbers.
Adding Fractions with Unlike Denominators
\frac{a}{b} + \frac{c}{d} = \frac{a \cdot (\frac{LCD}{b}) + c \cdot (\frac{LCD}{d})}{LCD}
To add fractions with different denominators, first find the Least Common Denominator (LCD). Then, convert each fraction to an equivalent fraction with the LCD as its denominator. Finally, add the numerators of the new fractions and place the sum over the LCD.
4 more steps in this tutorial
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Challenging
A student adds 5 2/3 and 3 3/4 by first adding the whole numbers (5+3=8) and then adding the fractions (2/3+3/4 = 8/12+9/12 = 17/12), getting a result of 8 17/12. According to the tutorial, why is this method considered problematic, even if the value is technically correct?
A.The method is mathematically flawed and the value 8 17/12 is incorrect.
B.It produces a confusing 'improper mixed number' that requires an extra, often forgotten, step of converting 17/12 to 1 5/12 and adding it to 8.
C.The LCD of 12 is incorrect for the fractions 2/3 and 3/4.
D.This method only works if the sum of the fractions is less than 1.
Easy
In the context of Grade 10 geometry, what is the most precise definition of two congruent figures?
A.They have the same area but may have different shapes.
B.They have the same shape but may have different sizes.
C.They have the exact same size and shape, with all corresponding parts being equal.
D.They have the same number of sides and angles.
Easy
According to the formula A b/c = ((A × c) + b)/c, how is the mixed number 7 2/5 correctly converted into an improper fraction?
A.(7 + 2) / 5 = 9/5
B.(7 × 5 + 2) / 5 = 37/5
C.(7 × 2 + 5) / 5 = 19/5
D.7 / (2 + 5) = 7/7
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