Add and subtract mixed numbers with like denominators

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...

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...

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.