Add 3 or more fractions: word problems

Learning Objectives Translate word problems involving congruent figures into mathematical expressions requiring the addition of three or more fractions. Calculate the least common multiple (LCM) of three or more denominators to establish a common denominator. Accurately convert multiple fractions to equivalent fractions with a common denominator. Sum three or more proper, improper, or mixed fractions and express the result in simplest form. Apply fraction addition to solve for the perimeter of composite shapes formed from congruent figures. Analyze geometric models by summing the fractional areas of distinct regions composed of congruent parts. Ever designed a logo or floor plan by combining identical shapes? How would you calculate the total length of the border if each sid...

TermDefinitionExample Congruent FiguresGeometric figures that have the exact same size and shape. All corresponding sides and corresponding angles are equal.Two triangles, ΔABC and ΔDEF, are congruent if AB=DE, BC=EF, AC=DF, and ∠A=∠D, ∠B=∠E, ∠C=∠F. Composite FigureA geometric figure formed by joining two or more basic geometric figures.An L-shaped polygon can be viewed as a composite figure made of two rectangles. PerimeterThe total distance around the exterior boundary of a two-dimensional shape. For composite figures, it is the sum of the lengths of the outer edges only.The perimeter of a shape made by placing two 3x3 squares side-by-side is 3+3+3+3+3+3 = 18, not the sum of their individual perimeters (12+12=24). Least Common Multiple (LCM)The smallest positive integer that is a multip...

Finding a Common Denominator \frac{a}{b} + \frac{c}{d} + \frac{e}{f} = \frac{a \cdot (\frac{LCM}{b})}{LCM} + \frac{c \cdot (\frac{LCM}{d})}{LCM} + \frac{e \cdot (\frac{LCM}{f})}{LCM} To add fractions with different denominators, first find the Least Common Multiple (LCM) of all denominators (b, d, f). Then, convert each fraction into an equivalent fraction with the LCM as the new denominator. Adding Fractions with a Common Denominator \frac{p}{n} + \frac{q}{n} + \frac{r}{n} = \frac{p+q+r}{n} Once all fractions share the same denominator (n), add their numerators (p, q, r) and place the sum over the common denominator.