Add and subtract fractions with unlike denominators: word problems

Learning Objectives Translate geometric word problems involving congruent figures into mathematical expressions with fractions. Identify corresponding parts of congruent figures to correctly set up fraction addition and subtraction problems. Calculate the least common denominator (LCD) for fractions derived from geometric measurements. Accurately add and subtract fractions with unlike denominators to determine unknown lengths and perimeters in geometric figures. Formulate a concluding statement that correctly interprets the fractional answer in the context of the original geometric word problem. Verify solutions by applying the properties of congruent figures, such as the equality of corresponding side lengths. If two congruent, triangular steel plates must fit together perf...

TermDefinitionExample Congruent FiguresGeometric figures that have the exact same size and shape. All corresponding sides and corresponding angles are equal.If triangle ABC is congruent to triangle DEF (written as ΔABC ≅ ΔDEF), then side AB = DE, side BC = EF, side AC = DF, and ∠A = ∠D, ∠B = ∠E, ∠C = ∠F. Corresponding PartsThe sides or angles of congruent figures that are in the same relative position. The principle 'Corresponding Parts of Congruent Triangles are Congruent' (CPCTC) is a key tool in proofs.In the statement QUAD ≅ REXS, the corresponding vertices are Q→R, U→E, A→X, D→S. Therefore, the corresponding side to QU is RE. Unlike DenominatorsThe bottom numbers (denominators) of two or more fractions that are not the same value, indicating the wholes are divided into a di...

Addition of Fractions with Unlike Denominators \frac{a}{b} + \frac{c}{d} = \frac{ad + bc}{bd} To add fractions with different denominators, find a common denominator (ideally the LCD), convert each fraction to an equivalent fraction with that denominator, and then add the numerators. Subtraction of Fractions with Unlike Denominators \frac{a}{b} - \frac{c}{d} = \frac{ad - bc}{bd} To subtract fractions with different denominators, find a common denominator, convert each fraction to an equivalent fraction, and then subtract the numerators. Property of Congruence If Figure A ≅ Figure B, then any side length in Figure A is equal to its corresponding side length in Figure B. This geometric rule allows you to set up an equation. If you can calculate a length on one figure,...