Add and subtract fractions in recipes

Learning Objectives Apply the principles of fraction addition and subtraction to solve problems involving geometric compositions. Define the role of congruent figures in establishing a 'unit whole' for fractional calculations. Calculate the total fractional area of a design composed of different types of congruent figures. Determine the remaining fractional part of a geometric design when other fractional parts are known. Translate a word problem about a geometric 'recipe' or blueprint into a mathematical expression involving fractions. Verify the composition of a geometric figure by ensuring its fractional parts sum to the whole (1). Ever followed a blueprint to build something? 🏗️ What if that blueprint used fractions to describe the materials needed fo...

TermDefinitionExample Congruent FiguresFigures that have the exact same size and shape. All corresponding sides and angles are equal. In our 'recipes', these are our identical base ingredients.A set of 5cm x 5cm square tiles are all congruent to each other. A 5cm x 5cm square and a 6cm x 6cm square are not congruent. Geometric CompositionA larger figure or pattern created by arranging smaller, often congruent, shapes without overlap.A rectangular patio floor made by laying hundreds of congruent rectangular bricks. Unit WholeThe entire figure or design, which represents the total quantity '1'. All fractional parts are relative to this whole.In a mosaic made of 100 congruent tiles, the entire mosaic is the 'unit whole'. A section with 25 tiles represents 25/100...

Addition of Fractions \frac{a}{b} + \frac{c}{d} = \frac{ad + bc}{bd} Use this formula to combine two different fractional parts of a geometric design to find their total combined portion of the unit whole. You must find a common denominator first. Subtraction of Fractions \frac{a}{b} - \frac{c}{d} = \frac{ad - bc}{bd} Use this formula to find the remaining fractional part of a design after a known portion is accounted for. For example, if you know the total and one part, you can find the other part. Principle of Congruence in Fractions If a whole is composed of N congruent figures, each figure represents \frac{1}{N} of the whole. This principle is the foundation of our geometric recipes. Because each figure is congruent, we can be sure that each one represents an equ...