Mathematics
Grade 10
15 min
Add and subtract fractions in recipes
Add and subtract fractions in recipes
What you'll learn
- Identify the fractions representing ingredient amounts in a recipe with at least 80% accuracy.
- Solve addition problems involving fractions with unlike denominators (up to 12) found in recipes and express the answer in simplest form, achieving at least 70% accuracy on a worksheet.
- Solve subtraction problems involving fractions with unlike denominators (up to 12) found in recipes and express the answer in simplest form, achieving at least 70% accuracy on a worksheet.
- Apply fraction addition and subtraction skills to adjust a recipe to make a larger or smaller batch, demonstrating the correct adjusted ingredient amounts in a written explanation.
Tutorial Preview
1
Introduction & Learning Objectives
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...
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Key Concepts & Vocabulary
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...
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Core Formulas
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...
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Challenging
A blueprint for a composite material is made of three components, A, B, and C, which together form the unit whole. The fraction of component A is 'x'. The fraction of component B is 1/4 more than A. Component C makes up the remaining 1/3 of the material. Which equation correctly models this recipe?
A.x + (x - 1/4) + 1/3 = 1
B.x + 1/4 + 1/3 = 1
C.x + (x + 1/4) + 1/3 = 1
D.x + (1/4)x + 1/3 = 1
Challenging
A large rectangular patio is the unit whole. It is paved with two types of smaller rectangular tiles, Type X and Type Y, which are not congruent to each other. A Type X tile covers 1/12 of the total patio area. A Type Y tile covers 1/18 of the total patio area. If a design uses 4 Type X tiles and 3 Type Y tiles, what fraction of the patio is left unpaved?
A.1/3
B.1/2
C.2/3
D.5/6
Challenging
A 'recipe' for a metal alloy requires mixing copper, zinc, and tin. The ratio of the weights of copper to zinc to tin must be 5:3:2. What fraction of the alloy's total weight is made up of copper and tin combined?
A.8/10
B.5/10
C.2/10
D.7/10
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What grade level is "Add and subtract fractions in recipes"?
Add and subtract fractions in recipes is a Grade 10 Mathematics lesson on ExcelOS.
What will I learn in Add and subtract fractions in recipes?
You'll be able to: Identify the fractions representing ingredient amounts in a recipe with at least 80% accuracy; Solve addition problems involving fractions with unlike denominators (up to 12) found in recipes and express the answer in simplest….
Is "Add and subtract fractions in recipes" free to practice?
Yes. You can read the tutorial preview for free, and signing up for a free ExcelOS account unlocks the full tutorial and all practice questions with instant feedback.
How many practice questions are included with Add and subtract fractions in recipes?
This lesson includes 25 practice questions across multiple difficulty levels, each with instant feedback and explanations.