Mathematics
Grade 10
15 min
Multiply fractions and mixed numbers in recipes
Multiply fractions and mixed numbers in recipes
What you'll learn
- Calculate the amount of each ingredient needed when doubling or tripling a recipe by multiplying fractions and mixed numbers, with 80% accuracy.
- Solve word problems involving recipes that require multiplying fractions and mixed numbers to adjust ingredient quantities, showing all work and arriving at the correct answer in 3 out of 4 problems.
- Explain, using pictures or words, why multiplying a recipe ingredient by a fraction less than 1 will result in a smaller quantity of that ingredient.
- Apply the skill of multiplying fractions and mixed numbers to independently adjust a recipe to serve a different number of people, demonstrating accurate calculations and clear presentation of the adjusted recipe.
Tutorial Preview
1
Introduction & Learning Objectives
Learning Objectives
Convert mixed numbers to improper fractions to facilitate multiplication.
Calculate the volume and surface area of standard three-dimensional figures (cylinders, spheres, cones).
Apply the multiplication of fractions and mixed numbers to solve problems involving scaling the volume of 3D figures.
Determine the required quantity of materials for a 3D object based on a 'recipe' that specifies an amount per unit of volume or surface area.
Interpret a word problem to identify the correct 3D figure, the relevant formula (volume or surface area), and the fractional quantities involved.
Prove the material requirements for a scaled 3D model by applying the principles of geometric scaling and fractional multiplication.
Ever wonder how a baker knows exactl...
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Key Concepts & Vocabulary
TermDefinitionExample
Mixed NumberA number consisting of a whole number and a proper fraction.2 3/4 cups of flour. This means 2 whole cups and 3/4 of another cup.
Improper FractionA fraction in which the numerator (top number) is greater than or equal to the denominator (bottom number).To convert 2 3/4 to an improper fraction: (2 * 4 + 3) / 4 = 11/4.
VolumeThe amount of three-dimensional space an object occupies, measured in cubic units.The volume of a cylindrical can of soup tells you how much soup it can hold, e.g., 473 cm³.
Surface AreaThe total area of the surface of a three-dimensional object, measured in square units.The surface area of a spherical ornament determines how much paint is needed to cover it, e.g., 201 in².
Scale FactorA number which scales, or multiplies, some quantity...
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Core Formulas
Multiplying Mixed Numbers
a \frac{b}{c} \times d \frac{e}{f} = \frac{ac+b}{c} \times \frac{df+e}{f}
To multiply mixed numbers, first convert each mixed number into an improper fraction. Then, multiply the numerators together and the denominators together. Simplify the resulting fraction if possible.
Volume of a Cylinder
V = \pi r^2 h
The volume (V) of a cylinder is found by multiplying pi (π ≈ 3.14159) by the square of the radius (r) of the base, and then multiplying by the height (h).
Volume Scaling of Similar Figures
V_{new} = V_{original} \times (k)^3
When a 3D figure is scaled by a linear scale factor (k), its volume increases by a factor of k cubed. This is critical for calculating materials for scaled-up models.
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Challenging
A student claims that if a cylinder's recipe calls for an ingredient amount proportional to its volume, and you scale the cylinder's radius by a factor 'k' but leave the height unchanged, the amount of ingredient needed will scale by k³. Which statement correctly analyzes this claim?
A.The claim is correct because volume always scales by k³.
B.The claim is incorrect; the new volume is π(kr)²h = k²(πr²h), so the ingredient amount scales by k².
C.The claim is incorrect; the new volume is πr²(kh) = k(πr²h), so the ingredient amount scales by k.
D.The claim is correct because both radius and height must be scaled for the principle to change.
Challenging
A recipe for a 3D-printed model of a cone is based on its volume. A new, larger model is printed that is geometrically similar to the original, but requires 3 3/8 times the amount of filament. What was the linear scale factor (k) applied to the original model's dimensions?
A.1 1/2
B.3 3/8
C.1 7/8
D.11 3/8
Challenging
A spherical ball is made using a recipe that requires 1 1/2 cups of polymer. A larger ball is created by scaling the linear dimensions of the original by a factor of 2 1/2. What is the difference in the amount of polymer required between the new ball and the original ball?
A.15 5/8 cups
B.21 15/16 cups
C.23 7/16 cups
D.1 1/2 cups
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Frequently asked questions
What grade level is "Multiply fractions and mixed numbers in recipes"?
Multiply fractions and mixed numbers in recipes is a Grade 10 Mathematics lesson on ExcelOS.
What will I learn in Multiply fractions and mixed numbers in recipes?
You'll be able to: Calculate the amount of each ingredient needed when doubling or tripling a recipe by multiplying fractions and mixed numbers, with 80% accuracy; Solve word problems involving recipes that require multiplying fractions and mixed….
Is "Multiply fractions and mixed numbers 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 Multiply fractions and mixed numbers in recipes?
This lesson includes 25 practice questions across multiple difficulty levels, each with instant feedback and explanations.