Mathematics
Grade 10
15 min
Convert customary units involving fractions
Convert customary units involving fractions
What you'll learn
- Identify the correct conversion factor (e.g., 1 foot = 12 inches) for converting between customary units of length, weight, and volume with at least 80% accuracy.
- Solve word problems involving the conversion of customary units (length, weight, and volume) including fractions (e.g., 1/2 inch, 1/4 pound) by using multiplication or division with 70% accuracy.
- Explain the process of converting between two different customary units (e.g., converting feet to inches) using fractions, in a clear and understandable way, both verbally and in writing.
- Apply knowledge of customary unit conversions with fractions to solve multi-step real-world problems, demonstrating the steps taken to arrive at the solution.
Tutorial Preview
1
Introduction & Learning Objectives
Learning Objectives
Convert lengths between inches, feet, and yards when given as fractions or mixed numbers.
Apply unit conversions to ensure consistent units for all side lengths of a right triangle before performing calculations.
Use the Pythagorean theorem with side lengths that require conversion and involve fractions.
Solve for missing side lengths in right triangles where dimensions are given in different customary units (e.g., one leg in inches, the other in feet).
Calculate the perimeter and area of right triangles after converting all side lengths to a common fractional unit.
Set up trigonometric ratios (sine, cosine, tangent) for a right triangle after converting its side lengths to a single, consistent customary unit.
Ever seen a blueprint with measurements like...
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Key Concepts & Vocabulary
TermDefinitionExample
Customary Units of LengthThe primary units of length used in the United States: inches (in), feet (ft), and yards (yd).A standard ruler is 1 foot, which is equal to 12 inches. A yardstick is 3 feet long.
Conversion FactorA ratio, which is equal to 1, that expresses the relationship between two different units of measurement. It is used to convert from one unit to another.The conversion factor between feet and inches is `(12 in / 1 ft)` or `(1 ft / 12 in)`.
Mixed NumberA number consisting of a whole number and a proper fraction.A board length of `5 3/4` feet is a mixed number.
Improper FractionA fraction in which the numerator is greater than or equal to the denominator. It's often easier to use improper fractions in calculations.The mixed number `5 3/4` can be w...
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Core Formulas
Feet to Inches Conversion
L_{in} = L_{ft} \times \frac{12 \text{ in}}{1 \text{ ft}}
To convert a measurement from feet to inches, multiply the number of feet by 12. This is useful when working with mixed units (e.g., 5 feet 2 inches) and you need a single unit for calculations.
Inches to Feet Conversion
L_{ft} = L_{in} \times \frac{1 \text{ ft}}{12 \text{ in}}
To convert a measurement from inches to feet, divide the number of inches by 12. This is useful when you have a smaller unit and need to express it as part of a larger unit, often resulting in a fraction.
Pythagorean Theorem with Consistent Units
a^2 + b^2 = c^2
Where 'a' and 'b' are the lengths of the legs and 'c' is the length of the hypotenuse. Before applying this theorem, you...
4 more steps in this tutorial
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Challenging
In right triangle PQR, tan(P) = 4/3. The leg adjacent to angle P (side PQ) is 2 1/4 feet long. What is the length of the hypotenuse, PR, in inches?
A.36 inches
B.42 inches
C.45 inches
D.54 inches
Challenging
A right triangle is inscribed in a circle such that its hypotenuse is the diameter of the circle. The diameter measures 1 2/3 yards. One leg of the triangle is 3 feet long. What is the area of the triangle in square feet?
A.12 square feet
B.7.5 square feet
C.6 square feet
D.10 square feet
Challenging
A rectangular prism has a length of 4 feet, a width of 24 inches, and a height of 1 yard. What is the length of the space diagonal (the line connecting opposite corners of the prism) in feet?
A.sqrt(29) feet
B.sqrt(26) feet
C.29 feet
D.9 feet
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Frequently asked questions
What grade level is "Convert customary units involving fractions"?
Convert customary units involving fractions is a Grade 10 Mathematics lesson on ExcelOS.
What will I learn in Convert customary units involving fractions?
You'll be able to: Identify the correct conversion factor (e.g., 1 foot = 12 inches) for converting between customary units of length, weight, and volume with at least 80% accuracy; Solve word problems involving the conversion of customary units….
Is "Convert customary units involving fractions" 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 Convert customary units involving fractions?
This lesson includes 25 practice questions across multiple difficulty levels, each with instant feedback and explanations.