Mathematics
Grade 10
15 min
Divide whole numbers and unit fractions
Divide whole numbers and unit fractions
What you'll learn
- Identify the base, exponent, and result in a given exponential equation and accurately translate it into its equivalent logarithmic form, and vice-versa, in at least 8 out of 10 attempts.
- Rewrite exponential equations, including those with fractional and negative exponents, into logarithmic equations, and vice-versa, demonstrating accurate application of the logarithmic identity, with 75% accuracy on a formative assessment.
- Solve logarithmic equations by converting them to exponential form, and verify the solution by substituting it back into the original equation, achieving a minimum score of 80% on related practice problems.
- Explain the relationship between exponential and logarithmic functions, including their inverse nature and the implications for their graphs and domains, in a written explanation that demonstrates a comprehensive understanding of the concepts.
Tutorial Preview
1
Introduction & Learning Objectives
Learning Objectives
Define and identify unit fractions and their multiplicative inverses (reciprocals).
Prove the 'invert and multiply' rule for dividing a whole number by a unit fraction using algebraic principles.
Prove the 'invert and multiply' rule for dividing a unit fraction by a whole number using algebraic principles.
Apply the division of whole numbers and unit fractions to solve complex, multi-step word problems.
Model division scenarios involving whole numbers and unit fractions graphically and algebraically.
Evaluate expressions involving division of whole numbers and unit fractions as part of larger algebraic expressions.
If a 3D printer can print 1/20th of a prototype in one hour, how many hours will it take to print 4 complete prototypes?...
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Key Concepts & Vocabulary
TermDefinitionExample
Unit FractionA rational number written as a fraction where the numerator is 1 and the denominator is a positive integer.1/5, 1/12, 1/x (where x is a positive integer)
Multiplicative Inverse (Reciprocal)The number which, when multiplied by a given number, results in a product of 1 (the multiplicative identity).The reciprocal of 1/9 is 9, because (1/9) * 9 = 1. The reciprocal of 9 is 1/9.
Division as Multiplication by the ReciprocalThe operation of division is formally defined as multiplication by the multiplicative inverse (reciprocal) of the divisor.10 ÷ 2 is equivalent to 10 * (1/2).
Complex FractionA fraction in which the numerator, the denominator, or both contain a fraction. These are often used to represent division.The expression 8 ÷ (1/3) can be written as the...
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Core Formulas
Dividing a Whole Number by a Unit Fraction
For any whole number `a` and non-zero integer `b`, `a ÷ (1/b) = a * b`
To divide a whole number by a unit fraction, you multiply the whole number by the reciprocal of the unit fraction. The reciprocal of `1/b` is `b`.
Dividing a Unit Fraction by a Whole Number
For any non-zero integer `a` and whole number `b`, `(1/a) ÷ b = (1/a) * (1/b) = 1/(ab)`
To divide a unit fraction by a whole number, you multiply the unit fraction by the reciprocal of the whole number. The reciprocal of `b` is `1/b`.
The General Division Principle
For any numbers `x` and `y` (where `y ≠ 0`), `x ÷ y = x * (1/y)`
This is the foundational algebraic principle for all division. It states that division by a number is equivalent to multiplication by its reci...
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Challenging
Let the function `f(x, y)` be defined as `x ÷ (1/y)`. What is the simplified form of `f(f(k, m), n)`, where `k` is a whole number and `m, n` are non-zero integers?
A.k/(mn)
B.kmn
C.km/n
D.kn/m
Challenging
A cylindrical water tank has a total capacity of `V` cubic meters. Water flows into the tank at a constant rate of `1/r` cubic meters per minute (`r > 1`). The total time `T` (in minutes) to fill the tank is then divided equally among `p` identical pumps working together. Which expression represents the time each pump would need to run individually to fill the same portion of the tank?
A.Vrp
B.V / (rp)
C.(Vr) / p
D.p / (Vr)
Challenging
The slope of a line is defined as the ratio of the change in y (`Δy`) to the change in x (`Δx`). A line segment has a `Δy` of 10 units and a `Δx` of `1/5` of a unit. If this line segment is divided into 20 equal smaller segments, what is the slope of each of the smaller segments?
A.The slope remains the same.
B.The slope is 2.5.
C.The slope is 1000.
D.The slope is 2.
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Frequently asked questions
What grade level is "Divide whole numbers and unit fractions"?
Divide whole numbers and unit fractions is a Grade 10 Mathematics lesson on ExcelOS.
What will I learn in Divide whole numbers and unit fractions?
You'll be able to: Identify the base, exponent, and result in a given exponential equation and accurately translate it into its equivalent logarithmic form, and vice-versa, in at least 8 out of 10 attempts; Rewrite exponential equations, including….
Is "Divide whole numbers and unit 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 Divide whole numbers and unit fractions?
This lesson includes 24 practice questions across multiple difficulty levels, each with instant feedback and explanations.