Mathematics
Grade 10
15 min
Divide fractions and mixed numbers: word problems
Divide fractions and mixed numbers: word problems
What you'll learn
- Apply the power property of logarithms to simplify logarithmic expressions containing exponents with 100% accuracy in at least 3 out of 4 attempts.
- Solve logarithmic equations using the power property of logarithms, demonstrating a clear understanding of the property and its application by correctly solving a minimum of 3 out of 5 problems within a 20-minute time limit.
- Explain the relationship between the power property of logarithms and the laws of exponents, providing a coherent explanation that demonstrates understanding of how these concepts are interconnected on a written quiz with a score of 80% or higher.
- Identify instances where the power property of logarithms can be effectively utilized to simplify complex logarithmic expressions and justify their application in at least two distinct examples.
Tutorial Preview
1
Introduction & Learning Objectives
Learning Objectives
Analyze a word problem to correctly identify the dividend and the divisor.
Translate real-world scenarios involving division into mathematical expressions with fractions and mixed numbers.
Convert mixed numbers to improper fractions as a required step for division.
Apply the 'multiply by the reciprocal' method to solve division problems involving fractions.
Interpret the quotient, including any fractional part, in the context of the original word problem.
Formulate a complete sentence to answer the question posed in a word problem, ensuring the units are correct.
Justify the reasonableness of an answer by using estimation or logical reasoning.
Ever tried to figure out how many smaller pieces you can cut from a larger one for a project? 📐 That...
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Key Concepts & Vocabulary
TermDefinitionExample
DividendThe total quantity that is being divided or split up.In the problem 'A rope is 10 1/2 meters long and is cut into smaller pieces,' the dividend is 10 1/2, as it's the total amount you are starting with.
DivisorThe number by which the dividend is divided. It often represents the size of each group or piece.In the problem '...cut into smaller pieces that are each 3/4 of a meter long,' the divisor is 3/4, as it's the size of each resulting piece.
QuotientThe result of a division problem. In a word problem, it answers the question 'How many groups can be made?'The result of 10 1/2 ÷ 3/4 is the quotient, which tells you how many pieces of rope can be cut.
Reciprocal (Multiplicative Inverse)A number that, when multiplied by t...
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Core Formulas
Converting a Mixed Number to an Improper Fraction
For a mixed number A b/c, the equivalent improper fraction is (A * c + b) / c.
This conversion is the mandatory first step when multiplying or dividing mixed numbers. It consolidates the whole and fractional parts into a single fraction, making calculations possible.
The Division of Fractions Algorithm
a/b ÷ c/d = a/b * d/c
To divide one fraction by another, you multiply the first fraction (the dividend) by the reciprocal of the second fraction (the divisor). This is commonly remembered by the mnemonic 'Keep, Change, Flip'.
4 more steps in this tutorial
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Challenging
A roll of wire is 45 1/2 meters long. A technician needs to cut pieces that are 3/4 of a meter long. How many full pieces can be cut, and what is the length of the leftover wire?
A.60 full pieces with 1/2 meter leftover.
B.60 full pieces with 2/3 meter leftover.
C.61 full pieces with no wire leftover.
D.59 full pieces with 1/4 meter leftover.
Challenging
A project requires a total of 40 hours of work. A team of volunteers works in shifts, with each shift lasting 2 1/2 hours. After 12 shifts are completed, what fraction of the total project work remains?
A.1/4
B.3/4
C.1/2
D.1/3
Challenging
A cylindrical tank is being filled with water at a rate of 4 1/2 gallons per minute. The tank has a total capacity of 50 gallons. After 5 1/2 minutes, the water is turned off. How many more minutes will it take to fill the remaining volume of the tank at the same rate?
A.16 minutes
B.12 minutes
C.10 1/2 minutes
D.11 1/4 minutes
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Frequently asked questions
What grade level is "Divide fractions and mixed numbers: word problems"?
Divide fractions and mixed numbers: word problems is a Grade 10 Mathematics lesson on ExcelOS.
What will I learn in Divide fractions and mixed numbers: word problems?
You'll be able to: Apply the power property of logarithms to simplify logarithmic expressions containing exponents with 100% accuracy in at least 3 out of 4 attempts; Solve logarithmic equations using the power property of logarithms….
Is "Divide fractions and mixed numbers: word problems" 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 fractions and mixed numbers: word problems?
This lesson includes 25 practice questions across multiple difficulty levels, each with instant feedback and explanations.