Mathematics
Grade 9
15 min
Division with decimal quotients: word problems
Division with decimal quotients: word problems
What you'll learn
- Identify Angle-Side-Angle (ASA) and Angle-Angle-Side (AAS) congruent triangle relationships within geometric diagrams with 80% accuracy.
- Apply the ASA and AAS congruence theorems to construct geometric proofs demonstrating that two triangles are congruent in at least 3 out of 4 given problems.
- Explain the logical reasoning behind the ASA and AAS congruence theorems in written or oral form, justifying each step in a proof with 100% accuracy.
- Solve for unknown angle measures or side lengths in geometric figures by applying the ASA and AAS theorems, achieving correct solutions in at least 75% of the assigned problems.
Tutorial Preview
1
Introduction & Learning Objectives
Learning Objectives
Translate a word problem into a correct division expression.
Perform long division that results in a decimal quotient.
Correctly place the decimal point in the quotient.
By the end of a this lesson, students will be able to interpret the meaning of a decimal quotient in the context of a real-world problem.
Round decimal answers appropriately based on the problem's context (e.g., money, measurements).
Connect division word problems to the concept of rates and averages as simple rational expressions.
Ever tried to split a pizza bill of $52 among 5 friends and wondered what each person *exactly* owes? 🍕 Let's find out!
This tutorial focuses on solving word problems where the division doesn't result in a whole number. You will learn how to se...
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Key Concepts & Vocabulary
TermDefinitionExample
DividendThe total amount that is being divided or distributed.In '15 apples shared among 4 people', the dividend is 15.
DivisorThe number you are dividing by; it represents the number of equal groups.In '15 apples shared among 4 people', the divisor is 4.
QuotientThe result of a division problem. In this lesson, it will often be a decimal.15 ÷ 4 = 3.75. The quotient is 3.75.
RateA ratio that compares two quantities with different units. It's a practical application of a rational expression.A car travels 120 miles in 2 hours. The rate (speed) is 120 miles / 2 hours = 60 miles per hour.
Unit CostThe cost for one single item or unit of measure, found by dividing the total cost by the number of items.If 8 notebooks cost $18, the unit cost is $18...
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Core Formulas
Division Setup from Word Problems
\text{Quotient} = \frac{\text{Total Amount (Dividend)}}{\text{Number of Groups (Divisor)}}
Use this fundamental structure to translate word problems into a mathematical expression. The quantity being 'split up' or 'distributed' is always the dividend (numerator).
Decimal Point Placement
\frac{a.b}{c} \rightarrow c \overline{)a.b}
When dividing a decimal by a whole number, the decimal point in the quotient goes directly above the decimal point in the dividend. Maintain place value by adding zeros to the dividend as needed to continue dividing.
Average as a Rational Expression
\text{Average} = \frac{\sum_{i=1}^{n} x_i}{n}
To find the average of a set of values, you sum the values (the dividend) and divide by the cou...
4 more steps in this tutorial
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Challenging
The density of a substance is a rate defined by the rational expression D = m/V, where m is mass and V is volume. An object has a mass of 455 grams and a volume of 50 cubic centimeters. A second object has a mass of 630 grams and a volume of 75 cubic centimeters. What is the difference in their densities (in g/cm³)?
A.0.7 g/cm³
B.1.3 g/cm³
C.8.4 g/cm³
D.9.1 g/cm³
Challenging
A rope is 18 meters long. It needs to be cut into pieces that are each 1.25 meters long. After cutting as many full pieces as possible, what is the length of the remaining piece of rope?
A.0.4 meters
B.0.5 meters
C.14.4 meters
D.4 meters
Challenging
A group of friends split the cost of a large pizza, which was $26.80. Each person's share was $5.36. Which equation, where 'x' represents the number of friends, models this situation?
A.5.36x = 26.80
B.26.80x = 5.36
C.x / 26.80 = 5.36
D.x - 5.36 = 26.80
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Frequently asked questions
What grade level is "Division with decimal quotients: word problems"?
Division with decimal quotients: word problems is a Grade 9 Mathematics lesson on ExcelOS.
What will I learn in Division with decimal quotients: word problems?
You'll be able to: Identify Angle-Side-Angle (ASA) and Angle-Angle-Side (AAS) congruent triangle relationships within geometric diagrams with 80% accuracy; Apply the ASA and AAS congruence theorems to construct geometric proofs demonstrating that….
Is "Division with decimal quotients: 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 Division with decimal quotients: word problems?
This lesson includes 25 practice questions across multiple difficulty levels, each with instant feedback and explanations.