Mathematics
Grade 10
15 min
Choose numbers with a particular quotient
Choose numbers with a particular quotient
What you'll learn
- Identify at least 8 out of 10 number pairs from a given set that result in a specific quotient (e.g., quotient of 5).
- Solve division problems, including those with remainders, to determine if two numbers produce a target quotient with 80% accuracy.
- Explain the relationship between division and multiplication by creating 3 different division problems that all have the same quotient, demonstrating understanding of inverse operations.
- Apply knowledge of division to create 2 word problems that require choosing numbers with a specific quotient and solve the problems correctly.
Tutorial Preview
1
Introduction & Learning Objectives
Learning Objectives
Define a quotient in the context of geometric similarity.
Identify the quotient as the scale factor between similar figures.
Generate pairs of numbers that satisfy a given quotient (scale factor).
Apply the concept of a particular quotient to solve for unknown side lengths in similar polygons.
Verify if two figures are similar by checking if the quotients of their corresponding sides are constant.
Use a given quotient to determine the ratio of perimeters and areas of similar figures.
Ever tried to resize a picture on your phone without distorting it? 🖼️ You were actually choosing numbers with a particular quotient to keep the proportions right!
This tutorial explores the core concept of similarity: the constant quotient, or ratio, that links proportional...
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Key Concepts & Vocabulary
TermDefinitionExample
QuotientThe result obtained by dividing one quantity by another. In the context of similarity, it is the ratio between corresponding measurements of two figures.If a large triangle has a side of length 15 and the corresponding side of a smaller, similar triangle is 5, the quotient is 15 ÷ 5 = 3.
RatioA comparison of two numbers by division. It expresses the relative size of two quantities.The ratio of 8 to 4 can be written as 8:4, 8/4, or 2. This means the first number is twice as large as the second.
ProportionAn equation that states that two ratios are equal. Proportions are the foundation for solving problems with similar figures.The equation 6/3 = 10/5 is a proportion because both ratios simplify to 2.
Similar FiguresTwo geometric figures that have the same shape...
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Core Formulas
The Proportionality Rule
\frac{\text{side}_A'}{\text{side}_A} = \frac{\text{side}_B'}{\text{side}_B} = k
For two similar figures, the quotient of any pair of corresponding sides is a constant value, known as the scale factor (k). This rule is used to find missing side lengths.
Generating Numbers with a Quotient
\text{new number} = k \times \text{original number}
To find a new number that has a specific quotient (k) relative to an original number, multiply the original number by the quotient (scale factor).
Quotient of Perimeters and Areas
\frac{\text{Perimeter}'}{\text{Perimeter}} = k \quad \text{and} \quad \frac{\text{Area}'}{\text{Area}} = k^2
If the quotient of side lengths (scale factor) is k, the quotient of the perimeters is also k, but the...
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Challenging
The area of polygon A is 72 sq units and the area of a similar polygon B is 50 sq units. If a side in polygon A is 12 units long, what number must be chosen for the length of the corresponding side in polygon B?
A.8.33
B.10
C.14.4
D.9
Challenging
Triangle ABC has side lengths x, x+4, and 15. A similar triangle, DEF, has corresponding side lengths 5, 7, and y. To maintain a constant quotient, what must be the value of x?
A.5
B.6
C.8
D.10
Challenging
In right triangle ABC (right-angled at C), an altitude CD is drawn to the hypotenuse AB. This creates two smaller triangles, ADC and CDB, which are similar to ABC. If AD = 9 and DB = 16, what length must be chosen for the altitude CD to satisfy the similarity quotient between ΔADC and ΔCDB?
A.12.5
B.7
C.12
D.15
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What grade level is "Choose numbers with a particular quotient"?
Choose numbers with a particular quotient is a Grade 10 Mathematics lesson on ExcelOS.
What will I learn in Choose numbers with a particular quotient?
You'll be able to: Identify at least 8 out of 10 number pairs from a given set that result in a specific quotient (e.g., quotient of 5); Solve division problems, including those with remainders, to determine if two numbers produce a target….
Is "Choose numbers with a particular quotient" free to practice?
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This lesson includes 24 practice questions across multiple difficulty levels, each with instant feedback and explanations.