Mathematics
Grade 10
15 min
Put assorted decimals, fractions, and mixed numbers in order
Put assorted decimals, fractions, and mixed numbers in order
What you'll learn
- Identify the place value of digits in decimals up to the hundredths place to compare and order them correctly in at least 8 out of 10 problems.
- Convert fractions with denominators of 2, 4, 5, 10, 20, 25, 50, and 100 to decimals, and vice versa, with 90% accuracy.
- Order a set of 5-7 assorted decimals, fractions, and mixed numbers from least to greatest and greatest to least, providing the correct order in at least 4 out of 5 problems.
- Explain the strategy used to order a set of decimals, fractions, and mixed numbers, including why each step was taken, in a written explanation that demonstrates understanding of equivalent forms.
Tutorial Preview
1
Introduction & Learning Objectives
Learning Objectives
Convert any fraction, mixed number, or percentage into its decimal equivalent with a specified degree of precision.
Compare any two numbers in different formats (e.g., a fraction and a decimal) by establishing a common representation.
Justify the ordering of a set of rational numbers using a number line or by proving inequalities.
Construct a logically sequenced argument to order a set of at least five assorted numbers from least to greatest or greatest to least.
Analyze and evaluate the efficiency of different comparison strategies (e.g., converting to decimals vs. finding a common denominator).
Apply logical deduction to place an irrational number, such as π or √2, within an ordered set of rational numbers.
You're a scientist comparing experimental...
2
Key Concepts & Vocabulary
TermDefinitionExample
Rational NumberAny number that can be expressed as a quotient or fraction p/q of two integers, where the denominator q is not zero.0.75 can be expressed as 3/4. The integer 5 can be expressed as 5/1.
Mixed NumberA number consisting of an integer and a proper fraction. It represents the sum of the two parts.4 1/2 represents the sum 4 + 1/2.
Improper FractionA fraction in which the numerator is greater than or equal to the denominator, representing a value greater than or equal to 1.9/2 is the improper fraction equivalent of 4 1/2.
Common RepresentationA uniform format used to compare different types of numbers. The most common representations are decimals or fractions with a common denominator.To compare 3/4 and 0.8, you can convert 3/4 to its decimal representation,...
3
Core Formulas
Mixed Number to Improper Fraction Conversion
A \frac{b}{c} = \frac{A \times c + b}{c}
To convert a mixed number into an improper fraction, multiply the whole number (A) by the denominator (c), add the numerator (b), and place the result over the original denominator (c). This is a key step before finding a common denominator.
Fraction to Decimal Conversion
\frac{a}{b} = a \div b
To convert any fraction into its decimal form, perform the division of the numerator (a) by the denominator (b). This is the most universal strategy for creating a common representation for comparison.
The Trichotomy Property
For any two real numbers a and b, exactly one of the following is true: a < b, a = b, or a > b.
This fundamental property of logic and number systems guarantees th...
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Sign Up Free to ContinueSample Practice Questions
Easy
Which decimal is equivalent to the mixed number 7 1/5?
A.7.1
B.7.2
C.7.5
D.7.02
Easy
Which of the following inequality statements is true?
A.3/4 > 0.8
B.1/2 < 0.45
C.0.6 > 5/8
D.1/3 < 0.34
Easy
Which statement correctly compares -2.75 and -2.5?
A.-2.75 > -2.5
B.-2.75 = -2.5
C.-2.75 < -2.5
D.The relationship cannot be determined.
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Frequently asked questions
What grade level is "Put assorted decimals, fractions, and mixed numbers in order"?
Put assorted decimals, fractions, and mixed numbers in order is a Grade 10 Mathematics lesson on ExcelOS.
What will I learn in Put assorted decimals, fractions, and mixed numbers in order?
You'll be able to: Identify the place value of digits in decimals up to the hundredths place to compare and order them correctly in at least 8 out of 10 problems; Convert fractions with denominators of 2, 4, 5, 10, 20, 25, 50, and 100 to decimals….
Is "Put assorted decimals, fractions, and mixed numbers in order" 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 Put assorted decimals, fractions, and mixed numbers in order?
This lesson includes 25 practice questions across multiple difficulty levels, each with instant feedback and explanations.