Mathematics
Grade 9
15 min
Compare mixed numbers and improper fractions
Compare mixed numbers and improper fractions
What you'll learn
- Identify whether a given number is a mixed number or an improper fraction with 100% accuracy.
- Convert mixed numbers to improper fractions and improper fractions to mixed numbers, demonstrating the process correctly in at least 4 out of 5 attempts.
- Compare two mixed numbers or improper fractions using symbols (, =) by converting them to a common form (either both mixed numbers or both improper fractions) and justifying the comparison in writing with at least 80% accuracy.
- Explain the relationship between mixed numbers and improper fractions using mathematical vocabulary (numerator, denominator, whole number, fraction) in a written paragraph with at least three accurate statements.
Tutorial Preview
1
Introduction & Learning Objectives
Learning Objectives
Convert any mixed number into its equivalent improper fraction.
Convert any improper fraction into its equivalent mixed number.
Compare two rational numbers, one in mixed number form and one in improper fraction form, by converting them to a common format.
Determine the least common denominator (LCD) for two fractions to facilitate comparison.
Use inequality symbols (<, >, =) correctly to express the relationship between two mixed numbers or improper fractions.
Apply comparison skills to solve contextual word problems involving mixed numbers and improper fractions.
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2
Key Concepts & Vocabulary
TermDefinitionExample
Mixed NumberA number composed of a whole number and a proper fraction. It represents a value greater than one.3 1/4 (read as 'three and one-fourth')
Improper FractionA fraction where the numerator (top number) is greater than or equal to the denominator (bottom number). It represents a value greater than or equal to one.13/4 (read as 'thirteen-fourths')
NumeratorThe top number in a fraction, representing how many parts of the whole are being considered.In the fraction 13/4, the numerator is 13.
DenominatorThe bottom number in a fraction, representing the total number of equal parts the whole is divided into.In the fraction 13/4, the denominator is 4.
Least Common Denominator (LCD)The smallest positive integer that is a multiple of the denominators...
3
Core Formulas
Converting a Mixed Number to an Improper Fraction
a \frac{b}{c} = \frac{(a \times c) + b}{c}
To convert, multiply the whole number (a) by the denominator (c), add the numerator (b) to the result, and place this new value over the original denominator (c).
Converting an Improper Fraction to a Mixed Number
\frac{d}{c} \rightarrow q \frac{r}{c}, \text{ where } d \div c = q \text{ with remainder } r
To convert, divide the numerator (d) by the denominator (c). The quotient (q) becomes the whole number, the remainder (r) becomes the new numerator, and the denominator (c) stays the same.
Comparing Fractions with a Common Denominator
\text{If } c > 0, \text{ then } \frac{a}{c} > \frac{b}{c} \iff a > b
When two fractions have the same positive denominator, the fracti...
4 more steps in this tutorial
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Sign Up Free to ContinueSample Practice Questions
Easy
According to the tutorial, which of the following best defines an improper fraction?
A.fraction where the denominator is larger than the numerator.
B.fraction where the numerator is greater than or equal to the denominator.
C.number composed of a whole number and a proper fraction.
D.fraction that cannot be simplified further.
Easy
Using the formula a b/c = ((a × c) + b) / c, convert the mixed number 3 1/4 into its equivalent improper fraction.
A.13/4
B.7/4
C.12/4
D.31/4
Easy
How do you convert the improper fraction 13/4 into a mixed number?
A.Multiply 13 by 4 and add the remainder.
B.Divide 4 by 13.
C.Divide 13 by 4. The quotient is the whole number and the remainder is the new numerator.
D.Subtract 4 from 13 as many times as possible.
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Frequently asked questions
What grade level is "Compare mixed numbers and improper fractions"?
Compare mixed numbers and improper fractions is a Grade 9 Mathematics lesson on ExcelOS.
What will I learn in Compare mixed numbers and improper fractions?
You'll be able to: Identify whether a given number is a mixed number or an improper fraction with 100% accuracy; Convert mixed numbers to improper fractions and improper fractions to mixed numbers, demonstrating the process correctly in at least 4….
Is "Compare mixed numbers and improper 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 Compare mixed numbers and improper fractions?
This lesson includes 25 practice questions across multiple difficulty levels, each with instant feedback and explanations.