Podcast
Questions and Answers
Which of the following scenarios demonstrates the correct application of finding a common denominator when comparing $\frac{3}{5}$ and $\frac{2}{3}$?
Which of the following scenarios demonstrates the correct application of finding a common denominator when comparing $\frac{3}{5}$ and $\frac{2}{3}$?
- Converting both fractions to a common denominator of 15. (correct)
- Converting both fractions to a common denominator of 8.
- Converting both fractions to a common denominator of 3.
- Comparing the fractions directly without finding a common denominator.
A recipe calls for $\frac{2}{3}$ cup of sugar and $\frac{1}{4}$ cup of flour. If you want to double the recipe, how many cups of ingredients will you need in total?
A recipe calls for $\frac{2}{3}$ cup of sugar and $\frac{1}{4}$ cup of flour. If you want to double the recipe, how many cups of ingredients will you need in total?
- $\frac{3}{7}$ cup
- $\frac{5}{12}$ cup
- $\frac{11}{12}$ cup
- $\frac{11}{6}$ cups (correct)
If a pizza is cut into 12 slices and you eat $\frac{1}{3}$ of the pizza, how many slices did you eat?
If a pizza is cut into 12 slices and you eat $\frac{1}{3}$ of the pizza, how many slices did you eat?
- 3 slices
- 4 slices (correct)
- 6 slices
- 2 slices
Which of the following fractions is NOT equivalent to $\frac{2}{5}$?
Which of the following fractions is NOT equivalent to $\frac{2}{5}$?
What is the result of $\frac{3}{4} \div \frac{9}{20}$ expressed in simplest form?
What is the result of $\frac{3}{4} \div \frac{9}{20}$ expressed in simplest form?
If you have $\frac{7}{8}$ of a pizza and you eat $\frac{1}{4}$ of the whole pizza, how much of the pizza is left?
If you have $\frac{7}{8}$ of a pizza and you eat $\frac{1}{4}$ of the whole pizza, how much of the pizza is left?
Which expression correctly converts the mixed number $3\frac{2}{5}$ into an improper fraction?
Which expression correctly converts the mixed number $3\frac{2}{5}$ into an improper fraction?
What is the simplified form of the fraction $\frac{24}{36}$?
What is the simplified form of the fraction $\frac{24}{36}$?
Arrange the following fractions in ascending order: $\frac{2}{3}$, $\frac{1}{2}$, $\frac{3}{4}$
Arrange the following fractions in ascending order: $\frac{2}{3}$, $\frac{1}{2}$, $\frac{3}{4}$
Calculate: $\frac{2}{5} + \frac{1}{3} - \frac{1}{6}$
Calculate: $\frac{2}{5} + \frac{1}{3} - \frac{1}{6}$
Flashcards
What is a fraction?
What is a fraction?
Part of a whole, written as a/b.
What is a proper fraction?
What is a proper fraction?
Numerator is less than the denominator (e.g., 1/2).
What is an improper fraction?
What is an improper fraction?
Numerator is greater than or equal to the denominator (e.g., 5/3).
What is a mixed number?
What is a mixed number?
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Mixed to improper fraction?
Mixed to improper fraction?
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What are equivalent fractions?
What are equivalent fractions?
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What does simplifying a fraction mean?
What does simplifying a fraction mean?
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Equivalent Fractions.
Equivalent Fractions.
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Adding/subtracting fractions?
Adding/subtracting fractions?
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Multiplying fractions?
Multiplying fractions?
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Study Notes
Fraction Basics
- Represents a part of a whole
- Written as a/b, where a = numerator, b = denominator
- Numerator signifies the # of parts taken
- Denominator signifies the total # of parts
- Denominator ≠ zero
Types of Fractions
- Proper: numerator < denominator (e.g., 1/2, 3/4)
- Improper: numerator ≥ denominator (e.g., 5/3, 7/7)
- Mixed numbers: whole number + proper fraction (e.g., 1 1/2, 2 3/4)
Converting Between Improper Fractions and Mixed Numbers
- Improper to mixed: divide numerator by denominator
- Quotient = whole number
- Remainder = numerator of the fractional part
- Denominator remains constant
- Example: 7/3 = 2 1/3 (7 ÷ 3 = 2, remainder of 1)
- Mixed to improper: multiply whole number by denominator, add numerator
- Result becomes the new numerator
- Denominator remains constant
- Example: 2 1/4 = (2 * 4 + 1)/4 = 9/4
Equivalent Fractions
- Represent the same value, with different numerators/denominators
- Found by multiplying/dividing both numerator and denominator by the same non-zero number
- Example: 1/2 = 2/4 = 3/6
Simplifying Fractions
- Reducing a fraction to its lowest terms
- Divide numerator and denominator by their greatest common divisor (GCD)
- Simplest form: GCD of numerator and denominator = 1
- Example: 4/6 simplified is 2/3 (GCD of 4 and 6 is 2)
Comparing Fractions
- Same denominator: larger numerator = greater fraction
- Different denominators: find a common denominator, then compare numerators
- Common denominator: least common multiple (LCM) of the denominators
- Example: Comparing 1/3 and 1/4, LCM of 3 and 4 is 12
- 1/3 = 4/12 and 1/4 = 3/12, so 1/3 > 1/4
Adding and Subtracting Fractions
- Must have a common denominator
- Add/subtract the numerators
- Denominator remains constant
- Simplify the result, if possible
- Example: 1/4 + 2/4 = 3/4
- Example: 2/3 - 1/6 = 4/6 - 1/6 = 3/6 = 1/2
Multiplying Fractions
- Multiply the numerators
- Multiply the denominators
- Simplify, if possible
- Example: 1/2 * 2/3 = (12)/(23) = 2/6 = 1/3
Dividing Fractions
- Multiply by the reciprocal of the second fraction
- Reciprocal: swap numerator and denominator
- Simplify, if possible
- Example: 1/2 ÷ 2/3 = 1/2 * 3/2 = (13)/(22) = 3/4
Fractions on a Number Line
- Represented on a number line
- Divide space between whole numbers into equal parts based on the denominator
- Numerator indicates # of parts to count from zero
Real-World Applications
- Cooking (e.g., 1/2 cup of flour)
- Measurement (e.g., 1/4 inch)
- Telling time (e.g., a quarter past the hour)
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Description
Learn the basics of fractions including defining numerators and denominators. Explore the different types of fractions, including proper, improper, and mixed numbers. Also, learn how to convert between improper fractions and mixed numbers.
