Podcast
Questions and Answers
What is the equivalent fraction of 2/3 when both numerator and denominator are multiplied by 4?
What is the equivalent fraction of 2/3 when both numerator and denominator are multiplied by 4?
What is the sum of 1/6 and 1/4?
What is the sum of 1/6 and 1/4?
What is the product of 2/3 and 3/4?
What is the product of 2/3 and 3/4?
What is the result of dividing 2/3 by 3/4?
What is the result of dividing 2/3 by 3/4?
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What is the decimal equivalent of 3/4?
What is the decimal equivalent of 3/4?
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What is the least common multiple of 6 and 8?
What is the least common multiple of 6 and 8?
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What is the equivalent fraction of 0.5?
What is the equivalent fraction of 0.5?
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What is the result of multiplying 2/3 by 2?
What is the result of multiplying 2/3 by 2?
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What is the result of dividing 3/4 by 2?
What is the result of dividing 3/4 by 2?
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Study Notes
Equivalent Ratios
- Two fractions are equivalent if they have the same value
- Equivalent fractions can be found by multiplying or dividing both numerator and denominator by the same number
- Example: 1/2 = 2/4 = 3/6
- To find an equivalent fraction, multiply or divide both numbers by the same number
Adding and Subtracting Fractions
- To add or subtract fractions, they must have the same denominator
- If the denominators are different, find the least common multiple (LCM) of the two denominators
- Convert both fractions to have the LCM as the denominator
- Add or subtract the numerators and keep the denominator the same
- Example: 1/4 + 1/6 = 3/12 + 2/12 = 5/12
Multiplying Fractions
- To multiply fractions, multiply the numerators and multiply the denominators
- Example: 1/2 × 3/4 = (1 × 3) / (2 × 4) = 3/8
- Multiplying by a whole number is the same as multiplying by an equivalent fraction
- Example: 2 × 3/4 = 2/1 × 3/4 = 6/4 = 3/2
Dividing Fractions
- To divide fractions, invert the second fraction (i.e., flip the numerator and denominator) and then multiply
- Example: 1/2 ÷ 3/4 = 1/2 × 4/3 = (1 × 4) / (2 × 3) = 4/6
- Dividing by a whole number is the same as dividing by an equivalent fraction
- Example: 3/4 ÷ 2 = 3/4 ÷ 2/1 = 3/4 × 1/2 = 3/8
Converting to Decimals
- A fraction can be converted to a decimal by dividing the numerator by the denominator
- Example: 3/4 = 3 ÷ 4 = 0.75
- Decimals can be converted back to fractions by finding the equivalent fraction
- Example: 0.5 = 1/2
Equivalent Ratios
- Equivalent fractions have the same value, and can be found by multiplying or dividing both numerator and denominator by the same number
- Example of equivalent fractions: 1/2 = 2/4 = 3/6
- Multiplying or dividing both numbers by the same number finds an equivalent fraction
Adding and Subtracting Fractions
- Fractions must have the same denominator to add or subtract
- If denominators differ, find the least common multiple (LCM) of both denominators to convert fractions
- Add or subtract the numerators and keep the denominator the same after converting
- Example: 1/4 + 1/6 = 3/12 + 2/12 = 5/12
Multiplying Fractions
- Multiply the numerators and multiply the denominators to multiply fractions
- Example: 1/2 × 3/4 = (1 × 3) / (2 × 4) = 3/8
- Multiplying by a whole number is the same as multiplying by an equivalent fraction
- Example: 2 × 3/4 = 2/1 × 3/4 = 6/4 = 3/2
Dividing Fractions
- Invert the second fraction (flip numerator and denominator) and then multiply to divide fractions
- Example: 1/2 ÷ 3/4 = 1/2 × 4/3 = (1 × 4) / (2 × 3) = 4/6
- Dividing by a whole number is the same as dividing by an equivalent fraction
- Example: 3/4 ÷ 2 = 3/4 ÷ 2/1 = 3/4 × 1/2 = 3/8
Converting to Decimals
- Divide the numerator by the denominator to convert a fraction to a decimal
- Example: 3/4 = 3 ÷ 4 = 0.75
- Convert decimals back to fractions by finding the equivalent fraction
- Example: 0.5 = 1/2
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Description
Learn about equivalent ratios, finding equivalent fractions, and performing operations like addition and subtraction on fractions with different denominators.
