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2. Find the difference of \( \frac{3}{4}-\frac{2}{8} \). Begin by finding common multiples of the denominators. \( \frac{3}{4} \) Multiples of \( 4: 4 \), \( \frac{2}{8} \) Multiples of \( 8: 8 \), What is the least number that can be used as a common denominator? 3. Write equivalent fractions for \( \frac{3}{4} \) and \( \frac{2}{8} \) with the common denominator you found in Problem 2 \( \frac{3}{4} \times \frac{2}{8}=\frac{2}{8} \times \frac{\square}{8} \)

Ask by Weber Schultz. in the United States
Feb 27,2025

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Tutor-Verified Answer

Answer

The least common denominator is 8. Equivalent fractions are 6/8 and 2/8. The difference is 1/2.

Solution

Step 1. Finding a Common Denominator: • The denominators are 4 and 8. • Multiples of 4 are 4, 8, 12, … and multiples of 8 are 8, 16, 24, … • The least common multiple (and thus the common denominator) is 8. Step 2. Writing Equivalent Fractions: • For 3/4, we need to get a denominator of 8. Since 4 × 2 = 8, multiply the numerator by 2 as well:   3/4 = (3 × 2)/(4 × 2) = 6/8. • For 2/8, the denominator is already 8, so it remains 2/8. Step 3. Finding the Difference: Now subtract:   6/8 – 2/8 = (6 – 2)/8 = 4/8. This fraction can be simplified by dividing the numerator and denominator by 4:   4/8 = 1/2. Answers: 2. The least number that can be used as a common denominator is 8. 3. The equivalent fractions are 6/8 and 2/8 (since 3/4 = 6/8 and 2/8 remains 2/8).

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The Deep Dive

To find the least common denominator for \( \frac{3}{4} \) and \( \frac{2}{8} \), you can look for the smallest multiple that is common to both denominators. The multiples of \( 4 \) are \( 4, 8, 12, \) and so on, while the multiples of \( 8 \) are \( 8, 16, 24, \) and so on. The least common multiple (LCM) is \( 8 \), making it the perfect common denominator for these fractions. Now, let's express both fractions with a denominator of \( 8 \). For \( \frac{3}{4} \), we can multiply both the numerator and the denominator by \( 2 \): \( \frac{3 \times 2}{4 \times 2} = \frac{6}{8} \). For \( \frac{2}{8} \), it stays the same since its denominator is already \( 8 \): \( \frac{2}{8} \). We can now subtract them: \( \frac{6}{8} - \frac{2}{8} = \frac{4}{8} \), which simplifies to \( \frac{1}{2} \)!

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