Podcast
Questions and Answers
Which of the following fractions is the largest when comparing $\frac{1}{4}$, $\frac{3}{8}$, $\frac{2}{5}$, and $\frac{5}{16}$?
Which of the following fractions is the largest when comparing $\frac{1}{4}$, $\frac{3}{8}$, $\frac{2}{5}$, and $\frac{5}{16}$?
Which fraction is the smallest among $\frac{1}{3}$, $\frac{5}{12}$, $\frac{2}{5}$, and $\frac{3}{10}$?
Which fraction is the smallest among $\frac{1}{3}$, $\frac{5}{12}$, $\frac{2}{5}$, and $\frac{3}{10}$?
When ordering the fractions $\frac{7}{10}$, $\frac{1}{2}$, $\frac{3}{4}$, and $\frac{2}{3}$ from smallest to largest, which order is correct?
When ordering the fractions $\frac{7}{10}$, $\frac{1}{2}$, $\frac{3}{4}$, and $\frac{2}{3}$ from smallest to largest, which order is correct?
Which of these statements about ordering the fractions $\frac{4}{5}$, $\frac{3}{5}$, $\frac{1}{2}$, and $\frac{7}{10}$ is true?
Which of these statements about ordering the fractions $\frac{4}{5}$, $\frac{3}{5}$, $\frac{1}{2}$, and $\frac{7}{10}$ is true?
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In the fractions $\frac{5}{6}$, $\frac{1}{8}$, $\frac{3}{4}$, and $\frac{1}{2}$, which fraction is located in the middle when arranged in ascending order?
In the fractions $\frac{5}{6}$, $\frac{1}{8}$, $\frac{3}{4}$, and $\frac{1}{2}$, which fraction is located in the middle when arranged in ascending order?
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Study Notes
Ordering Dissimilar Fractions
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To order dissimilar fractions (fractions with different denominators) from smallest to largest, or vice versa, the first step is to find a common denominator for all the fractions.
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The common denominator is a multiple that is divisible by all the denominators of the given fractions.
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This is achieved by finding the least common multiple (LCM) of the denominators. Finding the least common multiple ensures the fractions have the smallest possible common denominator. This simplifies the process and minimizes unnecessary work.
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Once the common denominator is identified, rewrite each fraction as an equivalent fraction with the common denominator. This process involves multiplying both the numerator and the denominator of each fraction by the same factor. This factor is the result of dividing the common denominator by the fraction's original denominator.
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With all the fractions written with a common denominator, it becomes easy to compare and order them. The fractions are ordered from smallest to largest by considering the numerators. The fraction with the smallest numerator is the smallest fraction, the one with the largest numerator is the largest.
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Example: Order 1/2, 2/3, and 3/4 from smallest to largest.
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The denominators are 2, 3, and 4. The LCM of 2, 3, and 4 is 12.
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Convert each fraction to an equivalent fraction with a denominator of 12:
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1/2 = (1 × 6)/(2 × 6) = 6/12
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2/3 = (2 × 4)/(3 × 4) = 8/12
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3/4 = (3 × 3)/(4 × 3) = 9/12
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Now, compare the numerators: 6, 8, 9. 6 < 8 < 9
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The fractions ordered from smallest to largest are 1/2, 2/3, 3/4.
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In the case of ordering a larger number of fractions, or fractions with larger values, using a systematic and organized process of finding the LCM and converting the fractions to equivalent fractions with the common denominator remains essential. This minimizes errors, particularly when dealing with more complex problems.
Advanced Techniques and Considerations
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When fractions have very large denominators or are extremely complex. A methodical approach is necessary.
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Sometimes, estimations can be used to quickly place fractions in an approximate order before converting to a common denominator. This is especially helpful when comparing many fractions.
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If fractions include mixed numbers first convert the mixed numbers to improper fractions then follow the same procedure as for pure fractions.
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Pay close attention to the instructions – ordering from largest to smallest is the opposite process.
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Description
Test your understanding of how to order dissimilar fractions from smallest to largest using a common denominator. This quiz covers finding the least common multiple and rewriting fractions as equivalent fractions. It's an essential skill for mastering fraction comparison in mathematics.
