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Unlike Denominators: Definition and Example | EDU.COMEDU.COMResourcesBlogGuidePodcastPlanBackHomesvg]:size-3.5">Math Glossarysvg]:size-3.5">Unlike DenominatorsUnlike Denominators: Definition and ExampleTable of ContentsDefinition of Unlike Denominators

A fraction represents a part of a whole and is written in the form pq\frac{p}{q}qp​, where p is the numerator and q is the denominator. The numerator indicates the number of parts being considered, while the denominator represents the total number of equal parts the whole is divided into. For example, in the fraction 45\frac{4}{5}54​, 4 is the numerator and 5 is the denominator, indicating 4 out of 5 equal parts.

Fractions can be categorized into two types based on their denominators. Like fractions have the same denominator, such as 27\frac{2}{7}72​ and 57\frac{5}{7}75​. Unlike fractions have different denominators, such as 57\frac{5}{7}75​ and 49\frac{4}{9}94​. When two or more fractions have different denominators, they are called fractions with unlike denominators. Working with unlike denominators can be challenging, which is why we often convert them to like denominators before comparing, adding, or subtracting them.

Examples of Unlike Denominators Example 1: Arranging Fractions in Descending Order Problem:

Arrange 511\frac{5}{11}115​, 57\frac{5}{7}75​, 517\frac{5}{17}175​ and 513\frac{5}{13}135​ in descending order.

Step-by-step solution: Step 1, notice that all fractions have the same numerator (5), but different denominators. This makes our comparison easier. Step 2, when fractions have the same numerator but different denominators, the fraction with the smallest denominator is the greatest. Think of it this way: if you divide a pizza into fewer pieces (smaller denominator), each piece is larger. Step 3, let's analyze: When comparing 57\frac{5}{7}75​, 511\frac{5}{11}115​, 513\frac{5}{13}135​, and 517\frac{5}{17}175​, we need to compare the denominators: 7, 11, 13, and 17. Step 4, since 7 57>511>513>517\frac{5}{7} > \frac{5}{11} > \frac{5}{13} > \frac{5}{17}75​>115​>135​>175​ Example 2: Comparing Fractions in a Word Problem Problem:

Candy read 47\frac{4}{7}74​ of the book on Monday and 23\frac{2}{3}32​ of the book on Tuesday. On which day did she read more and by how much?

Step-by-step solution: Step 1, identify the fractions we need to compare: Monday: 47\frac{4}{7}74​ Tuesday: 23\frac{2}{3}32​ Step 2, since these fractions have unlike denominators, we need to convert them to equivalent fractions with the same denominator. Step 3, find the common denominator: We need the least common multiple (LCM) of 7 and 3. Multiples of 7: 7, 14, 21, 28... Multiples of 3: 3, 6, 9, 12, 15, 18, 21... The LCM of 7 and 3 is 21 Step 4, convert both fractions to equivalent fractions with denominator 21: Monday: 47=4×37×3=1221\frac{4}{7} = \frac{4 \times 3}{7 \times 3} = \frac{12}{21}74​=7×34×3​=2112​ Tuesday: 23=2×73×7=1421\frac{2}{3} = \frac{2 \times 7}{3 \times 7} = \frac{14}{21}32​=3×72×7​=2114​ Step 5, compare the fractions: Since 1421\frac{14}{21}2114​ > 1221\frac{12}{21}2112​, Candy read more on Tuesday. Step 6, calculate the difference: Difference = 1421−1221=14−1221=221\frac{14}{21} - \frac{12}{21} = \frac{14-12}{21} = \frac{2}{21}2114​−2112​=2114−12​=212​ Therefore, she read 221\frac{2}{21}212​ more of the book on Tuesday than on Monday. Example 3: Adding Unlike Fractions Problem:

Add: 23+25+34\frac{2}{3} + \frac{2}{5} + \frac{3}{4}32​+52​+43​.

Step-by-step solution: Step 1, observe that all three fractions have different denominators: 3, 5, and 4. We need to find a common denominator. Step 2, find the least common multiple (LCM) of 3, 5, and 4: Multiples of 3: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30... Multiples of 5: 5, 10, 15, 20, 25, 30... Multiples of 4: 4, 8, 12, 16, 20, 24, 28, 32, 36, 40... The LCM is 60 Step 3, convert each fraction to an equivalent fraction with denominator 60: For 23\frac{2}{3}32​: Multiply by 2020\frac{20}{20}2020​ to get 2×203×20=4060\frac{2 \times 20}{3 \times 20} = \frac{40}{60}3×202×20​=6040​ For 25\frac{2}{5}52​: Multiply by 1212\frac{12}{12}1212​ to get 2×125×12=2460\frac{2 \times 12}{5 \times 12} = \frac{24}{60}5×122×12​=6024​ For 34\frac{3}{4}43​: Multiply by 1515\frac{15}{15}1515​ to get 3×154×15=4560\frac{3 \times 15}{4 \times 15} = \frac{45}{60}4×153×15​=6045​ Step 4, add the numerators while keeping the common denominator: 4060+2460+4560=40+24+4560=10960\frac{40}{60} + \frac{24}{60} + \frac{45}{60} = \frac{40 + 24 + 45}{60} = \frac{109}{60}6040​+6024​+6045​=6040+24+45​=60109​ Step 5, convert to a mixed number: Divide 109 by 60: 109 ÷ 60 = 1 remainder 49 Therefore, 10960=14960\frac{109}{60} = 1\frac{49}{60}60109​=16049​ Comments(6)MCMs. CarterSeptember 17, 2025This definition of unlike denominators made explaining fractions so much easier for my 5th grader! The examples were super clear, and we loved the step-by-step approach to finding common denominators. Thanks, EDU!

MMomOf3AdventurersSeptember 10, 2025This glossary made teaching fractions so much easier! The clear definition and step-by-step examples helped my kids finally understand unlike denominators. We even practiced converting them together—great resource!

TTravelingSoulAugust 27, 2025I used the explanation and examples on unlike denominators to help my kids with their homework, and it worked great! The step-by-step approach made it so much easier for them to understand.

MCMs. CarterAugust 19, 2025I used the examples on this page to help my kids understand adding fractions with unlike denominators—it’s so clear and easy to follow! They finally got it after struggling for weeks. Thanks for this resource!

MMathMom25August 6, 2025This glossary page made fractions way easier for my 4th grader! Comparing and adding them now feels like a breeze thanks to the step-by-step examples. Highly recommend it!

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