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Dividing Mixed Numbers: Definition and Example | EDU.COMEDU.COMResourcesBlogGuidePodcastPlanBackHomesvg]:size-3.5">Math Glossarysvg]:size-3.5">Dividing Mixed NumbersDividing Mixed Numbers: Definition and ExampleTable of ContentsDefinition of Mixed Numbers and Division

A mixed number is a combination of a whole number and a proper fraction represented together, such as 3123\frac{1}{2}321​ or 2352\frac{3}{5}253​. Mixed numbers always represent values greater than 111 and are positioned between consecutive whole numbers (for example, 3123\frac{1}{2}321​ lies between 333 and 444). It's important to note that the unwritten sign between the whole number part and the fractional part indicates addition, not multiplication. For instance, 1121\frac{1}{2}121​ glasses of milk means one glass plus half a glass.

Fractions can be categorized into three types based on the relationship between numerator and denominator. Proper fractions have numerators smaller than denominators (like 25\frac{2}{5}52​, 37\frac{3}{7}73​) and always represent values between 000 and 111. Improper fractions have numerators equal to or greater than denominators (such as 54\frac{5}{4}45​, 75\frac{7}{5}57​) and represent values greater than or equal to 111. Mixed numbers are essentially improper fractions written in a different format, combining a whole number with a proper fraction.

Examples of Dividing Mixed Numbers Example 1: Dividing a Mixed Number by a Whole Number Problem:

Divide 3123\frac{1}{2}321​ muffins equally among 222 friends. How much will each friend receive?

Step-by-step solution: Step 1, We need to convert the mixed number to an improper fraction to make the division easier: 312=(3×2)+12=6+12=723\frac{1}{2} = \frac{(3 \times 2) + 1}{2} = \frac{6 + 1}{2} = \frac{7}{2}321​=2(3×2)+1​=26+1​=27​ Step 2, Set up the division problem. We can write the whole number 222 as a fraction with denominator 111: 72÷21\frac{7}{2} \div \frac{2}{1}27​÷12​ Step 3, To divide by a fraction, multiply by its reciprocal: 72×12=74\frac{7}{2} \times \frac{1}{2} = \frac{7}{4}27​×21​=47​ Step 4, Convert the answer back to a mixed number: 74=134\frac{7}{4} = 1\frac{3}{4}47​=143​ Step 5, Therefore, each friend will receive 1341\frac{3}{4}143​ muffins. Example 2: Dividing a Mixed Number by a Fraction Problem:

Divide 2232\frac{2}{3}232​ by 25\frac{2}{5}52​.

Step-by-step solution: Step 1, Convert the mixed number to an improper fraction: 223=(2×3)+23=6+23=832\frac{2}{3} = \frac{(2 \times 3) + 2}{3} = \frac{6 + 2}{3} = \frac{8}{3}232​=3(2×3)+2​=36+2​=38​ Step 2, Set up the division problem: 83÷25\frac{8}{3} \div \frac{2}{5}38​÷52​ Step 3, Apply the division ruleWhen dividing by a fraction, multiply by its reciprocal: 83×52=8×53×2=406\frac{8}{3} \times \frac{5}{2} = \frac{8 \times 5}{3 \times 2} = \frac{40}{6}38​×25​=3×28×5​=640​ Step 4, Simplifythe resulting fraction: 406=203\frac{40}{6} = \frac{20}{3}640​=320​ Step 5, Convert back to a mixed number: 203=623\frac{20}{3} = 6\frac{2}{3}320​=632​ Step 6, Therefore, 223÷25=6232\frac{2}{3} \div \frac{2}{5} = 6\frac{2}{3}232​÷52​=632​ Example 3: Dividing a Mixed Number by Another Mixed Number Problem:

Divide 3253\frac{2}{5}352​ by 2152\frac{1}{5}251​.

Step-by-step solution: Step 1, Convert both mixed numbers to improper fractions:

325=(3×5)+25=15+25=1753\frac{2}{5} = \frac{(3 \times 5) + 2}{5} = \frac{15 + 2}{5} = \frac{17}{5}352​=5(3×5)+2​=515+2​=517​

215=(2×5)+15=10+15=1152\frac{1}{5} = \frac{(2 \times 5) + 1}{5} = \frac{10 + 1}{5} = \frac{11}{5}251​=5(2×5)+1​=510+1​=511​

Step 2, Set up the division problem: 175÷115\frac{17}{5} \div \frac{11}{5}517​÷511​ Step 3, Apply the division ruleMultiply the first fraction by the reciprocal of the second: 175×511=17×55×11=1711\frac{17}{5} \times \frac{5}{11} = \frac{17 \times 5}{5 \times 11} = \frac{17}{11}517​×115​=5×1117×5​=1117​ Step 4, Convert the result to a mixed number: 1711=1611\frac{17}{11} = 1\frac{6}{11}1117​=1116​ Step 5, Therefore, 325÷215=16113\frac{2}{5} \div 2\frac{1}{5} = 1\frac{6}{11}352​÷251​=1116​ Comments(9)FFloristVivianNovember 5, 2025I've been struggling to teach dividing mixed numbers. This page's clear defs and examples made it a breeze! Thanks for the great resource.

SSoccerFanOscarNovember 4, 2025I've been struggling to teach dividing mixed numbers. This page's clear examples made it easy for my students to grasp. Thanks!

EElectricianSamNovember 4, 2025I've been struggling to teach dividing mixed numbers. This page's clear examples made it easy for my students to grasp. Thanks!

MCMs. CarterSeptember 17, 2025I’ve been struggling to teach my kids mixed numbers, but this page made it so simple! The step-by-step examples were super clear, and they finally got it. Thanks for breaking it down!

MCMs. CarterSeptember 10, 2025I’ve been struggling to help my daughter with dividing mixed numbers, but this page broke it down so clearly! The step-by-step examples made a huge difference. Highly recommend it for parents teaching at home!

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