Improper Fractions to Mixed Numbers Worksheets

Worksheets for converting improper fractions to mixed numbers, and mixed numbers back to improper fractions, each with an answer key that shows the working. The sheet below turns improper fractions like 19/4 into mixed numbers like 4 3/4. Switch Kind of sheet to Mixed numbers to improper fractions for the reverse.

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Converting & simplifyingAdding & subtractingMultiplying & dividingMixed practiceEquivalent & comparing

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Converting & simplifying

Improper to mixedMixed to improperSimplifySimplify improper

Adding & subtracting

Add, likeAdd, unlikeAdd mixed numbersSubtract, likeSubtract, unlikeSubtract mixed numbers

Multiplying & dividing

MultiplyMultiply by a wholeMultiply mixed numbersDivideDivide with wholesDivide mixed numbers

Mixed practice

Add & subtractAdd & subtract mixedMultiply & divide

Equivalent & comparing

Equivalent fractionsCompare, unlikeCompare, like

Improper fractions to mixed numbers. Divide, then put the remainder over the denominator.Mixed numbers to improper fractions. Whole times denominator, plus the numerator.Simplifying fractions. Divide top and bottom by the greatest common factor.Simplifying improper fractions. Reduce, then write it as a mixed number.Adding fractions, like denominators. Add the tops, keep the bottom.Adding fractions, unlike denominators. Find the least common denominator, then add.Adding mixed numbers. Make them improper fractions first, then add.Subtracting fractions, like denominators. Subtract the tops, keep the bottom.Subtracting fractions, unlike denominators. Find a common denominator, then subtract.Subtracting mixed numbers. Improper fractions first, so no borrowing.Multiplying fractions. Cross-cancel, then multiply straight across.Multiplying fractions by whole numbers. Write the whole number over 1, then multiply.Multiplying mixed numbers. Improper fractions first, then cross-cancel.Dividing fractions. Keep, change, flip, then multiply.Dividing fractions and whole numbers. The whole number goes over 1 before it flips.Dividing mixed numbers. Improper fractions first, then keep, change, flip.Adding and subtracting fractions. Both on one sheet, unlike denominators.Adding and subtracting mixed numbers. Both on one sheet, with mixed numbers.Multiplying and dividing fractions. Both on one sheet.Equivalent fractions. Find the missing number that keeps them equal.Comparing fractions, unlike denominators. Greater than, less than, or equal to.Comparing fractions, like denominators. Same denominators: compare the tops.

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The problems

Kind of sheetAdding fractionsSubtracting fractionsMultiplying fractionsDividing fractionsAdding and subtractingMultiplying and dividingImproper fractions to mixed numbersMixed numbers to improper fractionsSimplifying fractionsEquivalent fractionsComparing fractions

Which denominatorsA rangeChosen ones

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Whole numbers

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New problems

The sheet

How many problemsUp to 40, if they fit.

ColumnsFewer columns leave more room to write each answer.

Answer keyShow the working on the keyEach step on the problem's own line, the way the fraction calculator works it.

Different versionsUp to 8, each with different problems and its own key.

Title and instructions

TitleLeft empty, the sheet is titled "Improper Fractions to Mixed Numbers", as the printed fraction sheets are.

Instructions

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Name line Border DadsWorksheets logo at the foot

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Improper fractions to mixed numbers · denominators 2–12 · whole numbers 1–9 · 10 problems · with worked answer key · name line · border · logo

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Improper fractions to mixed numbers · denominators 2–12 · whole numbers 1–9 · 10 problems · with worked answer key · name line · border · logoUS Letter · print at 100%

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Improper Fraction to Mixed Number

Divide the numerator by the denominator. The quotient is the whole number, and the remainder goes over the same denominator. For 19/4, 19 ÷ 4 is 4 remainder 3, so 19/4 = 4 3/4.

If the remainder's fraction can be reduced, reduce it: 15/6 is 2 remainder 3, which is 2 3/6, and 3/6 reduces to 1/2, giving 2 1/2. If there is no remainder, the answer is a whole number: 20/4 = 5. The answer keys show each of these steps, so a wrong answer can be traced to the step where it went wrong.

Mixed Number to Improper Fraction

Multiply the whole number by the denominator, add the numerator, and keep the same denominator. For 3 2/5, 3 × 5 = 15, plus 2 is 17, so 3 2/5 = 17/5. This is the first step of adding, subtracting, multiplying or dividing mixed numbers, which is why it is worth practicing on its own.

Choosing the Numbers

The denominators can be a range or a chosen set, such as halves, quarters and eighths. The whole numbers can be kept small for a first sheet or taken up to 20. Ask for several versions to give each student a different sheet, each with its own answer key.

Where to Go Next

To check an answer, the mixed number calculator shows these conversions step by step. For more practice with fractions in lowest terms, see reducing fractions, and for the full set of fraction topics see fractions worksheets.

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