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Mixed Numbers and Improper Fractions

Introduction

Traditional fractions are usually written with a lower numerator and higher denominator. An improper fraction is one where the denominator is higher than the numerator. A mixed fraction (or mixed number) is when a whole number is combined with a fraction.

Terms

Fraction - Fractions are used when using numbers to express parts of whole.
Improper Fraction - A fraction where the numerator is greater than the denominator.
Mixed Fraction - A fraction where a whole number is combined with a fraction.
Numerator - The top part of the fraction, referring to the parts taken from the whole.
Denominator - The bottom part of the fraction, referring to the number of parts that make up the whole.
Whole Number - A whole number is a number with nothing but zeroes after the decimal point.

Lesson

An improper fraction can always be expressed as a mixed fraction. If we are given 107 rac{10}{7}, we need to perform the division and then write the answer as a mixed fraction.

So 10÷7=110 div 7 = 1 (with 3 as the remainder) – this can be written as 1371 rac{3}{7}

Similarly, if we are given a mixed fraction and asked to express it as a improper fraction, we multiply the whole number by the denominator and add the numerator. The result becomes the new numerator and the denominator remains the same.

So in the case of 1131 rac{1}{3}, the whole number is first multiplied by the denominator (1*3) then added to the numerator (3+1). The final result is 43 rac{4}{3}.

Examples

Write Improper Fraction as Mixed Number (Example #1)

103\dfrac{10}{3}
Because 103\dfrac{10}{3} is an improper fraction (the numerator is greater than the denominator), we need to convert it to a mixed number
103=313\dfrac{10}{3} = 3\dfrac{1}{3}

Write Mixed Number as Improper Fraction (Example #1)

1341\dfrac{3}{4}
134=1 * 4 + 34=741\dfrac{3}{4} = \dfrac{\text{1 * 4 + 3}}{\text{4}} = \dfrac{7}{4}

Write Improper Fraction as Mixed Number (Example #3)

115\dfrac{11}{5}
Because 115\dfrac{11}{5} is an improper fraction (the numerator is greater than the denominator), we need to convert it to a mixed number
115=215\dfrac{11}{5} = 2\dfrac{1}{5}

Write Mixed Number as Improper Fraction (Example #2)

4124\dfrac{1}{2}
412=4 * 2 + 12=924\dfrac{1}{2} = \dfrac{\text{4 * 2 + 1}}{\text{2}} = \dfrac{9}{2}

Mixed Numbers and Improper Fractions Worksheets (PDF)

Mixed Numbers and Improper Fractions Worksheet 1

Mixed Numbers and Improper Fractions Worksheet 2

Mixed Numbers and Improper Fractions Worksheet 3

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