Mixed Fraction Calculator
This mixed fraction calculator simplifies converting between mixed numbers and improper fractions, ensuring quick and accurate results for various calculations.
Understanding Mixed Fractions
A mixed fraction, also known as a mixed number, consists of two parts: a whole number and a proper fraction. It represents a value that is greater than one but not quite a whole number, such as 2 1/3, which means “two whole units and one-third of another unit.”
What is a Mixed Fraction?
A mixed fraction, or mixed number, is a combination of a whole number and a proper fraction. For example, 2 1/3 is a mixed fraction, which means two whole units and one-third of another unit. Mixed fractions are used to represent quantities that are greater than one but not complete whole numbers.
They appear frequently in everyday contexts, such as measuring ingredients in cooking, distances, or time intervals.
How to Change a Mixed Number into an Improper Fraction
To convert a mixed number into an improper fraction, follow these steps:
Multiply the whole number by the denominator of the fraction.
Add the result to the numerator.
Write the new value as the numerator, keeping the original denominator.
Practical Examples of Mixed Fraction Calculations
Mixed fractions are practical in many real world contexts, such as measuring time, length, or ingredients in recipes. Knowing how to convert, add, and subtract them allows for greater precision in these everyday tasks.
Examples with Calculations
Convert 11/3 to a mixed fraction:
11 ÷ 3 = 3 remainder 2
Result: 3 2/3
Convert 25/7 to a mixed fraction:
25 ÷ 7 = 3 remainder 44
Result: 3 4/7
Add 1 1/2 + 2 2/5:
Whole numbers: 1 + 2 = 3
Fractions: 1 1/2 + 2/5 = 5/10 + 4/10 = 9/10
Result: 3 9/10
Subtract 4 3/4 − 2 1/2:
Whole numbers: 4 − 2 = 2
Fractions: 3/4 − 1/2 = 3/4 − 2/4 = 1/4
Result: 2 1/4
Convert 14/5 to a mixed fraction:
14 ÷ 5 = 2 remainder 4
Result: 2 4/5
Multiply 2 1/3 × 3 1/2:
Convert to improper fractions: 7/3 × 7/2 = 49/6
Convert back to mixed fraction: 49 ÷ 6 = 8 1/6
Result: 8 1/6
Add 3 3/4 + 1 1/2:
Whole numbers: 3 + 1 = 4
Fractions: 3/4 + 1/2= 3/4 + 2/4 = 5/4 = 1 1/4
Result: 4 + 1 1/4 = 5 1/4
Subtract 6 5/6 − 3 2/3 665:
Whole numbers: 6 − 3 =3
Fractions: 5/6 − 2/3 = 5/6 − 4/6 = 1/6
Result: 3 1/6
Convert 20/9 to a mixed fraction: 20 ÷ 9 = 2 remainder 22
Result: 2 2/9
Convert 17/6 to a mixed fraction:
17 ÷ 6 = 2 remainder 5
Result: 2 5/6
Understanding Mixed Fractions
A mixed fraction, also known as a mixed number, consists of two parts: a whole number and a proper fraction. It represents a value that is greater than one but not quite a whole number, such as 2 1/3, which means “two whole units and one-third of another unit.” Mixed fractions are common in everyday life and are often used in measurements, recipes, and when dealing with practical problems involving quantities that are not whole numbers.
Adding and Subtracting Mixed Fractions
When adding or subtracting mixed fractions, you first handle the whole numbers separately and then add or subtract the fractions. If necessary, the fractions can be simplified or converted to have a common denominator. For example, to add 1 1/4 + 2 2/3, first add 1 and 2 to get 3, then find a common denominator for the fractions, resulting in 1 3/12 + 2 8/12, which simplifies to 3 11/12.
Converting Improper Fractions to Mixed Fractions
An improper fraction, where the numerator is larger than the denominator (such as 9/4), can be converted into a mixed fraction. To do this, divide the numerator by the denominator to get the whole number, and the remainder becomes the new numerator of the fraction.
For example, 9/4 can be converted by dividing 9 by 4, which gives a quotient of 2 and a remainder of 1. Thus, 9/4 is equivalent to 2 1/4.
How to Change a Mixed Number into an Improper Fraction
To convert a mixed number into an improper fraction, follow these steps:
Multiply the whole number by the denominator of the fraction.
Add the result to the numerator.
Write the new value as the numerator, keeping the original denominator.
For example, to convert 3 2/5 to an improper fraction:
Multiply 3 × 5 = 15
Add 15 + 2 = 17
The improper fraction is 17/5
How to Turn an Improper Fraction into a Mixed Number
To convert an improper fraction into a mixed number, you divide the numerator by the denominator. The quotient becomes the whole number, and the remainder becomes the new numerator of the fraction.
Example, to convert 23/4 into a mixed number:
Divide 23 ÷ 4 = 5 remainder 3
The mixed number is 5 3/4
How to Convert Decimal to Mixed Fraction
To convert a decimal into a mixed fraction, separate the whole number from the decimal part. Convert the decimal part into a fraction by determining the place value of the digits. For example:
Convert 2.752.75 into a mixed fraction:
22 is the whole number.
0.75 =75/100 = 3/4
The mixed fraction is 2 3/4
Example Calculations
Convert 1 3/8 into an improper fraction:
1 × 8 + 3 = 11
Improper fraction: 11/8
Convert 22/7 into a mixed number:
22÷7=3 remainder 1
Mixed number: 3 1/7
Convert 150% to a fraction:
150/100 = 1 1/2
Convert 3.23.2 into a mixed fraction:
3.2 = 3 2/10 = 3 1/5
Convert 50% to a fraction:
50/100 = 1/2
Converting Percentages to Fractions or Mixed Numbers
Percentages can easily be converted into fractions, mixed numbers, or whole numbers by dividing by 100.
150% as a Fraction or Mixed Number:
150/100 = 1 1/2 (or simply 1.5)
50% as a Fraction or Whole Number:
50/100 = 1/2
100% as a Fraction or Whole Number:
100/100 = 1
40% as a Fraction:
40/100 = 2/5
75% as a Fraction or Mixed Number:
75/100 = 3/4
60% as a Fraction:
60/100 = 3/5