# Fraction calculator

The calculator performs basic and advanced operations with fractions, expressions with fractions combined with integers, decimals, and mixed numbers. It also shows detailed step-by-step information about the fraction calculation procedure. Solve problems with two, three, or more fractions and numbers in one expression.

## Result:

### -83/8 - 101/6 = -445/24 = -18 13/24 ≅ -18.5416667

Spelled result in words is minus four hundred forty-five twenty-fourths (or minus eighteen and thirteen twenty-fourths).

### How do you solve fractions step by step?

1. Conversion a mixed number 8 3/8 to a improper fraction: 8 3/8 = 8 3/8 = 8 · 8 + 3/8 = 64 + 3/8 = 67/8

To find a new numerator:
a) Multiply the whole number 8 by the denominator 8. Whole number 8 equally 8 * 8/8 = 64/8
b) Add the answer from previous step 64 to the numerator 3. New numerator is 64 + 3 = 67
c) Write a previous answer (new numerator 67) over the denominator 8.

Eight and three eighths is sixty-seven eighths
2. Unary minus: -67/8 = -67/8
3. Conversion a mixed number 10 1/6 to a improper fraction: 10 1/6 = 10 1/6 = 10 · 6 + 1/6 = 60 + 1/6 = 61/6

To find a new numerator:
a) Multiply the whole number 10 by the denominator 6. Whole number 10 equally 10 * 6/6 = 60/6
b) Add the answer from previous step 60 to the numerator 1. New numerator is 60 + 1 = 61
c) Write a previous answer (new numerator 61) over the denominator 6.

Ten and one sixth is sixty-one sixths
4. Subtract: the result of step No. 2 - 61/6 = -67/8 - 61/6 = -67 · 3/8 · 3 - 61 · 4/6 · 4 = -201/24 - 244/24 = -201 - 244/24 = -445/24
For adding, subtracting, and comparing fractions, it is suitable to adjust both fractions to a common (equal, identical) denominator. The common denominator you can calculate as the least common multiple of both denominators - LCM(8, 6) = 24. In practice, it is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 8 × 6 = 48. In the following intermediate step, it cannot further simplify the fraction result by canceling.
In other words - minus sixty-seven eighths minus sixty-one sixths = minus four hundred forty-five twenty-fourths.

#### Rules for expressions with fractions:

Fractions - simply use a forward slash between the numerator and denominator, i.e., for five-hundredths, enter 5/100. If you are using mixed numbers, be sure to leave a single space between the whole and fraction part.
The slash separates the numerator (number above a fraction line) and denominator (number below).

Mixed numerals (mixed fractions or mixed numbers) write as integer separated by one space and fraction i.e., 1 2/3 (having the same sign). An example of a negative mixed fraction: -5 1/2.
Because slash is both signs for fraction line and division, we recommended use colon (:) as the operator of division fractions i.e., 1/2 : 3.

Decimals (decimal numbers) enter with a decimal point . and they are automatically converted to fractions - i.e. 1.45.

The colon : and slash / is the symbol of division. Can be used to divide mixed numbers 1 2/3 : 4 3/8 or can be used for write complex fractions i.e. 1/2 : 1/3.
An asterisk * or × is the symbol for multiplication.
Plus + is addition, minus sign - is subtraction and ()[] is mathematical parentheses.
The exponentiation/power symbol is ^ - for example: (7/8-4/5)^2 = (7/8-4/5)2

#### Examples:

subtracting fractions: 2/3 - 1/2
multiplying fractions: 7/8 * 3/9
dividing Fractions: 1/2 : 3/4
exponentiation of fraction: 3/5^3
fractional exponents: 16 ^ 1/2
adding fractions and mixed numbers: 8/5 + 6 2/7
dividing integer and fraction: 5 ÷ 1/2
complex fractions: 5/8 : 2 2/3
decimal to fraction: 0.625
Fraction to Decimal: 1/4
Fraction to Percent: 1/8 %
comparing fractions: 1/4 2/3
multiplying a fraction by a whole number: 6 * 3/4
square root of a fraction: sqrt(1/16)
reducing or simplifying the fraction (simplification) - dividing the numerator and denominator of a fraction by the same non-zero number - equivalent fraction: 4/22
expression with brackets: 1/3 * (1/2 - 3 3/8)
compound fraction: 3/4 of 5/7
fractions multiple: 2/3 of 3/5
divide to find the quotient: 3/5 ÷ 2/3

The calculator follows well-known rules for order of operations. The most common mnemonics for remembering this order of operations are:
PEMDAS - Parentheses, Exponents, Multiplication, Division, Addition, Subtraction.
BEDMAS - Brackets, Exponents, Division, Multiplication, Addition, Subtraction
BODMAS - Brackets, Of or Order, Division, Multiplication, Addition, Subtraction.
GEMDAS - Grouping Symbols - brackets (){}, Exponents, Multiplication, Division, Addition, Subtraction.
Be careful, always do multiplication and division before addition and subtraction. Some operators (+ and -) and (* and /) has the same priority and then must evaluate from left to right.

## Fractions in word problems:

• Math test Obelix filled a mathematical test in which he answered 25 questions. For every correct answer, he received 5 points, for each bad answer he had 3 points deducted. Obelix gained 36% of all points in the test. How many questions did he solve correctly?
• Package The package was 23 meters of textile. The first day sold 12.3 meters. How many meters of textile remained in the package?
• Difference between fractions What is the difference when you take away 1/6 from 2/8? Sadie practiced her spelling words for 3/4 of an hour, and Max practiced his spelling words for 5/12 of an hour. In the simplest form, how much longer did Sadie practice than Max?
• Cups of flour Jade was baking cupcakes for her class. She has 4 5/4 cups of flour.  For one batch, she used 1 2/3 cups of flour.  On another batch, she used 7/9 of a cup of flour.  How much flour does Jade have left after making the two batches of cupcakes? About 6/9 of the sixth- grade pupils will be going to the parents' seminar. If 1/6 of the participants are girls, what part of the portion of sixth graders are boys?
• Find the 24 Find the difference between 2/7 and 1/21 A basket contains three types of fruits weighing 87/4 kg in all. If 23/4 kilograms of these are oranges, 48/7 kg are mangoes, and the rest are apples. What is the weight of the apples in the basket? In a cookie jar, 1/4 of the cookies are chocolate chip and 1/2 of the rest are peanut butter. What fraction of all the cookies are peanut butter? Three pounds subtract 1/3 of a pound. From a rope that is 11 m long, two pieces of lengths 13/5 m and 33/10 m are cut off. What is the length of the remaining rope? Ali bought 5/6 litre of milk. He drank 1/2 litre and his brother drank 1/6 litre. How much litre of milk left? Of the shapes,1/6 are triangles, and 5/12 are pentagons. What fraction of the shapes are either triangles or pentagons?