# 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:

### 27/8 - 17/9 = 79/72 = 1 7/72 ≅ 1.0972222

Spelled result in words is seventy-nine seventy-seconds (or one and seven seventy-seconds).

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

1. Conversion a mixed number 2 7/8 to a improper fraction: 2 7/8 = 2 7/8 = 2 · 8 + 7/8 = 16 + 7/8 = 23/8

To find new numerator:
a) Multiply the whole number 2 by the denominator 8. Whole number 2 equally 2 * 8/8 = 16/8
b) Add the answer from previous step 16 to the numerator 7. New numerator is 16 + 7 = 23
c) Write a previous answer (new numerator 23) over the denominator 8.

Two and seven eighths is twenty-three eighths
2. Conversion a mixed number 1 7/9 to a improper fraction: 1 7/9 = 1 7/9 = 1 · 9 + 7/9 = 9 + 7/9 = 16/9

To find new numerator:
a) Multiply the whole number 1 by the denominator 9. Whole number 1 equally 1 * 9/9 = 9/9
b) Add the answer from previous step 9 to the numerator 7. New numerator is 9 + 7 = 16
c) Write a previous answer (new numerator 16) over the denominator 9.

One and seven ninths is sixteen ninths
3. Subtract: 23/8 - 16/9 = 23 · 9/8 · 9 - 16 · 8/9 · 8 = 207/72 - 128/72 = 207 - 128/72 = 79/72
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, 9) = 72. In practice, it is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 8 × 9 = 72. In the next intermediate step, the fraction result cannot be further simplified by canceling.
In words - twenty-three eighths minus sixteen ninths = seventy-nine seventy-seconds.

#### Rules for expressions with fractions:

Fractions - use the 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 non-zero 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:

adding fractions: 2/4 + 3/4
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:

• Akpan Akpan spent 3/8 of his time in school during the week. What fraction of his time does he spend at home during the week?
• Mixed numbers Rewrite mixed numbers, so the fractions have the same denominator: 5 1/5 - 2 2/3
• Magic bag Each time the prince crossed the bridge, the number of tolars in the magic bag doubled. But then the devil always conjured 300 tolars for him. When this happened for the third time, the prince had twice as much as he had in the beginning. How many tolars
• Savings Eva borrowed 1/3 of her savings to her brother, 1/2 of savings spent in the store and 7 euros left. How much did she save?
• Patel Patel squeezed oranges so that his family could have fresh-squeezed juice for breakfast. He squeezed 4/17 cups from the first orange, 3/10 cups from the second orange, StartFraction 9 over 20 E
• Empty and full An empty can has a mass of 1/6 lb. When it is filled with sand, it has a mass of 7/12 lb. Find the mass of the sand in the can?
• Find the 24 Find the difference between 2/7 and 1/21
• The pet Ananya has a bunny. She bought 4 7/8 pounds of carrots. She fed her bunny 1 1/4 pounds of carrots the first week. She fed her bunny 5/6 pounds of carrots the second week. All together, how many pounds of carrots did she feed her bunny? 1. Draw a tape diag
• From a From a 1 meter ribbon, Ericka cut 2/4 meter for her hat and another 1/4 meter for her bag. How long was the remaining piece?
• School There are 150 pupils in grade 5 . 2/3 of them are female. By what fractions are the males?
• Pupils Two classes want to collect money. Boys are four-seventh pupils. In time did not pay a quarter of the boys and a sixth of girls, which mean 12 sinners. How many pupils attend these two classes?
• Package The package was 23 meters of textile. The first day sold 12.3 meters. How many meters of textile remained in the package?
• Two cakes Two cakes were each cut into 8 slices. Maria ate   1/8 of the chocolate cake and 1 slice of carrot cake. Julia ate  1/2 of the carrot cake. Mark ate 1 slice of each. Thomas ate 3 slices of chocolate cake. How many slices were left?