# 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:

### 34/9 - 16/9 = 16/9 = 1 7/9 ≅ 1.7777778

Spelled result in words is sixteen ninths (or one and seven ninths).

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

1. Conversion a mixed number 3 4/9 to a improper fraction: 3 4/9 = 3 4/9 = 3 · 9 + 4/9 = 27 + 4/9 = 31/9

To find a new numerator:
a) Multiply the whole number 3 by the denominator 9. Whole number 3 equally 3 * 9/9 = 27/9
b) Add the answer from previous step 27 to the numerator 4. New numerator is 27 + 4 = 31
c) Write a previous answer (new numerator 31) over the denominator 9.

Three and four ninths is thirty-one ninths
2. Conversion a mixed number 1 6/9 to a improper fraction: 1 6/9 = 1 6/9 = 1 · 9 + 6/9 = 9 + 6/9 = 15/9

To find a 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 6. New numerator is 9 + 6 = 15
c) Write a previous answer (new numerator 15) over the denominator 9.

One and six ninths is fifteen ninths
3. Subtract: 31/9 - 15/9 = 31 - 15/9 = 16/9
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(9, 9) = 9. In practice, it is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 9 × 9 = 81. In the following intermediate step, the fraction result cannot be further simplified by canceling.
In other words - thirty-one ninths minus fifteen ninths = sixteen ninths.

#### 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:

• From a 2 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?
• Mixed numbers Five and two-thirds minus 2 and one-half equals what number? A three and one-sixth B three and two-thirds C three and one-half D three and five-sixths
• Square metal sheet We cut out four squares of 300 mm side from a square sheet metal plate with a side of 0,7 m. Express the fraction and the percentage of waste from the square metal sheet.
• Equation with mixed 2 A number, X, is subtracted from 8 1/4. The result is 12 3/5. What is the value of X?
• Mountain Mountain has an elevation of 7450 meters and in the morning is the middle portion thereof in the clouds. How many meters of height is in the sky if below the clouds are 2,000 meters, and above clouds are two-fifths of the mountain's elevation?
• 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?
• Benhur Benhur boiled 1 1/4 liters of water in a kettle. After 10 1/2 minutes he measured the water again. It had 3/4 liters left in the kettle. What is the amount of water that evaporates every minutes?
• Mrs. Susan Mrs. Susan bought 1/8 m of curtain cloth. She used 3/5 m to make a curtain for the living room window. How many meters of cloth were not used?
• Half of halves Half of the square we cut off, then half of the rest, etc. Five cuts we made in this way. What part of the content of the original square is the content of the cut part?
• Product and sum What is the product of two fourths  and the sum of three halves and four?
• Mother 7 Mother bought 18 fruits. 1/3 were pineapple and the rest  were mangoes . how many were mangoes
• Jose studied Jose studied for 4 and 1/2 hours on Saturday and another 6 and 1/4 hours on Sunday. How many subjects did he study if he has alloted 1 and 1/2 hours per subject on Saturday and 1 and 1/4 hours per subject on Sunday?
• Pounds Three pounds subtract 1/3 of a pound.