# 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:

### 3 1/4 - 2 7/8 = 3/8 = 0.375

Spelled result in words is three eighths.### How do you solve fractions step by step?

- Conversion a mixed number 3 1/4 to a improper fraction: 3 1/4 = 3 1/4 = 3 · 4 + 1/4 = 12 + 1/4 = 13/4

To find new numerator:

a) Multiply the whole number 3 by the denominator 4. Whole number 3 equally 3 * 4/4 = 12/4

b) Add the answer from previous step 12 to the numerator 1. New numerator is 12 + 1 = 13

c) Write a previous answer (new numerator 13) over the denominator 4.

Three and one quarter is thirteen quarters - 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 - Subtract: 13/4 - 23/8 = 13 · 2/4 · 2 - 23/8 = 26/8 - 23/8 = 26 - 23/8 = 3/8

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(4, 8) = 8. In practice, it is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 4 × 8 = 32. In the next intermediate step, the fraction result cannot be further simplified by canceling.

In words - thirteen quarters minus twenty-three eighths = three eighths.

#### 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:

- Cupcakes

In a bowl was some cupcakes. Janka ate one third and Danka ate one quarter of cupcakes. a) How many of cookies ate together? b) How many cookies remain in a bowl? Write the results as a decimal number and in notepad also as a fraction. - Michael

Michael had a bar of chocolate. He ate 1/2 of it and gave away 1/3. What fraction had he left? - 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? - Mr. Peter

Mr. Peter mowed 2/7 of his lawn. His son mowed 1/4 of it. Who mowed the most? How much of the lawn still need to be mowed? - 7th grade pupils

Pupils doing research which a winter sport do their classmates most popular. They found that 2/5 of classmates would most like to play hockey, skate prefer 2/9 pupils, 3/10 students prefer skiing and 1/15 classmates don't like any winter sport. What propo - Bitoo and Reena

Bitoo ate 3/5 part of an apple and the remaining part was eaten by his sister Reena. How much part of an apple did Renna eat? Who had the larger share? By how much? - 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? - Math test

Brayden was solving some math problems for the math team. He answered 2 math problems. Matthew answered 3, John answered 1 reasoning. Matthew 1/2 times as many. Brayden said that 2/6. Is he correct? Why or why not? Be sure to explain your answer. - Ali bought

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? - Emily

Emily had 20 minutes to do a three-problem quiz. She spent 11 3/4 minutes on question A and 5 1/2 minutes on question B. How much time did she have left for question C? - Interior designer

To make draperies an interior designer needs 11 1/4 yards of material for the den and 8 1/2 yards for the living room. If material comes only in 20 yard bolts, how much will be left over after completing both sets of draperies? - Three friends

John, Peter, and Pablo each carried a 24 liters bucket full of water down the hill. After they reached the bottom, John's bucket was only 3/4 full, Peter's bucket was 2/3 full, and Pablo's was 1/6 full. How much liters of water did they spill altogether o - Half of 2

Half of Ethan’s string is equal to 2/3 of Kayla’s string. The total length of their strings is 10 feet. How much longer is Ethan’s string than Kayla’s?

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