# 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:

### 11 3/7 - 8 6/8 = 75/28 = 2 19/28 ≅ 2.6785714

Spelled result in words is seventy-five twenty-eighths (or two and nineteen twenty-eighths).### How do you solve fractions step by step?

- Conversion a mixed number 11 3/7 to a improper fraction: 11 3/7 = 11 3/7 = 11 · 7 + 3/7 = 77 + 3/7 = 80/7

To find new numerator:

a) Multiply the whole number 11 by the denominator 7. Whole number 11 equally 11 * 7/7 = 77/7

b) Add the answer from previous step 77 to the numerator 3. New numerator is 77 + 3 = 80

c) Write a previous answer (new numerator 80) over the denominator 7.

Eleven and three sevenths is eighty sevenths - Conversion a mixed number 8 6/8 to a improper fraction: 8 6/8 = 8 6/8 = 8 · 8 + 6/8 = 64 + 6/8 = 70/8

To find 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 6. New numerator is 64 + 6 = 70

c) Write a previous answer (new numerator 70) over the denominator 8.

Eight and six eighths is seventy eighths - Subtract: 80/7 - 70/8 = 80 · 8/7 · 8 - 70 · 7/8 · 7 = 640/56 - 490/56 = 640 - 490/56 = 150/56 = 2 · 75/2 · 28 = 75/28

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(7, 8) = 56. In practice, it is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 7 × 8 = 56. In the next intermediate step, , cancel by a common factor of 2 gives 75/28.

In words - eighty sevenths minus seventy eighths = seventy-five twenty-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:

- Michael

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

Of 100 types of animals, 9/100 were discovered in ancient times, and 2/100 were discovered in the Middle Ages. Another 3/10 were discovered in the 1800s. What fraction of the 100 types of animals was discovered after the 1800s? Explain. - 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? - Sarah

Sarah has a photography blog. 3/7 of her photos are of nature, 1/4 of the rest are of her friends. What fraction of all of Sarah's photos is of her friends? - Circular garden

Alice creates a circular vegetable garden. Tomatoes are planted in 1/3 of the circular garden, carrots are planted in 2/5 of the circular garden, and green peppers are planted in 1/10 of the circular garden. What fraction represents the remaining unplante - 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? - On the floor 2

The floor area of a living room is 9 7/9 m^{2}. A carpet with an area of 5 5/8 m^{2}is placed on the floor. Find the area of the room that is not covered with carpet. - 5 2/5

5 2/5 hours a week mathematics, 3 3/4 hours a week Natural sciences, 4 3/8 hours a week Technology . how many hours does he spend on social sciences if he spend 17 1/2 hours a week for the four subject? - Shirts

In a classroom, 1/6 of the students are wearing blue shirts and 2/3 are wearing white shirts. There are 36 students in the class. How many students are wearing a shirt other than blue or white? - Larry

Larry received 1/3 pound of candy from his grandmother and 2/5 pound of candy from his best friend. Larry's sister ate 1/2 pound of Larry's candy. How many pounds of candy does Larry have left? - Grandmother

Stella's family traveled 5/8 of the distance to her grandmother’s house on Saturday. They traveled 2/3 of the remaining distance on Sunday. What fraction of the total distance to her grandmother’s house was traveled on Sunday? - Curtain

Mrs. Lazo bought 9 1/8 m curtain cloth. She used 3 5/6 m to make a curtain for their bedroom. How many meters of cloth were not used?

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