# 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:

### 2 1/7 + 1 2/5 = 124/35 = 3 19/35 ≅ 3.5428571

Spelled result in words is one hundred twenty-four thirty-fifths (or three and nineteen thirty-fifths).### How do you solve fractions step by step?

- Conversion a mixed number 2 1/7 to a improper fraction: 2 1/7 = 2 1/7 = 2 · 7 + 1/7 = 14 + 1/7 = 15/7

To find a new numerator:

a) Multiply the whole number 2 by the denominator 7. Whole number 2 equally 2 * 7/7 = 14/7

b) Add the answer from previous step 14 to the numerator 1. New numerator is 14 + 1 = 15

c) Write a previous answer (new numerator 15) over the denominator 7.

Two and one seventh is fifteen sevenths - Conversion a mixed number 1 2/5 to a improper fraction: 1 2/5 = 1 2/5 = 1 · 5 + 2/5 = 5 + 2/5 = 7/5

To find a new numerator:

a) Multiply the whole number 1 by the denominator 5. Whole number 1 equally 1 * 5/5 = 5/5

b) Add the answer from previous step 5 to the numerator 2. New numerator is 5 + 2 = 7

c) Write a previous answer (new numerator 7) over the denominator 5.

One and two fifths is seven fifths - Add: 15/7 + 7/5 = 15 · 5/7 · 5 + 7 · 7/5 · 7 = 75/35 + 49/35 = 75 + 49/35 = 124/35

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, 5) = 35. In practice, it is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 7 × 5 = 35. In the following intermediate step, the fraction result cannot be further simplified by canceling.

In other words - fifteen sevenths plus seven fifths = one hundred twenty-four thirty-fifths.

#### 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:

• 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:

- An orchard

During a visit to an orchard, Greg picked 3/5 of a bag of delicious golden apples, 4/5 of a bag of Macintosh apples, 2/5 of a bag of Cortland apples, 1/5 of a bag of Bartlett pears, and 4/5 of a bag of Bosch pears. How many bags of fruit to Greg pick in t - 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 - Weigh in total

I put 3/5 kg of grapes into a box which is 1/4kg in weight. How many kilograms do the grapes and the box weigh in total? - Honey 3

Honey jogged 1 3/4 km on Monday,1 1/2 km on Wednesday and 1 2/3 km on Friday . how far did he jog? - 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. - Evaluate 17

Evaluate 2x+6y when x=- 4/5 and y=1/3. Write your answer as a fraction or mixed number in simplest form. - Submerging

Monika dove 9 meters below the ocean's surface. She then dove 13 meters deeper. Then she rose 19 and one-fourth meters. What was her position concerning the water's surface (the water surface = 0, minus values = above water level, plus = above water level - Flowers 4

A flower seller has 4.05 kg of orange flowers and 6.50 kg of red flowers. He made flower baskets with 2.11 kg of both red and orange flowers in each. How many baskets did he make? - Bus vs train

Milada took the bus and the journey took 55 minutes. Jarmila was 1h 20 min by train. They arrived in Prague at the same time 10h45 min. At what time did each have to go out? - Fractions and mixed numerals

(a) Convert the following mixed numbers to improper fractions. i. 3 5/8 ii. 7 7/6 (b) Convert the following improper fraction to a mixed number. i. 13/4 ii. 78/5 (c) Simplify these fractions to their lowest terms. i. 36/42 ii. 27/45 2. evaluate the follow - Three rectangles

Some wire is used to make 3 rectangles: A, B, and C. Rectangle B's dimensions are 3/5 cm larger than Rectangle A's dimensions, and Rectangle C's dimensions are again 3/5 cm larger than Rectangle B's dimensions. Rectangle A is 2 cm by 3 1/5 cm. What is the - Stock

Enterprise sold 7/12 of their products to foreign markets and 2/5 of the remainder sold at home. How many % of the products is still in stock? - Adding denominators

Max is working out 2/3+7/9. He says the answer is 9/12. What mistake have Max made?

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