# Calculator expression with brackets

This calculator performs basic and advanced fraction operations, expressions with fractions combined with integers, decimals, and mixed numbers. It also shows detailed step-by-step information about the fraction calculation procedure. The calculator helps in finding value from multiple fractions operations. Solve problems with two, three, or more fractions and numbers in one expression.

### 1/3 * (1/2 - 3 3/8) = -23/24 ≅ -0.9583333

Spelled result in words is minus twenty-three twenty-fourths.### How do we solve fractions step by step?

- Conversion a mixed number 3 3/8 to a improper fraction: 3 3/8 = 3 3/8 = 3 · 8 + 3/8 = 24 + 3/8 = 27/8

To find a new numerator:

a) Multiply the whole number 3 by the denominator 8. Whole number 3 equally 3 * 8/8 = 24/8

b) Add the answer from previous step 24 to the numerator 3. New numerator is 24 + 3 = 27

c) Write a previous answer (new numerator 27) over the denominator 8.

Three and three eighths is twenty-seven eighths - Subtract: 1/2 - 27/8 = 1 · 4/2 · 4 - 27/8 = 4/8 - 27/8 = 4 - 27/8 = -23/8

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(2, 8) = 8. In practice, it is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 2 × 8 = 16. In the following intermediate step, it cannot further simplify the fraction result by canceling.

In other words - one half minus twenty-seven eighths is minus twenty-three eighths. - Multiple: 1/3 * the result of step No. 2 = 1/3 * (-23/8) = 1 · (-23)/3 · 8 = -23/24

Multiply both numerators and denominators. Result fraction keep to lowest possible denominator GCD(-23, 24) = 1. In the following intermediate step, it cannot further simplify the fraction result by canceling.

In other words - one third multiplied by minus twenty-three eighths is minus twenty-three twenty-fourths.

#### Rules for expressions with fractions:

**Fractions**- use a forward slash to divide the numerator by the denominator, i.e., for five-hundredths, enter

**5/100**. If you use mixed numbers, leave a space between the whole and fraction parts.

**Mixed numerals**(mixed numbers or fractions) keep one space between the integer and

fraction and use a forward slash to input fractions i.e.,

**1 2/3**. An example of a negative mixed fraction:

**-5 1/2**.

Because slash is both signs for fraction line and division, use a colon (:) as the operator of division fractions i.e.,

**1/2 : 1/3**.

Decimals (decimal numbers) enter with a decimal point

**.**and they are automatically converted to fractions - i.e.

**1.45**.

### Math Symbols

Symbol | Symbol name | Symbol Meaning | Example |
---|---|---|---|

+ | plus sign | addition | 1/2 + 1/3 |

- | minus sign | subtraction | 1 1/2 - 2/3 |

* | asterisk | multiplication | 2/3 * 3/4 |

× | times sign | multiplication | 2/3 × 5/6 |

: | division sign | division | 1/2 : 3 |

/ | division slash | division | 1/3 / 5 |

: | colon | complex fraction | 1/2 : 1/3 |

^ | caret | exponentiation / power | 1/4^3 |

() | parentheses | calculate expression inside first | -3/5 - (-1/4) |

The calculator follows well-known rules for

**the 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.

**MDAS**- Multiplication and Division have the same precedence over Addition and Subtraction. The MDAS rule is the order of operations part of the PEMDAS rule.

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:

- Someone

Someone ate 1/10 of a cake, leaving only 9/10. If you eat 2/3 of the cake that is left, how much of a whole cake will you have eaten? - Trent

Trent operates a hot dog stand. On Wednesday he used 2 bags of hot dog buns. On Thursday he used 1/5 as many hot dog buns as on Wednesday. How many bags of hot dog buns did Trent use on Thursday? - Ms. Sheppard

Ms. Sheppard cuts ½ of a piece of construction paper. She uses ⅙ of the piece to make a flower. What fraction of the sheet of paper does she use to make the flower? - There 12

There are 42 students in the class and 2/3 of them are girls. How may girls are there in the class? - Scouts 4

4/7 of the students in a school are boys. If 3/8 of the boys are scouts, how many scouts are there in a school of 1878 students? - Write 3

Write a real-world problem involving the multiplication of a fraction and a whole number with a product that is between 8 and 10, then solve the problem. - Learnes

There are 800 learnes in a school 7/8 of the learners walk to school . how many learners walk in school? - Roy harvested

Roy harvested 3/4 crate of guavas. He sold 1/2 of them in the neighborhood. What part of crate of guavas sold. - One-third 2

One-third of the people in a barangay petitioned the council to allow them to plant in vacant lots, and another 1/5 of the people petitioned to have a regular garbage collection. What FRACTION of the barangay population made the petition? - Fractions 3

Calculate 1/9 of 27: - Farmers 2

On Wednesday the farmers at the Grant Farm picked 2 barrels of tomatoes. Thursday, the farmers picked 1/2 as many tomatoes as on Wednesday. How many barrels of tomatoes did the farmers pick on Thursday?

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