Fraction calculator
This fraction 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.
The result:
-8 3/8 - 10 1/6 = -445/24 = -18 13/24 ≅ -18.5416667
Spelled result in words is minus four hundred forty-five twenty-fourths (or minus eighteen and thirteen twenty-fourths).How do we solve fractions step by step?
- Conversion a mixed number 8 3/8 to a improper fraction: 8 3/8 = 8 3/8 = 8 · 8 + 3/8 = 64 + 3/8 = 67/8
To find a 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 the previous step 64 to the numerator 3. New numerator is 64 + 3 = 67
c) Write a previous answer (new numerator 67) over the denominator 8.
Eight and three eighths is sixty-seven eighths. - Unary minus: -67/8 = -67/8
- Conversion a mixed number 10 1/6 to a improper fraction: 10 1/6 = 10 1/6 = 10 · 6 + 1/6 = 60 + 1/6 = 61/6
To find a new numerator:
a) Multiply the whole number 10 by the denominator 6. Whole number 10 equally 10 * 6/6 = 60/6
b) Add the answer from the previous step 60 to the numerator 1. New numerator is 60 + 1 = 61
c) Write a previous answer (new numerator 61) over the denominator 6.
Ten and one sixth is sixty-one sixths. - Subtract: the result of step No. 2 - 61/6 = -67/8 - 61/6 = -67 · 3/8 · 3 - 61 · 4/6 · 4 = -201/24 - 244/24 = -201 - 244/24 = -445/24
It is suitable to adjust both fractions to a common (equal, identical) denominator for adding, subtracting, and comparing fractions. The common denominator you can calculate as the least common multiple of both denominators - LCM(8, 6) = 24. It is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 8 × 6 = 48. In the following intermediate step, it cannot further simplify the fraction result by canceling.
In other words - minus sixty-seven eighths minus sixty-one sixths is minus four hundred forty-five 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 sign 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 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) |
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
• reciprocal of a fraction: 1 : 3/4
• square of a fraction: 2/3^2
• cube of a fraction: 2/3^3
• exponentiation of a fraction: 1/2^4
• 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) : 4/22 - dividing the numerator and denominator of a fraction by the same non-zero number - equivalent fraction
• 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 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 /) have the same priority and must be evaluated from left to right.
Fractions in word problems:
- Closer to one
Here are two sums: A=1/2 + 1/3 and B=1/5 + 1/3. Which of the two sums is closer in value to 1? You must show your work and state clearly whether the answer is A or B.
- Anesa
Anesa ate 3/4 of her pizza, and Eman ate 1/4 of her pizza. Who ate the greater part of the pizza? - Compare two fractions
Find which is the larger of the two fractions: 11/32, 7/24, by expressing the numbers as a) fractions with the same denominator, b) decimals. - From least to greatest
Which set of rational numbers is arranged from least to greatest? A) -3.5, negative 1 over 4, 2, 1 over 3 B) -3.5, negative 1 over 4, 1 over 3, 2 C) 2, 1 over 3, negative 1 over 4, -3.5 D) negative 1 over 4, 1 over 3, 2, -3.5
- Rhea answered
Rhea answered 5/11 of the questions correctly, and Precious answered 7/11 of them correctly. Who got the higher score if each problem is worth the same amount? - Fraction multiplication Solve six times three-sixths equals blank. Leave your answer as an improper fraction. thirty-six thirds eighteen-sixths eighteen-sixteenths three thirty-sixths
- A student 4
A student knows that ¾ x 4 is the same as 4 x ¾ The student assumes that 4 ÷ ¾ is the same as ¾ ÷ 4 Is the student correct? - What number 2
What number is between 3 1/4 and 3 1/8? Write at least three numbers. - Which 15 Which is larger, 1 2/7 or 10/4?
- Subtract and compare
1-5/8 is the same as 11/8, true or false? - Identify improper fraction How do you identify improper fractions? Which is improper: A) 3/4 B) 32/15 C) 3/9 D) 2 2/11
- Playing games
In a school, 9/10 of the students take part. 2/3 of these play football. What fraction of the students play football? - Three friends
You and your friends are playing basketball. You make 7 out of 15 shots. Your first friend makes 6 out of 10 shots, and your second friend makes 5 out of 12 shots. Who is the better shooter (write a, b, c)? How would you solve the problem using what you k - Four children
Father saved a certain amount of money in the bank. He divided this amount equally among his four children. One of the daughters donated 3/7 of the amount she received to her son and 4/9 of it to her daughter. What part of the total amount saved did the s
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