Calculator reciprocal of a fraction
This calculator finds the reciprocal of a fraction. To find the reciprocal of a fraction, exchange the numerator and the denominator. Simply speaking, the reciprocal of a/b is b/a.
1 : 3/4 = 4/3 = 1 1/3 ≅ 1.3333333
Spelled result in words is four thirds (or one and one third).How do we solve fractions step by step?
- Divide: 1 : 3/4 = 1/1 · 4/3 = 1 · 4/1 · 3 = 4/3
Dividing two fractions is the same as multiplying the first fraction by the reciprocal value of the second fraction. The first sub-step is to find the reciprocal (reverse the numerator and denominator, reciprocal of 3/4 is 4/3) of the second fraction. Next, multiply the two numerators. Then, multiply the two denominators. In the following intermediate step, it cannot further simplify the fraction result by canceling.
In other words - one divided by three quarters is four thirds.
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 | 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 /) have the same priority and must be evaluated from left to right.
Fractions in word problems:
- Three 210
Three friends share 4/5 of a pizza. What fraction of pizza does each person get? - Division by reciprocal
What is the corresponding illustration/model of 7÷ 1/3? - Soup 4
Cornell makes 11/12 of a gallon of soup. He eats equal portions of soup for 5 days, with no soup remaining after the 5th day. How many gallons of soup did Cornell eat each day? - A lawn
Sean and his sister, Betty, equally mowed 8/9th of the total area of a lawn. What fraction of the total area did each of them mow? - Julian 2
Julian and two of his friends will share 1/4 of a pizza. How much will each person get? - Frac answer
What is the answer to 1/2 ÷ 5/7? - Fraction 77774
Express the value of the fraction 25/12 as a decimal number. - Jaenette
Janette served 3/4 of a pizza to her friends. Each visitor was given 1/4 of the pizza. How many visitors shared the pizza? - Barbara 2
Barbara gets six pizzas to divide equally among four people. How much pizza can each person have? - Julian 3
Julian had 7 cookies and gave half of them to a friend. How many cookies did his friend get? - Convert 6
Convert to a decimal 15/100. - Why is
Why is three divided by one-fifth different from one-fifth divided by three? - Candy bars
Sheldon has four candy bars and wants to split them among his five friends. If each person gets the same amount, what part of the candy bar will each friend get? Show your work. - Two-thirds 15
Two-thirds of a pie has already been eaten. What fraction of the pie would still leave if John ate 1/2 of what of the remaining pie? - What is 16
What is the quotient of 11 over 12 divided by one-third?
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