Fraction calculator
This calculator divides fractions. The first step makes the reciprocal value of the second fraction - exchange numerator and denominator of 2nd fraction. Then multiply both numerators and place the result over the product of both denominators. Then simplify the result to the lowest terms or a mixed number.
The result:
5/8÷4/10 = 25/16 = 1 9/16 = 1.5625
Spelled result in words is twenty-five sixteenths (or one and nine sixteenths).How do we solve fractions step by step?
- Divide: 5/8 : 4/10 = 5/8 · 10/4 = 5 · 10/8 · 4 = 50/32 = 2 · 25 /2 · 16 = 25/16
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 4/10 is 10/4) of the second fraction. Next, multiply the two numerators. Then, multiply the two denominators. In the following intermediate step, cancel by a common factor of 2 gives 25/16.
In other words - five eighths divided by four tenths is twenty-five sixteenths.
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) |
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:
- Fraction and a decimal
Write as a fraction and a decimal. One and two plus three and five hundredths
- A class IV.A
In a class, there are 15 girls and 30 boys. What fraction of the class represents the boys?
- Out 550,000.00
Out of 550,000.00, an amount of 325,000.00 was used. What fraction of the total amount was used?
- Fractions 80134
There are 420 pupils in the school. Two hundred fifty-two pupils go to the 1st level. Write as a fraction what part of the pupils goes to the 1st grade and what part to the 2nd grade. Shorten both fractions to their basic form.
- A quarter
A quarter of the number 72 is:
- The following 3
The following fraction is reduced to its lowest terms except one. Which of these: A.98/99 B.73/179 C.1/250 D.81/729
- Someone
Someone ate 1/10 of a cake, leaving only 9/10. If you eat 2/3 of the cake left, how much of a whole cake will you have eaten?
- Simplify 12
Simplify {1/3 + 1/12} ÷ {2/3 - 5/8}
- Brown or black
Max has 13 pairs of socks. From this, six pairs are blue, three pairs are brown, two are black, and two are white. What fraction of Max's socks are either brown or black?
- Using money
Out of 575,000.00 given to a school, an amount of 25,000.00 was used. What fraction of the total amount was used?
- Lowest terms 2
We can write the expression 4/12 in its lowest term as 1/3. What is 3/15 expressed in its lowest term?
- Fraction to decimal
Write the fraction 3/22 as a decimal.
- Samantha
Samantha took 72 pictures on her beach vacation. 3/4 of those pictures are on the beach. How many pictures from her vacation are on the beach?
- Oranges
There are 50 oranges in a bag. If ten of these oranges are bad, what fraction of them are good?
- In fractions
An ant climbs 2/5 of the pole in the first hour and climbs 1/4 of the pole in the next hour. What part of the pole does the ant climb in two hours?
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