Use this fraction calculator for adding, subtracting, multiplying and dividing fractions. Answers are fractions in lowest terms or mixed numbers in reduced form. Show
Input proper or improper fractions, select the math sign and click Calculate. This is a fraction calculator with steps shown in the solution. If you have negative fractions insert a minus sign before the numerator. So if one of your fractions is -6/7, insert -6 in the numerator and 7 in the denominator. Sometimes math problems include the word "of," as in What is 1/3 of 3/8? Of means you should multiply so you need to solve 1/3 × 3/8. To do math with mixed numbers (whole numbers and fractions) use the Mixed Numbers Calculator. Math on Fractions with Unlike DenominatorsThere are 2 cases where you need to know if your fractions have different denominators:
How to Add or Subtract Fractions
How to Multiply Fractions
How to Divide Fractions
Fraction FormulasThere is a way to add or subtract fractions without finding the least common denominator (LCD). This method involves cross multiplication of the fractions. See the formulas below. You may find that it is easier to use these formulas than to do the math to find the least common denominator. The formulas for multiplying and dividing fractions follow the same process as described above. Adding FractionsThe formula for adding fractions is: \( \dfrac{a}{b} + \dfrac{c}{d} = \dfrac{ad + bc}{bd} \) Example steps: \( \dfrac{2}{6} + \dfrac{1}{4} = \dfrac{(2\times4) + (6\times1)}{6\times4} \) \( = \dfrac{14}{24} = \dfrac {7}{12} \) The formula for subtracting fractions is: \( \dfrac{a}{b} - \dfrac{c}{d} = \dfrac{ad - bc}{bd} \) Example steps: \( \dfrac{2}{6} - \dfrac{1}{4} = \dfrac{(2\times4) - (6\times1)}{6\times4} \) \( = \dfrac{2}{24} = \dfrac {1}{12} \) Multiplying FractionsThe formula for multiplying fractions is: \( \dfrac{a}{b} \times \dfrac{c}{d} = \dfrac{ac}{bd} \) Example steps: \( \dfrac{2}{6} \times \dfrac{1}{4} = \dfrac{2\times1}{6\times4} \) \( = \dfrac{2}{24} = \dfrac {1}{12} \) Dividing FractionsThe formula for dividing fractions is: \( \dfrac{a}{b} \div \dfrac{c}{d} = \dfrac{ad}{bc} \) Example steps: \( \dfrac{2}{6} \div \dfrac{1}{4} = \dfrac{2\times4}{6\times1} \) \( = \dfrac{8}{6} = \dfrac {4}{3} = 1 \dfrac{1}{3} \) Related CalculatorsTo perform math operations on mixed number fractions use our Mixed Numbers Calculator. This calculator can also simplify improper fractions into mixed numbers and shows the work involved. If you want to simplify an individual fraction into lowest terms use our Simplify Fractions Calculator. For an explanation of how to factor numbers to find the greatest common factor (GCF) see the Greatest Common Factor Calculator. If you are simplifying large fractions by hand you can use the Long Division with Remainders Calculator to find whole number and remainder values. Notes
The below solved example with step by step work shows how to find what is 1/3 times 1/3 or 1/3 times 1/3 as a fraction. Solved Example: What to be found: 1/3 x 1/3 = ?step 2 Arrange the fractions in the product expression form as like the below: = 1/3 x 1/3 = (1 x 1)/(3 x 3) step 3 Check the numerator and denominator and cancel if anything cancelled each other: = (1 x 1)/(3 x 3) = 1/9 1/3 x 1/3= 1/9 Hence, 1/3 times 1/3 as a fraction equals to 1/9
Are you looking to work out and calculate how to multiply 1/3 by 3/10? In this really simple guide, we'll teach you exactly what 1/3 times 3/10 is and walk you through the step-by-process of how to multiply two fractions together. Just a quick reminder here that the number above the fraction line is called the numerator and the number below the fraction line is called the denominator. To multiply two fractions, all we need to do is multiply the numerators and the denominators together and then simplify the fraction if we can. Let's set up 1/3 and 3/10 side by side so they are easier to see: The next step is to multiply the numerators on the top line and the denominators on the bottom line: From there, we can perform the multiplication to get the resulting fraction: You're done! You now know exactly how to calculate 1/3 x 3/10. Hopefully you understood the process and can use the same techniques to add other fractions together. The complete answer is below (simplified to the lowest form): Convert 1/3 times 3/10 to DecimalHere's a little bonus calculation for you to easily work out the decimal format of the fraction we calculated. All you need to do is divide the numerator by the denominator and you can convert any fraction to decimal: Cite, Link, or Reference This PageIf you found this content useful in your research, please do us a great favor and use the tool below to make sure you properly reference us wherever you use it. We really appreciate your support!
Preset List of Fraction Multiplication ExamplesBelow are links to some preset calculations that are commonly searched for: Below are multiple fraction calculators capable of addition, subtraction, multiplication, division, simplification, and conversion between fractions and decimals. Fields above the solid black line represent the numerator, while fields below represent the denominator. Mixed Numbers CalculatorSimplify Fractions CalculatorDecimal to Fraction CalculatorFraction to Decimal CalculatorBig Number Fraction CalculatorUse this calculator if the numerators or denominators are very big integers.
 In mathematics, a fraction is a number that represents a part of a whole. It consists of a numerator and a denominator. The numerator represents the number of equal parts of a whole, while the denominator is the total number of parts that make up said whole. For example, in the fraction of , the numerator is 3, and the denominator is 8. A more illustrative example could involve a pie with 8 slices. 1 of those 8 slices would constitute the numerator of a fraction, while the total of 8 slices that comprises the whole pie would be the denominator. If a person were to eat 3 slices, the remaining fraction of the pie would therefore be as shown in the image to the right. Note that the denominator of a fraction cannot be 0, as it would make the fraction undefined. Fractions can undergo many different operations, some of which are mentioned below. Addition:Unlike adding and subtracting integers such as 2 and 8, fractions require a common denominator to undergo these operations. One method for finding a common denominator involves multiplying the numerators and denominators of all of the fractions involved by the product of the denominators of each fraction. Multiplying all of the denominators ensures that the new denominator is certain to be a multiple of each individual denominator. The numerators also need to be multiplied by the appropriate factors to preserve the value of the fraction as a whole. This is arguably the simplest way to ensure that the fractions have a common denominator. However, in most cases, the solutions to these equations will not appear in simplified form (the provided calculator computes the simplification automatically). Below is an example using this method.
This process can be used for any number of fractions. Just multiply the numerators and denominators of each fraction in the problem by the product of the denominators of all the other fractions (not including its own respective denominator) in the problem.
An alternative method for finding a common denominator is to determine the least common multiple (LCM) for the denominators, then add or subtract the numerators as one would an integer. Using the least common multiple can be more efficient and is more likely to result in a fraction in simplified form. In the example above, the denominators were 4, 6, and 2. The least common multiple is the first shared multiple of these three numbers.
The first multiple they all share is 12, so this is the least common multiple. To complete an addition (or subtraction) problem, multiply the numerators and denominators of each fraction in the problem by whatever value will make the denominators 12, then add the numerators.
Subtraction:Fraction subtraction is essentially the same as fraction addition. A common denominator is required for the operation to occur. Refer to the addition section as well as the equations below for clarification.
Multiplication:Multiplying fractions is fairly straightforward. Unlike adding and subtracting, it is not necessary to compute a common denominator in order to multiply fractions. Simply, the numerators and denominators of each fraction are multiplied, and the result forms a new numerator and denominator. If possible, the solution should be simplified. Refer to the equations below for clarification. Division:The process for dividing fractions is similar to that for multiplying fractions. In order to divide fractions, the fraction in the numerator is multiplied by the reciprocal of the fraction in the denominator. The reciprocal of a number a is simply . When a is a fraction, this essentially involves exchanging the position of the numerator and the denominator. The reciprocal of the fraction would therefore be . Refer to the equations below for clarification.
Simplification:It is often easier to work with simplified fractions. As such, fraction solutions are commonly expressed in their simplified forms. for example, is more cumbersome than . The calculator provided returns fraction inputs in both improper fraction form as well as mixed number form. In both cases, fractions are presented in their lowest forms by dividing both numerator and denominator by their greatest common factor. Converting between fractions and decimals:Converting from decimals to fractions is straightforward. It does, however, require the understanding that each decimal place to the right of the decimal point represents a power of 10; the first decimal place being 101, the second 102, the third 103, and so on. Simply determine what power of 10 the decimal extends to, use that power of 10 as the denominator, enter each number to the right of the decimal point as the numerator, and simplify. For example, looking at the number 0.1234, the number 4 is in the fourth decimal place, which constitutes 104, or 10,000. This would make the fraction , which simplifies to , since the greatest common factor between the numerator and denominator is 2. Similarly, fractions with denominators that are powers of 10 (or can be converted to powers of 10) can be translated to decimal form using the same principles. Take the fraction for example. To convert this fraction into a decimal, first convert it into the fraction of . Knowing that the first decimal place represents 10-1, can be converted to 0.5. If the fraction were instead , the decimal would then be 0.05, and so on. Beyond this, converting fractions into decimals requires the operation of long division. Common Engineering Fraction to Decimal ConversionsIn engineering, fractions are widely used to describe the size of components such as pipes and bolts. The most common fractional and decimal equivalents are listed below. |
What is 1 3 times 3
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