Fraction Calculator
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Answer |
\(\frac{17}{9} × \frac{3}{16} =\frac{17}{48}\)
In decimal: 0.35416666666667
Solution breakdown:
\(\frac{17}{9} × \frac{3}{16}\)
▶ Solving by the fractions formula:
\(\frac{17 × 3}{9 × 16} = \frac{51}{144}\)
▶ This fraction can be reduced by dividing the numerator and denominator by 3, which stands for the GCF of 51 and 144. Reducing and simplifying, we receive:
\(\frac{51 ÷ 3}{144 ÷ 3} = \frac{17}{48}\)
What Does This Fraction Calculator Compute?
This calculator comprises several tools that primarily execute fundamental arithmetic operations with common fractions and mixed numbers. Beyond performing addition, subtraction, multiplication, and division of fractions, these calculators can also simplify fractions and convert between fractions and decimal representations.
A fraction is a numerical expression consisting of a numerator and denominator that represents a portion of a whole. For instance, ¾ of an apple means 3 parts of a complete apple (the numerator) that has been divided into 4 equal portions (the denominator). The denominator of any fraction must always be non-zero.
Adding and Subtracting Fractions
When adding fractions that share identical denominators, you combine the numerators while keeping the denominator constant. However, when the denominators differ, you must first determine the least common multiple (LCM) of the denominators—in other words, find a common denominator for the fractions. Once the denominators are equalized, the numerators can be added. Subtracting fractions follows a similar procedure to addition. Formula:
, where bd can be replaced with LCM(b,d) to obtain a simplified result.
Multiplying Fractions
The multiplication of fractions involves multiplying the numerators together and multiplying the denominators together: Formula:
Before performing multiplication, you may simplify the fractions if the numerator of one fraction and the denominator of another share common divisors.
Dividing Fractions
Division by a fraction is equivalent to multiplication by its reciprocal (inverted fraction). Formula:
Simplifying Fractions
Simplifying (reducing) a fraction means dividing both the numerator and denominator by their greatest common divisor (GCD). Formula:
For example, the fraction 12/16 can be simplified by dividing both values by GCD(12, 16) = 4, yielding 3/4. A fraction is considered fully reduced when the GCD of the numerator and denominator equals 1.
Converting Mixed Numbers to Improper Fractions
An improper fraction is one where the numerator is greater than or equal to the denominator. You can convert a mixed number to an improper fraction using this formula:
Where:
- A - is the whole number part
- a - is the numerator of the fractional part
- b - is the denominator of the fractional part
Converting Decimal Numbers to Fractions
To transform a decimal into a fraction:
- Write the decimal value without the decimal point as the numerator
- Place the appropriate power of 10 in the denominator based on the number of decimal places
- Simplify the resulting fraction
0.75 = 75/100 = 3/4 (after simplification)
0.125 = 125/1000 = 1/8 (after simplification)