A fraction is considered simplified if there are no common factors, other than 1 in the numerator and denominator. If a fraction does have common factors in the numerator and denominator, we can reduce the fraction to its simplified form by removing the common factors.[br][br][br]

No. [br][br]When we simplify an improper fraction, there is no need to[br]change it to a mixed number. We just need to make sure that the numerator and the denominator of the improper fraction share no common factors.[br]

Step 1.  Rewrite the numerator and denominator to show the common factors. If needed, factor the numerator and denominator into prime numbers.[br]  [br]Step 2. Simplify, using the equivalent fractions property, by removing common factors.[br][br]Step 3. Multiply any remaining factors[br][br][br]

To multiply fractions, we multiply the numerators and multiply the denominators. Then we write the fraction in simplified form.

The reciprocal of the fraction [math]\frac{a}{b}[/math] is [math]\frac{b}{a}[/math], where [math]a\ne0[/math] and [math]b\ne0[/math].

A number and its reciprocal have a product of 1.[br][br][br]

To divide fractions, we multiply the first fraction by the reciprocal of the second fraction.

The least common denominator (LCD) of two fractions is the[br]least common multiple (LCM) of their denominators.[br][br][br]

     [br]Step 1.  [br]Factor each denominator into its primes.[br][br]Step 2.  [br]List the primes, matching primes in columns when possible.[br][br]Step 3.  [br]Bring down the columns.[br]       [br]Step 4.  [br]Multiply the factors. The product is the LCM of the denominators.[br][br]   [br]Step 5.  [br]The LCM of the denominators is the LCD of the fractions.[br][br][br]

If a, b, c are whole numbers where [math]b\ne0[/math] and [math]c\ne0[/math], then[math]\frac{a}{b}=\frac{a\cdot c}{b\cdot c}[/math] and [math]\frac{a\cdot c}{b\cdot c}=\frac{a}{b}[/math].

Step 1. [br]Find the LCD.[br]        [br]Step 2.  [br]For each fraction, determine the number needed to multiply the denominator to get the LCD.[br][br][br]Step 3.[br]Use the Equivalent Fractions Property to multiply both the numerator and[br]denominator by the number you found in Step 2.[br]      [br]Step 4. [br]Simplify the numerator and denominator.[br][br][br]

Step 1.  [br]Find the LCD.[br] [br]Step 2.  [br]Convert each fraction to an equivalent form with the LCD as the[br]denominator.[br][br]Step 3. [br]Add or subtract the fractions.[br]  [br]Step 4.  [br]Write the result in simplified form.[br][br][br] [br][br][br]

[math]-\frac{1}{12}[/math]

[math]-\frac{6}{4}=-\frac{3}{2}[/math]

[math]\frac{25x-9}{30}[/math]

[math]\frac{5x\cdot3}{6\cdot10}=\frac{15x}{60}=\frac{x}{4}[/math]