Subtraction Of Fraction

How do you add and subtract fractions?

First, make sure that all of the fractions have the SAME DENOMINATOR. Then, add the numerators (the top numbers of each fraction) and put that value over the numerator. Let’s take an example for addition:2/3 + 3/4 = 8/12 + 9/12 = 17/12 = 1 5/12Notice that the commutative property 3/4 + 2/3 =9/12 + 8/12 = 17/12 = 1 5/12. THEY ARE EQUAL.The smallest number that BOTH 3 and 4 have in common is 122/3 = 8/12 since the cross products are 2* 12 = 24 and 3 *8 =24.3/4 = 9/12 since the cross products are 3*12 =36 and 4*9 = 36.So, the sum of 8/12 + 9/12 = 17/12, which reduces to 1 5/12.The same procedure illustrated in the above problem applies to subtraction:2/3 - 3/4 = 8/12 - 9/12 = - 1/12. Let’s see if the commutative property holds true for subtraction:3/4 - 2/3 = 9/12-8/12=1/12. NO since -1/12 is NOT equal to 1/12.I simply wanted to illustrate that the order that the fractions are solved makes a difference in subtraction but not in addition. The key to remember, however, in both addition and subtraction of fractions is to find a common denominator.

What are some tips to add and subtract fractions?

If you want to add [math]\frac ab[/math] to [math]\frac cd[/math] the first thing to do is get common denominators by multiplying both fractions by judiciously chosen fractions of the form [math]\frac ee.[/math] Thats right you multiply both fractions by 1 but in different shapes. You multiplay [math]\frac ab[/math] by [math]\frac dd[/math] and [math] \frac cd[/math] by [math]\frac bb.[/math] Then all of a sudden you miraculously end up with[math]\frac {ad}{bd} + \frac {cb}{bd}=\frac {ad+bc}{bd}[/math]If numerator and denominator have a common factor you can divide that out. There all kinds of nifty tricks with least common multiples and greatest common divisors, but the above is the easiest way. Incidentally: this is the way addition of rationals is defined.

How do I teach someone addition and subtraction of fractions?

It sounds like your friend is inexperienced with the algebra of fractions.  If she knows how addition and multiplication of numerical fractions works, you can start by abstracting from that knowledge some general properties.It's useful to know several properties on sight, but also be able to recognize what's not valid.Identities for addition and subtraction                 [math]a\pm\frac{b}{c}=\frac{ac\pm b}{c}[/math]                 [math]\frac{a}{c}\pm\frac{b}{c}=\frac{a\pm b}{c}[/math]                 [math]\frac{a}{b}\pm\frac{c}{d}=\frac{ad\pm bc}{bd}[/math]And be sure to recognize that in general                 [math]\frac{a}{b\pm c}\neq\frac{a}{b}\pm\frac{a}{c}[/math]Identities for multiplication and division                 [math]a\;\frac{b}{c}=\frac{ab}{c}[/math]                 [math]-\frac{a}{b}=\frac{-a}{b}=\frac{a}{-b}[/math]                 [math]\frac{a}{b}\;\frac{c}{d}=\frac{ac}{bd}[/math]                 [math]\frac{1}{a/b}=\frac{b}{a}[/math]                 [math]\frac{a/b}{c}=\frac{a}{bc}[/math]                 [math]\frac{a}{b/c}=\frac{ac}{b}[/math]                 [math]\frac{a/b}{c/d}=\frac{ad}{bc}[/math]Valid simplification                 [math]\frac{ac}{bc}=\frac{a}{b}[/math]But know some simplifications are invalid.  For example,                 [math]\frac{ab+ c}{ad}\neq \frac{b+c}{d}[/math]                  [math]\frac{a}{a+b}\neq\frac{1}{b}[/math]

What is the process of subtracting multiple fractions?

The process of subtracting multiple fractions:Find the LCM of all the denominators of all the fractions. Convert all numerators keeping in view the value of the fraction and the latest denominator. Then you successively subtract the numerators and what remains is divided by the denominator to get the final answer.

How do I add, divide, multiply and subtract fractions with and without the same denominator?

Same denominator:Addition:You add the numerators in the fraction.Example:[math]\frac{1}{8}[/math] + [math]\frac{2}{8}[/math] = [math]\frac{3}{8}[/math]Subtraction:You subtract the numerators in the fraction.Example:[math]\frac{5}{6}[/math] - [math]\frac{4}{6}[/math] = [math]\frac{1}{6}[/math]Multiplication:You multiply the numerators and denominators of the multiplicand and multiplier respectively.Example:[math]\frac{1}{9}[/math] * [math]\frac{2}{9}[/math] = [math]\frac{2}{81}[/math]Division:For division, you need to flip the numerator and denominator values of the divisor (reciprocal) so that you can work out the expression using multiplication.Example:[math]\frac{5}{9}[/math] ÷ [math]\frac{4}{9}[/math]= [math]\frac{5}{9}[/math] * [math]\frac{9}{4}[/math]= [math]\frac{5}{4}[/math]Different denominator:Addition:You have to convert either one of or both of the addends (fractions) such that the denominators of both addends are the same.Example:[math]\frac{3}{15}[/math] + [math]\frac{2}{5}[/math]= [math]\frac{3}{15}[/math] + [math]\frac{6}{15}[/math]= [math]\frac{9}{15}[/math]= [math]\frac{3}{5}[/math] (reduced to simplest form)Subtraction:You have to convert either the subtrahend or minuend (or both) such that the denominators of both the subtrahend or minuend are the same.Example:[math]\frac{6}{9}[/math] - [math]\frac{1}{3}[/math]= [math]\frac{6}{9}[/math] - [math]\frac{3}{9}[/math]= [math]\frac{3}{9}[/math]= [math]\frac{1}{3}[/math] (reduced to simplest form)Multiplication:Same for multiplication for same denominators.Example:[math]\frac{3}{4}[/math] * [math]\frac{5}{6}[/math]= [math]\frac{15}{24}[/math]= [math]\frac{5}{8}[/math] (reduced to simplest form)Division:Same as division for same denominators.Example:[math]\frac{4}{11}[/math]÷[math]\frac{6}{7}[/math]= [math]\frac{4}{11}[/math] * [math]\frac{7}{6}[/math]= [math]\frac{28}{66}[/math]=[math]\frac{14}{33}[/math](reduced to simplest form)Note:[math]\frac{5}{4}[/math] is an improper fraction, as the numerator is larger than the denominator. Some school syllabus requires students to present their final answer as mixed fraction.Example:[math]\frac{5}{4}[/math] = 1[math]\frac{1}{4}[/math](Mixed fraction)