We can add, subtract, multiply and divide fractions in algebra in the same way we do in simple arithmetic. Show
Adding FractionsTo add fractions there is a simple rule:  (See why this works on the Common Denominator page). Example:x 2 + y 5 = (x)(5) + (2)(y) (2)(5) = 5x+2y 10 Example:x + 4 3 + x − 3 4 = (x+4)(4) + (3)(x−3) (3)(4) = 4x+16 + 3x−9 12 = 7x+7 12 Subtracting FractionsSubtracting fractions is very similar, except that the + is now − Example:x + 2 x − x x − 2 = (x+2)(x−2) − (x)(x) x(x−2) = (x2 − 22) − x2 x2 − 2x = −4 x2 − 2x Multiplying FractionsMultiplying fractions is the easiest one of all, just multiply the tops together, and the bottoms together: Example:3x x−2 × x 3 = (3x)(x) 3(x−2) = 3x2 3(x−2) = x2 x−2 Dividing FractionsTo divide fractions, first "flip" the fraction we want to divide by, then use the same method as for multiplying: Example:3y2 x+1 ÷ y 2 = 3y2 x+1 × 2 y = (3y2)(2) (x+1)(y) = 6y2 (x+1)(y) = 6y x+1
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National 5 Applying the four operations to algebraic fractionsAlgebraic fractions can be added, subtracted, multiplied or divided using the same basic rules as working with other fractions. Part of Maths Algebraic skills
quiz Test
Adding and subtracting algebraic fractionsWhen adding and subtracting fractions, we must ensure that we have the same denominator. For adding and subtracting fractions:Step 1Multiply the two terms on the bottom to get the same denominator. Step 2Multiply the top number on the first fraction by the bottom number of the second fraction to get the new top number of the first fraction. Step 3Multiply the top number on the second fraction by the bottom number of the first fraction to get the new top number of the second fraction. Step 4Now add/subtract the top numbers and keep the bottom number so that there is now one fraction. Step 5Simplify the fraction if required. ExampleCalculate \(\frac{2}{5} + \frac{3}{7}\) \[=\frac{2\times 7}{35}+\frac{3\times 5}{35}\] \[= \frac{{14}}{{35}} + \frac{{15}}{{35}} = \frac{{29}}{{35}}\] Now try the example questions that follow. QuestionCalculate \(\frac{2}{3} - \frac{y}{{18}}\) \[=\frac{2\times 18}{54}-\frac{3y}{54}\] \[= \frac{{36}}{{54}} - \frac{{3y}}{{54}}\] \[= \frac{{36 - 3y}}{{54}}\] \[= \frac{{3(12 - y)}}{{54}}\] Take out a common factor of 3 on the numerator, then you notice that you can simplify by dividing top and bottom by 3. \[= \frac{{12 - y}}{{18}}\] Question\[\frac{x}{y} + \frac{y}{x}\] \[= \frac{{{x^2}}}{{xy}} + \frac{{{y^2}}}{{xy}}\] \[= \frac{{{x^2} + {y^2}}}{{xy}}\] Question\[\frac{2}{x} - \frac{5}{{x + 2}}\] \[= \frac{{2(x + 2)}}{{x(x + 2)}} - \frac{{5 \times x}}{{x(x + 2)}}\] Multiply the brackets out on the numerator, but not the denominator as we are going to be subtracting the two numerators together so need to collect like terms then factorise if required. \[= \frac{{2x + 4}}{{x(x + 2)}} - \frac{{5x}}{{x(x + 2)}}\] \[= \frac{{2x + 4 - 5x}}{{x(x + 2)}}\] \[= \frac{{4 - 3x}}{{x(x + 2)}}\]
National 5 Subjects
How do you add and subtract algebraic fractions with different denominators?To add or subtract algebraic fractions: Find the lowest common multiple of the denominators. Express all fractions in terms of the lowest common denominator. Simplify the numerators to obtain the numerator of the answer.
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How to add algebraic fractions with different denominators
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