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Mathematics I (Math 1132)

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Durham College, Mathematics
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Mathematics I (Math 1132)

Combining Complex Fractions

When a fraction contains fractions in its numerator and/or its denominator,  it’s called a complex fractions, otherwise it’s a simple fraction.

Examples of simple fractions:

35   or   ab

Examples of complex fractions:

 2 79   or   811+545   or    5a bc

To simplify a complex fraction, you have to ensure that you reduce individually the numerator and denominator into simple fractions. Once you’ve done that, then you can divide them out using the method that was taught in the previous lesson.

Question:   Simplify. Leave your answers as improper fractions.

a   23+3415      b   5256+13

Answers:

(a) Start by combining the numerator fractions:

24+3334=8+912=1712

Now the numerator and denominator are simple fractions:

171215=1712÷15=1712×51=8512
Solution to (b)

(b) We start by combining the numerator terms together, and the denominator terms too:

Numerator:   525=5525=235Denominator:   6+13=63+13=193

Now the numerator and denominator are simple fractions:

235193=235÷193=235×319=6995

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The video below shows three examples of complex fractions being simplified. The first example is non-algebraic, while the second and third are. Given how little we’ve focused on algebra thus far in this course, you may skip the last two questions, though the principles are the same.

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