Simplifying Fractions and Understanding Algebraic Fractions
Explore how to simplify fractions, identify which fractions are greater than 1, analyze fractions as products of prime factors, and delve into algebraic fractions with expressions in the numerator and denominator.
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Presentation Transcript
On your whiteboards Simplify the following fractions: 4) 57 33 1) 35 40 2) 18 5) 625 750 20 9 6 6) 168 672 3) 7. Which fractions have a value that is greater than 1?
On your whiteboards Simplify the following fractions: 4) 57 33 1) 35 =7 =19 11 40 8 9 10 =5 2) 18 5) 625 750 = 20 6 9 6 6) 168 672 =1 =3 3) 4 2 7. Which fractions have a value that is greater than 1?
On your whiteboards Simplify the following fractions: 4) 57 33 1) 35 =7 =19 11 40 8 9 10 =5 2) 18 5) 625 750 = 20 6 9 6 6) 168 672 =1 =3 3) 4 2 7. Which fractions have a value that is greater than 1?
Lets look at question 5 in more detail. Write the numerator and denominator as a product of prime factors (think back to year 8) 1 1 1 625 750 5 5 5 5 2 3 5 5 5 1 = 1 1 = 5 6 Why can we cancel numbers on the numerator with those on the denominator
What if we wrote the numerators and denominators using index form? 625 750 5 5 5 5 2 3 5 5 5 54 = = 2 3 53 We know from Year 8 that we can divide indices by subtracting the powers of numbers with the same base 51 2 3 =5 = 6
On your whiteboards, show that 168 672=1 4 by finding the product of primes of the numerator and denominator and cancelling down. Now repeat by writing the numerators and denominators in index form and cancelling down.
Algebraic Fractions ?3?5? ?2?5?5 This fraction is algebraic. A fraction is algebraic if the numerator and/or the denominator are expressions
Algebraic Fractions ?3?5? ?2?5?5 In pairs discuss: How would you simplify this algebraic fraction?
We could write it out in full: v ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ?4 = ? ? ? ?= Or we could use index rules: ?3?5? ?2?5?5 ? ?4 = ?1?0? 4=
In your books Title: Cancelling Algebraic Fractions 6?? 15??2circle your answer Simplify fully 1 2? 5 2 5? 6? 15 6 15? Simplify fully 6?2??3 3?2?2circle your answer 2 6?2? 3 2?2? 3 2?2? ? 6?2 3? ?4??2 ??2circle your answer 3 Simplify fully ?2 ?2? ??2 ? ?2?3 ?? ?3?2 ?
Challenge Problem: Simplify fully 18?2? 3?2 3?2
David is simplifying 5? + 35 ? + 4 Do you agree with David s solution? Discuss with your partner
David then attempts to simplify ?2 + 2? ? What has David done differently this time? Discuss with your partner
David then attempts to simplify ?2 + 2? ? In order to simplify an algebraic fraction, we must divide the numerator and denominator by a common factor. Sometimes, this means we must factorise first.
State whether the following are true or false. Where you think the answer is false, write the correct simplification ?2+ 5? ? = ? + 5 ? 3 ?2 3= 1 ? 3 3? + 12 ? + 4 = 3 3?2+ 6? ?2+ 2?=3? ?
State whether the following are true or false. Where you think the answer is false, write the correct simplification ?2+ 5? ? = ? + 5 ? 3 ?2 3= 1 ? 3 3? + 12 ? + 4 = 3 3?2+ 6? ?2+ 2?=3? ?
State whether the following are true or false. Where you think the answer is false, write the correct simplification ?2+ 5? ? = ? + 5 ? 3 ?2 3= 1 ? 3 3? + 12 ? + 4 = 3 3?2+ 6? ?2+ 2?=3? ?
State whether the following are true or false. Where you think the answer is false, write the correct simplification ?2+ 5? ? = ? + 5 ? 3 ?2 3= 1 ? 3 3? + 12 ? + 4 = 3 3?2+ 6? ?2+ 2?=3? ?
State whether the following are true or false. Where you think the answer is false, write the correct simplification ?2+ 5? ? = ? + 5 ? 3 ?2 3= 1 ? 3 3? + 12 ? + 4 = 3 3?2+ 6? ?2+ 2?=3? ?
Challenge Problem Simplify xy2(x + y)3 y(x + y)4
