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Understanding and Simplifying Equivalent Fractions: A Comprehensive Guide

This guide explains the concept of equivalent fractions, focusing on how to simplify them effectively. It defines numerators and denominators while exploring relationships that create equivalent fractions such as one half and one third. The importance of finding common divisors is emphasized, along with practical methods for simplification. We provide examples to illustrate how various numbers relate to their denominators, making fraction simplification straightforward. Whether you are a beginner or need a refresher, this resource will enhance your understanding of fractions in mathematics.

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Understanding and Simplifying Equivalent Fractions: A Comprehensive Guide

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Presentation Transcript

  1. Fractions Simplifying Equivalences

  2. Equivalent Fractions of one half The bottom number is twice the top number The top number is half the bottom number

  3. In a fraction the top number is the numerator. The bottom number is the denominator. Which of these fractions are equivalent to a half. Look at the relationship between the numerator and the denominator. 8x2=16 so no It is relatively easy to see if a fraction equals a half or not. 11x2=22 so yes 15x2= 30 so yes

  4. Which of these are equivalent to a third? Is the bottom number three times the top number? No Yes Yes No Yes Yes Yes

  5. Simplifying fractions – a general method You have to find a common divisor – a number which will go into both the top number and the bottom number and leave no remainder

  6. Find a number that will go into the numerator and denominator and leave no remainder What number will go into 25 and 100 and leave no remainder? 5 is a possibility What number will go into 5 and 20 and leave no remainder? 5 is a possibility again We can’t go any further

  7. Find a number that will go into the numerator and denominator and leave no remainder What number will go into 28 and 42 and leave no remainder? They are both even numbers so two will work What number will go into 14 and 21 and leave no remainder? 7 will We can’t go any further

  8. Simplifying fractions- You need to know your times tables Even numbers end in 0, 2, 4, 6, 8 – Two will always go into and even number. Here are some even numbers 18 74 32 96 110

  9. Simplifying fractions- You need to know your times tables To see if 3 goes into a number – see if three goes into the sum of the digits – example - 39 (3+9=12=3x4) Here are some numbers that are divisible by three 51 5+1=6=3x2 108 1+0+8=9=3x3 48 4+8=12=3x4 63 6+3=9=3x3

  10. Simplifying fractions- You need to know your times tables Five will go into any number that ends in zero or five Ten will go into any number that ends in zero Twenty five will go into any number that ends in 00, 25, 50, 75

  11. Try to simplify these fractions

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