Introduction to Equivalent Fractions

Introduction to Equivalent Fractions

• Equivalent fractions represent the same portion or part of a whole, even though they may use different numbers in the numerator and denominator.
• They are different ways of expressing the same value.

Finding Equivalent Fractions

• Multiplying or dividing both the numerator and denominator of a fraction by the same non-zero number results in an equivalent fraction.
• This process does not change the value of the fraction, only how it is represented.

Examples (Illustrative)

• Example 1: 1/2 = 2/4 = 3/6
  • To get 2/4 from 1/2, multiply both numerator (1) and denominator (2) by 2.
  • To get 3/6 from 1/2, multiply both numerator and denominator by 3.
• Example 2: 4/6 = 2/3.
  • To get 2/3 from 4/6, divide both numerator (4) and denominator (6) by 2.
• Notice that 1/2 * 2/2 = 2/4 is equivalent to 1/2. The result is different but expresses the same amount.

Simplifying Fractions

• Simplifying fractions involves finding the greatest common factor (GCF) of the numerator and denominator and dividing both by it.
• This process reduces the fraction to its lowest terms, making it easier to work with.

Examples (Illustrative)

• Example 3: 6/8 can be simplified to 3/4.

  • The GCF of 6 and 8 is 2. Divide both numerator and denominator by 2.

• Example 4: 10/15 simplified is 2/3

  • The GCF of 10 and 15 is 5. Divide both numerator and denominator by 5.

Visual Representation of Equivalent Fractions

• Use diagrams like fraction bars, circles, or other visual aids to show that different fractions represent the same part of a whole.
• This helps understand the concept more intuitively.

Identifying Equivalent Fractions (by Multiplication)

• Finding equivalent fractions by multiplying the numerator and denominator by the same positive integer.

Examples (Illustrative)

• Start with the fraction 2/3. Multiply top and bottom by 2 : 2/3 * 2/2 = 4/6
• Multiply top and bottom by 3: 2/3 * 3/3 = 6/9
• Notice that 2/3, 4/6, and 6/9 are all equivalent fractions

Identifying Equivalent Fractions (by Division)

• Finding equivalent fractions by dividing the numerator and denominator by the same positive integer.

Examples (Illustrative)

• Start with the fraction 6/8. Dividing top and bottom by 2: 6/8 ÷ 2/2 = 3/4
• Dividing top and bottom by 3: 6/8 ÷4/4 = 1/2

Key Concept:

• Identifying that equivalent fractions are different representations of the same portion of a whole, using different numbers in the numerator and denominator.

Common Errors and Pitfalls

• Not dividing both parts, numerator and denominator, uniformly to get equivalent fractions
• Understanding 'division' and 'multiplication' related to fractions
• Not employing GCF (greatest common factor) for simplifying.

Practice for grade 6, 10 practice problems (Illustrative)

• Problem 1: What fractions are equivalent to 1/4 using multiplication?

• Problem 2: What fractions are equivalent to 1/4 using division?

• Problem 3: Write 3 equivalent fractions for 2/5.

• Problem 4: Simplify 8/12 into lowest terms.

• Problem 5: Simplify 10/20 into lowest terms.

• Problem 6: Are 3/5 and 9/15 equivalent fractions? Show how to arrive at your answer.

• Problem 7: 2/10 = ____ / 5

• Problem 8: Find an equivalent fraction for 4/7 using multiplication.

• Problem 9: Identify the equivalent fraction to 1/5 that uses 25 in the denominator.

• Problem 10: Reduce 18/24 to lowest terms.

This quiz covers the concept of equivalent fractions, which represent the same value despite having different numerators and denominators. It explains how to find equivalent fractions through multiplication and division. Examples illustrate how these fractions relate to each other and how to simplify them.