Generating Multiple Equivalent Fractions Using Common Factors
Generating Multiple Equivalent Fractions Using Common Factors is a Grade 4 math skill in enVision Mathematics, Chapter 8: Extend Understanding of Fraction Equivalence and Ordering. Students multiply or divide both numerator and denominator by the same common factor to generate equivalent fractions.
Key Concepts
To find all possible equivalent fractions for $\frac{a}{b}$ using division, identify all common factors of the numerator $a$ and the denominator $b$ that are greater than 1. For each common factor $c$, a new equivalent fraction is found by calculating $\frac{a \div c}{b \div c}$.
Common Questions
How do you generate equivalent fractions using common factors?
Multiply or divide both the numerator and denominator by the same non-zero number. For example, 2/3 equals 4/6 (multiply both by 2) and equals 6/9 (multiply both by 3).
What is a common factor in fraction equivalence?
A common factor is a number that divides evenly into both the numerator and denominator. Dividing by a common factor simplifies a fraction while multiplying by it creates an equivalent fraction with larger numbers.
What is an example of generating multiple equivalent fractions?
Starting with 1/4, multiply by 2 to get 2/8, by 3 to get 3/12, by 4 to get 4/16. These are all equivalent to 1/4.
How do you know two fractions are equivalent?
Two fractions are equivalent if their cross products are equal, or if one can be obtained from the other by multiplying or dividing both parts by the same number.
What chapter covers equivalent fractions in enVision Mathematics Grade 4?
Generating equivalent fractions using common factors is covered in Chapter 8: Extend Understanding of Fraction Equivalence and Ordering in enVision Mathematics Grade 4.