What Are Equivalent & Nonequivalent Fractions?
A fraction is a mathematical term used to express the division of a whole value into parts. A fraction is a numerical value with two parts– a numerator and a denominator. The numerator in a fraction is a number at the top of the fraction, which represents the number of parts whereas, the denominator is the number at the bottom that represents the total number of parts. When two fractions are equal to each other, they are called equivalent fractions. The concept of fraction equivalence is foundational for students to possess the understanding of complex fraction skills like simplification of fractions, finding their common denominators, and applying arithmetic operations on them.
What are Equivalent Fractions?
Two fractions are said to be equivalent if they possess the same value, which means even if the numbers are different, still the overall value of the two fractions is the same. For example, 3/4 and 15/20 are equivalent fractions as they both depict the three-fourth of something. To check if two fractions are equivalent or not, you can simply cross multiply. To cross multiply, multiply the numerator of the first fraction by the denominator of the second. Then multiply the denominator of the first fraction by the numerator of the second. If the two numbers are equal, the fractions are equivalent. In this example 3 X 20 = 60 and 4 X 15 = 60. Therefore the fractions are equivalent.
What are Nonequivalent Fractions?
Nonequivalent fractions are fractions that are not equal to each other. To examine if two fractions are equivalent or nonequivalent, we need to follow the same process of cross multiplication. For example, to identify if 2/3 and 5/7 are equivalent or nonequivalent, we have to multiply 2 times 7, which is equal to 14, and 3 times 5, which equals 15. Since the product of cross-multiplication is not equal, these fractions are nonequivalent.
Teaching Fractions Using Math Manipulatives
The concept of fractions is usually illustrated using pies, pizzas, cake, or any other circular object. To explain equivalent fractions, cut one pizza into half; this shows each part is 1/2. Next, make eight pieces of the two halves to illustrate that four pieces of the pizza are equal to one half. This example teaches that 1/2 and 4/8 are equivalent fractions. Pies or other circular shapes can be divided in other ways to illustrate more examples of both equivalent and nonequivalent fractions.
How to Find Equivalent Fractions?
To find equivalent fractions, begin with a fraction, for example, ⅔ and multiply the numerator and denominator both by two, which results in 4/6. Keep multiplying the original fraction with numbers, for instance, by three to get 6/9, then multiply by four to get 8/24. We can continue to multiply with more numbers to get equivalent fractions, for example, 5, 6, 7, and 8. As long as we multiply both numerator and denominator by the same number, the results will be an equivalent fraction.
Conclusion
The concept of equivalence fraction is extremely important for students to learn about important things in life. Learning the concept of fractions equality also forms the foundation for other math topics and life skills like comparing and calculating marks. Hence, it is vital for students to master this valuable skill of comparing fractions by constant practice. Cuemath offers various learning resources for students in 3rd grade and 4th grade to efficiently implement the understanding of fractions. To find some free resources like math worksheets and puzzles to learn fractions visit cuemath.com.
