What makes Equivalent Fractions so Important?

What makes understanding equivalent fractions such a big deal?

Fractions open the door to other math concepts. They are the heart of what makes rational numbers tricky to learn and important to understand.

Understanding equivalent fractions is an important math skill.

Comparing fractions is easier when they all have the same denominators. Students may have to find substitutes for some of the numbers by looking for equivalents with specific denominators.

For example:

A student is trying to compare three-sixths and three-fourths. They don’t yet know that when numerators are the same, the number with the smallest denominator is the largest. They do know that multiplying by one will not change a number. They decide to multiply each number by a fraction equivalent to one that will change the denominators to twelve. Once the denominators are both twelve, they can see that six is only half of twelve while nine is more than half of twelve so nine-twelfths represents the larger amount.

When adding or subtracting numbers with unlike denominators, students need to be able to find substitutes that have like denominators in order to continue their calculations.

For example: 

A student has to subtract five-tenths from three-fifths. They know that three-fifths times one, or in this case two over two will create a number equal to three-fifths with a denominator of ten. They can substitute six-tenths for three-fifths because they are the same number. Now, the equation can be solved. 

Students are usually required to show their answers in simplest form.

Understanding that equivalent fractions are the exact same number is an essential mathematical concept. 

Rational numbers like fractions, decimals, and percents represent a portion of the whole.  Since the relationship between the numerator and denominator can be expressed in many different ways, understanding equivalent fractions is essential in order to make sense of rational numbers. This includes making sense of whole numbers represented as rational numbers.

In math we frequently exchange one term for an equivalent substitute that makes the equation easier to solve. Making these kind of fair trades can be difficult for young students to conceptualize at first. Learning to use equivalent fractions is their first introduction to substituting equivalent terms in math.

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