Simplest Form (of a Fraction)

A fraction in simplest form (or lowest terms) means its numerator and denominator are relatively prime. In other words, they have no common factors other than 1. Anytime you encounter a fraction not in simplest form, you'll most likely want to reduce it. Let's look at the steps involved in writing a fraction in simplest form.

How to reduce a fraction to simplest form

In order to write a fraction in simplest form, you'll want to find the greatest common factor for the numerator and denominator. A greatest common factor is the largest number that can be divided evenly into both numbers.

For the fraction $6/9$, the number that can be divided evenly into both the numerator and denominator is 3. This is your greatest common factor.

To write $6/9$ in simplest form, we'll divide both the numerator and denominator by the greatest common factor.

$(6÷3)/(9÷3)$ = $2/3$

Therefore, $6/9$ in simplest form is $2/3$.

Let's try one more.

Write $12/64$ in simplest form.

The greatest common factor is 4.

$(12÷4)/(64÷4)$

So, $12/64$ in simplest form is $3/16$.

Practice questions on simplest form of a fraction

a. True or false: $19/38$ is in simplest form.

False, $19/38$ in simplest form is $1/2$.

b. True or false: $15/16$ is in simplest form.

True, the only common factor is 1.

c. What is the greatest common factor of $20/25$?

5

d. What is the greatest common factor of $28/49$?

7

e. Reduce $6/10$ to simplest form.

Greatest common factor: 2.

$(6÷2)/(10÷2)$

$3/5$

f. Reduce $9/21$ to simplest form.

Greatest common factor: 3.

$(9÷3)/(21÷3)$

$3/7$

g. Reduce $4/44$ to simplest form.

Greatest common factor: 4.

$(4÷4)/(44÷4)$

$1/11$

Topics related to the Simplest Form (of a Fraction)

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Improper Fractions

Adding Fractions with Unlike Denominators

Flashcards covering the Simplest Form (of a Fraction)

ACCUPLACER Arithmetic Flashcards

Practice tests covering the Simplest Form (of a Fraction)

Basic Arithmetic Diagnostic Tests

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Delve deeper into simplest form of a fraction

While learning new math concepts like simplest form can be exciting, it's common to feel a bit intimidated when asked to identify the greatest common factor of a fraction or write a fraction in simplest form. Whether your student is challenged by this concept or feels pretty confident in their knowledge but would like homework or test prep assistance, working with a tutor can help. Get to know all about the perks of taking part in tutoring by reaching out to the Educational Directors at Varsity Tutors today.