A simplify fractions calculator is a calculator which simplifies fractions into their simplest form, in which there is no common factor greater than one between the two numbers. The calculation can be done without this calculator also, but you can still use it for homework.
Learning to do it manually is also a good choice because it helps you understand the concept of factors, GCF and equivalent fractions.
What Does “Simplified” Actually Mean?
Simplified fractions are a type of equivalent fraction with the smallest possible numerator and denominator, such that there is no common factor between the two other than 1. The value remains the same, but the way it is presented becomes simpler.
The One Rule: Divide by the GCF
Divide the top and bottom parts of the fraction by their greatest common factor (GCF), which is the largest integer that can divide both:
a/b ÷ GCF(a, b) = reduced fraction
Consider 24/36. The common factors between 24 and 36 are 1, 2, 3, 4, 6, and 12, so the GCF is 12:
24 ÷ 12 = 2
36 ÷ 12 = 3
Thus 24/36 = 2/3.
Try It Yourself: Two Quick Examples
Reduce 15/25. The GCF of 15 and 25 is 5. 15/5 = 3 and 25/5 = 5; thus the answer is 3/5.
Reduce 42/30. The GCF of 42 and 30 is 6. 42/6 = 7 and 30/6 = 5; thus the answer is 7/5, which can be written as 1 2/5 as a mixed fraction.
Improper Fractions Can Be Simplified Too
Even though the top number is bigger than the bottom, the fraction 7/5 is in simplest form. The same holds true for the fraction 18/12 whose GCF is six, thus producing the simplified fraction 3/2. Although still an improper fraction, 3/2 is already simple. If your assignment requires you to convert the improper fraction into a mixed number, then 3/2 becomes 1 ½
Is It Already Simplified? A Quick Test
Calculate the greatest common factor of the two numbers. If the greatest common factor equals 1, then don’t simplify the fraction any further.
Simplifying Step by Step on the TI-34 MultiView
The TI-34 MultiView can do the simplification in steps, so it is helpful for cases where the user wants to know the procedure. As explained in the official manual, the ►simp key is used to simplify using the least common prime factor.
In the MathPrint mode, input the fraction 24/36 through n/d.
Press ►simp, and then press ENTER.
Keep repeating steps 1 and 2 until the fraction is completely simplified.
Another feature is the AutoSimp mode, which automatically simplifies fractional results to lowest terms. For conversion between simple fraction and mixed number, use 2nd ↔︎U, while for converting fraction to decimal, use 2nd f↔︎d.
Before You Hand It In
- Did you divide both the numerator and denominator? Dividing only one changes the value.
- Is your divisor a factor of both numbers? 2 is not a common factor of 15 and 25.
- Is the GCF of your final numbers 1? If they still share a factor, keep going.
- Does your assignment want an improper fraction or a mixed number?
Questions About Simplifying Fractions
What does it mean to simplify a fraction?
It means expressing the fraction in its simplest terms, where both the numerator and denominator have the smallest possible values and cannot be reduced further because no factor other than 1 divides both of them.
What is the Greatest Common Factor (GCF)?
This refers to the greatest whole number that is a divisor of two numbers. This is the fastest way to simplify fractions.
Does simplification affect the value of a fraction?
No. When you divide both the numerator and denominator by the same number, you arrive at an equivalent fraction, so 24/36 can be simplified to 2/3.
Can simplifying fractions be done in more than 1 step?
Yes. You can continue to divide by any common factor until the GCF of the numerator and denominator is 1.
Is it possible for an improper fraction to be fully simplified?
Yes. For example, 7/5 is a fully simplified fraction.
What if the GCF is 1?
Leave the fraction as it is. It’s already in simplest form, and dividing both numbers by 1 changes nothing.
And what if there’s a zero in the fraction?
The fraction 0/5 reduces to 0, since anything divided by a non-zero number results in zero. A denominator cannot be zero.
Do I need to write the answer as a mixed number?
This will depend on your instructor. In either case, 7/5 or 1 2/5 will do. Both are reduced forms of the fraction.
TI34Calc is an independent educational site and is not affiliated with Texas Instruments. Key names are given for the TI-34 MultiView for reference; check your calculator’s manual for your exact model.