Last updated on July 4th, 2025
Reducing a fraction to its simplest form is called simplifying a fraction. If a fraction is simplified if it has a common factor in numerator and denominator. One important step in solving fraction problems is simplifying them.
Simplifying a fraction means reducing it to its lowest form. When the fraction has no common factors other than 1, then the fraction is in it’s simplest form. The simplified form of a fraction is still equivalent to the given fraction in value.
The steps to find the simplest form of fractions are mentioned below:
Step 1: Identify the Numerator and Denominator
In a fraction, the numerator is the number on top and denominator is the number on the bottom.
Step 2: Find the GCF
Identify the GCF of the numerator and denominator, it is the largest number that divides both exactly.
Step 3: Divide the Numerator and Denominator both by the GCF
Now, divide the fraction by the GCF to simplify the fraction.
Step 4: Check if the Fraction Can Be Simplified Further
If there are still common factors, repeat the process. If 1 is the only common factor, the fraction is already in its simplest form.
Step 5: Convert an Improper Fraction (If Needed)
If the numerator ≥ denominator, convert the improper fraction into a mixed number.
Step 6: Verify the Final Answer:
Check that the numerator and denominator have no common factors other than 1.
To simplify fractions with variables, we must follow the steps mentioned below:
Step 1: Identify the Common Factors
Look at both the numerator and denominator to identify common factors, including constants (numbers) and variables (letters).
Example: 6x3/9x
Step 2: Factor Out Common Terms
Factor out the greatest common factor (GCF) from both the numerator and denominator.
6x3/9x = (3 × 2x3)/ (3 × 3x)
Step 3: Cancel Out Common Terms
Any common factors in the numerator and denominator cancel out
2x3/ 3x = 2x3 –1/ 3 = 2x2/3
Step 4: Apply Exponent Rules (If Needed)
Use the quotient rule for exponents: am / an = am-n
For the given example: x3/x = x3 –1 = x2
Step 5: Handle Negative Exponents (If Any)
If any variable has a negative exponent, rewrite it in the denominator.
Rule:
a-m = 1/am
Example: x–2/y = 1/x2y
To simplify mixed fractions, we must follow the steps mentioned below:
Step 1: Convert the Mixed Fraction to an Improper Fraction
To simplify calculations, the first step is to convert them into improper fractions.
Formula:
Improper fraction = (Whole Number × Denominator) + Numerator / Denominator
For example: 2(¾) = (2 × 4) + 3 = 8 + 3 = 11/4
Step 2: Simplify the Fraction
If the fraction is not in its simplest form, divide the numerator and denominator both by their GCF.
If the numerator and denominator have no common factors other than 1, the fraction is already simplified.
Here, 11/4 is already in its simplest form.
Step 3: Convert Back to a Mixed Fraction
If the improper fraction needs to be expressed as a mixed fraction, follow these steps:
Divide the numerator by the denominator to convert it into a mixed number.
Write the quotient as a whole number.
The remainder becomes the numerator of the fraction.
Keep the denominator the same.
Divide 11/4
Quotient = 2, Remainder = 3
So, the mixed fraction is 2 ¾
Step 4: Final Answer
Check that the fraction part is fully simplified, and the final answer is in mixed fraction format if needed.
The final answer is 2 3/4
To simplify fractions with exponents, we must follow the steps mentioned below:
Step 1: Identify the Base Exponent
Identify the numbers and variables with exponents in the fraction.
A fraction with exponents may appear as:
am/an.
Step 2: Apply the Quotient Rule for Exponents
The quotient rule states:
am/an = am-n, where a ≠ 0.
Subtract the exponent in the denominator from the exponent in the numerator.
Step 3: Simplify Coefficients (If Present)
If the fraction contains numbers without exponents, simplify them as a normal fraction.
Step 4: Handle Negative Exponents
A negative exponent means the base should be moved to the denominator (or numerator) and made positive.
Rule:
a-m = 1/am
Step 5: Simplify Exponents Inside Parentheses (If Applicable)
If an exponent is outside a fraction, apply it to both the numerator and denominator.
Rule:
(a/b)m = am/bm
Step 6: Convert to Simplest Form
Ensure there are no negative exponents.
Write the final answer in a clean, simplified format.
Simplifying fractions has numerous applications across various fields. Let’s now learn how simplifying fractions is used in different areas:
Cooking and Baking:
When following a recipe, ingredient measurements are often given in fractions. Simplifying fractions helps adjust ingredient quantities when scaling a recipe up or down. If a recipe calls for 6/12 of a cup of flour, simplifying it to 1/2 cup makes it easier to measure. This is useful while doubling or halving a recipe.
Money and Finance:
Simplifying fractions plays a crucial role in financial calculations such as budgeting, discounts, and interest rates. If an item costs $100 and the discount is 25/100, simplifying the fraction to 1/4 shows that the discount is 25%. Similarly, when dividing expenses among a group, simplified fractions help distribute costs fairly. For example, if a dinner bill of $120 is split among four people, knowing that 120/4 simplifies to $30 per person makes calculations easier.
Time Management and Scheduling:
Time is often divided into fractions, such as half an hour, a quarter of a day, or three-fourths of a meeting. Simplifying fractions allows for efficient scheduling. For instance, if a student needs to study for 90 out of 180 minutes of a 3-hour period, simplifying the fraction to 1/2 shows that they need to study for half the total time available. This is helpful in work shifts, sports practice, and planning daily routines.
Students tend to make mistakes when learning how to simplify fractions. Let us look at a few common mistakes and how to avoid them:
Simplify the fraction 8/12.
⅔.
Find the GCF:
Factors of 8: 1, 2, 4, 8
Factors of 12: 1, 2, 3, 4, 6, 12
Common factors: 1, 2, 4 (GCF = 4).
Divide the numerator and denominator by the GCF:
Numerator: 8 ÷ 4 = 2
Denominator: 12 ÷ 4 = 3
8/12 reduces to 2/3.
By dividing both parts by 4, the fraction is reduced to its simplest form.
Simplify the fraction 45/60.
¾.
Find the GCF:
Factors of 45: 1, 3, 5, 9, 15, 45
Factors of 60: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60
Common factors: 1, 3, 5, 15 → Greatest is 15.
Divide by the GCF:
Numerator: 45 ÷ 15 = 3
Denominator: 60 ÷ 15 = 4
45/60 simplifies to 3/4.
Dividing both the numerator and the denominator by 15 gives the fraction in the simplest form.
Simplify the fraction 36/48.
¾.
Find the GCF:
Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36
Factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48
Common factors: 1, 2, 3, 4, 6, 12 → The Greatest is 12.
Divide by the GCF:
Numerator: 36 ÷ 12 = 3
Denominator: 48 ÷ 12 = 4
36/48 simplifies to 3/4.
Both numbers are divided by 12, resulting in the fraction's simplest form.
Simplify 100/125.
⅘.
Find the GCF:
Factors of 100: 1, 2, 4, 5, 10, 20, 25, 50, 100
Factors of 125: 1, 5, 25, 125
Common factors: 1, 5, 25 → Greatest is 25.
Divide by the GCF:
Numerator: 100 ÷ 25 = 4
Denominator: 125 ÷ 25 = 5
100/125 simplifies to 4/5.
Dividing by the GCF (25) reduces the fraction to its lowest terms.
Simplify 9/27
⅓.
Find the GCF:
Factors of 9: 1, 3, 9
Factors of 27: 1, 3, 9, 27
Common factors: 1, 3, 9 → Greatest is 9.
Divide by the GCF:
Numerator: 9 ÷ 9 = 1
Denominator: 27 ÷ 9 = 3
9/27 simplifies to 1/3.
The fraction is fully reduced by dividing both numbers by 9.
Hiralee Lalitkumar Makwana has almost two years of teaching experience. She is a number ninja as she loves numbers. Her interest in numbers can be seen in the way she cracks math puzzles and hidden patterns.
: She loves to read number jokes and games.