Simplifying Ratio Calculator

Ratio of…
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A : B = A/GCF : B/GCF
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    1
    Your Values
    —
    2
    GCF
    —
    3
    Divide Each
    —
    ✓
    Result
    —

    What is a Ratio?

    A ratio is a quantitative relationship between two or more numbers that shows how many times one value contains the other. The ratio A : B is read as "A to B" and describes the relative proportion of two amounts.

    Ratios appear everywhere in daily life. The water-to-rice ratio while cooking is 2 : 1, meaning you need two portions of water for one portion of rice. In maps, a scale of 1 : 63,360 means one inch (2.54 cm) represents one mile (1.6 km) in the real world.

    🍳
    Cooking
    2 : 1 water-to-rice ratio
    🗺️
    Maps
    1 : 63,360 scale
    💰
    Finance
    2 : 1 debt-to-equity ratio
    🖥️
    Screens
    16 : 9 aspect ratio
    🧪
    Chemistry
    2 : 1 H to O in water
    🏆
    Sports
    3 : 1 win-loss record

    Ratios can be expressed as fractions and follow the same mathematical operations. A ratio of 3 : 4 is the same as the fraction 3/4. This connection makes ratios a bridge between whole numbers, fractions, and decimal numbers in math.

    How to Simplify a Ratio

    To simplify a ratio A : B into its simplest form, divide both terms by their Greatest Common Factor (GCF), also called the Greatest Common Divisor (GCD).

    Simplified Ratio = (A ÷ GCF) : (B ÷ GCF)

    This tool handles whole numbers, decimals, and fractions. It converts them to whole numbers where needed, then reduces those whole numbers to lowest terms using the Greatest Common Factor (GCF). The full solution shows all work and the steps to get a ratio into simplest form.

    1
    Enter Ratio
    12 : 16
    →
    2
    Find GCF
    GCF(12, 16) = 4
    →
    3
    Divide Both
    12 ÷ 4, 16 ÷ 4
    →
    ✓
    Result
    3 : 4
    12 : 16 → GCF = 4 → 12 ÷ 4 : 16 ÷ 4 = 3 : 4

    The result 3 : 4 is the simplest form because the GCF of 3 and 4 is 1 — the numbers are co-prime.

    Step One: Find the Greatest Common Factor

    To find the GCF, list all numbers that divide evenly into both sides of the ratio — these are the common factors. Then pick the largest one.

    For the ratio 8 : 12, the factors of 8 are [1, 2, 4, 8] and the factors of 12 are [1, 2, 3, 4, 6, 12]. The common factors are [1, 2, 4], so the GCF is 4.

    Finding GCF(48, 36) — Euclidean Algorithm
    48 ÷ 36 = 1 remainder 12
    36 ÷ 12 = 3 remainder 0
    GCF = 12 → 48 : 36 = 4 : 3

    Step Two: Divide Left Side and Right Side by the Common Factor

    Divide both terms of the ratio by the GCF. This reduces the ratio to the smallest possible form while keeping both parts as whole numbers.

    For 8 : 12, divide each side by 4. The result is 8 ÷ 4 : 12 ÷ 4 = 2 : 3. The simplified ratio is 2 : 3.

    The GCF is the largest number that divides evenly into both A and B. Use the Euclidean algorithm or list all factors of each number to find the GCF. A GCF calculator speeds this up for large numbers.

    Equivalent ratios — all simplify to 2 : 3
    4 : 6
    = 2 : 3
    6 : 9
    = 2 : 3
    10 : 15
    = 2 : 3
    20 : 30
    = 2 : 3

    The full solution shows all work and the steps to get a ratio into simplest form. Use it to verify homework, check proportions, or convert ratios between forms. You can also explore equivalent ratios when you need the same relationship at a different scale.

    Examples of Ratio Simplification
    Input A Input B Original Ratio Simplified Ratio Steps
    812 8 : 12 2 : 3 ÷4 both sides
    1215 12 : 15 4 : 5 ÷3 both sides
    1824 18 : 24 3 : 4 ÷6 both sides
    1636 16 : 36 4 : 9 ÷4 both sides
    2510 25 : 10 5 : 2 ÷5 both sides
    4560 45 : 60 3 : 4 ÷15 both sides

    Simplifying Whole-Number Ratios

    To simplify a ratio of two whole numbers, follow 5 steps: list the factors of A, list the factors of B, find the Greatest Common Factor (GCF) of A and B, divide A and B each by the GCF, and rewrite the ratio in simplest form.

    Simplify 20 : 30 — Find common factors
    20
    1 2 4 5 10 20
    GCF
    10
    30
    1 2 3 5 6 10 15 30
    20 ÷ 10 : 30 ÷ 10 = 2 : 3

    The ratio is already in simplest form, if the GCF equals 1. The two numbers are then co-prime — they share no common factors other than 1.

    Example: 45 : 60 simplifies to 3 : 4
    Before
    A = 45
    B = 60
    ÷ GCF(15)
    After
    A = 3
    B = 4
    The proportion stays the same — only the numbers change.

    For example, the ratio 4 : 8 is not in simplest form because the common factors of 4 and 8 are 1, 2, and 4. Divide both sides by the GCF (4) to get the simplified ratio: 4 ÷ 4 : 8 ÷ 4 = 1 : 2.

    4 : 8 =
    44
    :
    84
    = 1 : 2

    Simplifying Decimal and Fraction Ratios

    Convert mixed numbers to improper fractions first, if A or B are mixed numbers. Multiply both values by the same factor of 10 that eliminates all decimal places, if A or B are decimal numbers. For more examples, see the decimal ratio calculator. Find the Least Common Denominator (LCD) and rewrite, if both are fractions with unlike denominators. For fraction-specific steps, use the fraction ratio calculator. Then simplify as whole numbers.

    Decimal: 0.5 : 1.5
    1
    Identify decimal places (1 place each)
    ↓
    2
    Multiply both by 10 → 5 : 15
    ↓
    3
    GCF(5, 15) = 5 → divide both
    ↓
    ✓
    1 : 3
    Same approach for fractions — multiply by the LCD first
    Fraction: ½ : ¾
    1
    LCD of 2 and 4 = 4
    ↓
    2
    Multiply both by 4 → 2 : 3
    ↓
    ✓
    GCF(2,3) = 1 → Already simplified: 2 : 3

    Decimal ratios are converted to whole number ratios by multiplying all terms by a power of 10 that eliminates all decimal places. The calculator handles this conversion automatically for terminating decimals.

    Terminating Decimal
    1 : 2.5
    × 2
    Whole Number Ratio
    2 : 5
    Repeating Decimal
    1 : 3.3̄
    × 3
    Whole Number Ratio
    3 : 10
    Choose the smallest multiplier that eliminates all decimals.
    Tip: The multiplier needed depends on the specific repeating decimal. For example, 0.3̄ (repeating 3) can be written as 1/3. The appropriate multiplier eliminates the repeating part and produces whole numbers.

    Example: Simplify the ratio 6 : 10

    The factors of 6 are: 1, 2, 3, 6. The factors of 10 are: 1, 2, 5, 10.

    Step 1: Find Greatest Common Factor
    6 : 10
    Factors of 6:
    1 2 3 6
    Factors of 10:
    1 2 5 10
    GCF ← 2
    Step 2: Divide by the Common Factor
    6 ÷ 2 = 3
    10 ÷ 2 = 5
    6 : 10 = 3 : 5 in simplest form

    The Greatest Common Factor (GCF) of 6 and 10 is 2. Divide both terms by 2: 6 ÷ 2 = 3 and 10 ÷ 2 = 5.

    Example: Simplify the ratio 8 : 36

    The factors of 8 are: 1, 2, 4, 8. The factors of 36 are: 1, 2, 3, 4, 6, 9, 12, 18, 36.

    Step 1: Find Greatest Common Factor
    8 : 36
    Factors of 8:
    1 2 4 8
    Factors of 36:
    1 2 3 4 6 9 12 18 36
    GCF ← 4
    Step 2: Divide by the Common Factor
    8 ÷ 4 = 2
    36 ÷ 4 = 9
    8 : 36 = 2 : 9 in simplest form

    The Greatest Common Factor (GCF) of 8 and 36 is 4. Divide both terms by 4: 8 ÷ 4 = 2 and 36 ÷ 4 = 9.

    Example: Simplify the ratio 3 : 8

    The factors of 3 are: 1, 3. The factors of 8 are: 1, 2, 4, 8.

    Step 1: Find Greatest Common Factor
    3 : 8
    Factors of 3:
    1 3
    Factors of 8:
    1 2 4 8
    GCF ← 1
    3 : 8 is already fully simplified. A GCF of 1 means the ratio cannot be reduced further.

    The Greatest Common Factor (GCF) of 3 and 8 is 1. The ratio is already in its simplest form.

    Converting Ratios to 1:n and n:1 Forms

    A ratio A : B can be expressed in 1 : m form or n : 1 form. This shows how many parts of one quantity relate to one part of the other.

    Input
    A = 8, B = 12
    →
    GCF
    GCF(8,12) = 4
    →
    Simplified
    2 : 3
    Standard form 2 : 3
    Unit form (1 : n) 1 : 1.5
    Fraction form 2/3
    1 : m form — divide both sides by A:
    10 : 12 =
    1010
    :
    1210
    = 1 : 1.2
    n : 1 form — divide both sides by B:
    10 : 12 =
    1012
    :
    1212
    = 0.833 : 1

    Calculating ratios of 3 numbers

    Simplifying 3-number ratios works the same as 2-number ratios. Find the Greatest Common Factor (GCF) of all 3 numbers and divide each term by the GCF.

    15 : 30 : 45 → GCF = 5 → 1 : 2 : 3

    Visualizing a 3-Part Ratio

    12 : 18 : 24 simplifies to 2 : 3 : 4 (GCF = 6)

    Before
    12
    18
    24
    ÷ 6
    After
    2
    3
    4

    Consider a chemical reaction where two moles of nitrogen (N₂) and six moles of hydrogen (H₂) produce four moles of ammonia (NH₃). The mole ratio is 2 : 6 : 4. The GCF is 2, so the simplified ratio is 1 : 3 : 2.

    1. Simplified ratio by dividing all sides with their GCF (2):
    2 : 6 : 4 =
    22
    :
    62
    :
    42
    = 1 : 3 : 2
    2. 1 : n : m form by dividing all sides by A (i.e., by 2):
    2 : 6 : 4 =
    22
    :
    62
    :
    42
    = 1 : 3 : 2
    3. n : 1 : m form by dividing all sides by B (i.e., by 6):
    2 : 6 : 4 =
    26
    :
    66
    :
    46
    = 0.33 : 1 : 0.66
    4. n : m : 1 form by dividing all sides by C (i.e., by 4):
    2 : 6 : 4 =
    24
    :
    64
    :
    44
    = 0.5 : 1.5 : 1

    Simplifying Ratios of 4 Numbers

    Four-number ratios follow the exact same GCF-based simplification as 2- and 3-number ratios. Find the Greatest Common Factor of all four terms and divide each one.

    12 : 18 : 24 : 30 → GCF = 6 → 2 : 3 : 4 : 5
    Before
    12
    18
    24
    30
    ÷ GCF(6)
    After
    2
    3
    4
    5

    Four-part ratios work the same way — the GCF must divide evenly into all four values. Divide each term by the GCF to get the simplified ratio.

    Why Is Simplifying Ratios Important?

    Simplifying ratios makes them easier to read, compare, and use in real-world calculations. A ratio of 48 : 72 conveys the same proportion as 2 : 3, but the simplified version is instantly clear.

    There are 4 direct benefits of simplifying ratios:

    👁️
    Readability
    Smaller numbers are faster to process and less prone to errors in calculations.
    ✅
    Comparison
    Simplified ratios make it easy to compare multiple ratios side by side.
    📏
    Standardization
    Scientific formulas, recipes, and blueprints use simplified ratios as standard practice.
    ⚡
    Efficiency
    Reduced numbers speed up mental math and reduce computation time.
    ❌ Unsimplified
    48 : 72
    Harder to read
    →
    ✓ Simplified
    2 : 3
    Crystal clear

    Simplifying ratios is a foundational skill in math that connects to fractions, proportions, percentages, and scaling across science, business, and daily life. For percent-based comparisons, see the ratio percentage calculator.

    A ratio is fully simplified when the Greatest Common Factor (GCF) of all terms equals 1.

    How to Scale a Ratio Up or Down

    Scaling a ratio means multiplying or dividing all terms by the same number to create an equivalent ratio with larger or smaller values.

    Scaling up multiplies all terms. Scaling down divides all terms. The proportion stays identical in both cases.

    📈
    Scale Up
    Multiply all terms by the same factor to increase values proportionally.
    📉
    Scale Down
    Divide all terms by a common factor to reduce values proportionally.
    Before
    2 : 3
    × 5
    After
    10 : 15
    Before
    20 : 30
    ÷ 10
    After
    2 : 3

    Scaling is the reverse of simplifying. Simplifying finds the smallest equivalent ratio; scaling creates larger equivalent ratios for practical use.

    Scaling preserves proportion. The ratio 2 : 3 and 10 : 15 represent the same relationship — only the magnitude differs.
    FAQ

    Frequently Asked Questions

    Common questions about simplifying ratios.

    To simplify a ratio A : B, find the Greatest Common Factor (GCF) of A and B, then divide both sides by the GCF. The result is A/GCF : B/GCF. You can use the calculator above to check your answer.
    <strong>The simplest form of the ratio 25 : 10 is 5 : 2.</strong> The Greatest Common Factor (GCF) of 25 and 10 is 5. Divide both sides by 5 to get 25/5 : 10/5 = 5 : 2.
    A ratio is in simplest form when the Greatest Common Factor (GCF) of all terms equals 1 — meaning the numbers are co-prime and share no common factors other than 1.
    Yes. Multiply both terms by a power of 10 to eliminate decimal places first, then simplify using the GCF method. For example, 0.5 : 1.5 → multiply by 10 → 5 : 15 → GCF is 5 → 1 : 3.
    Yes. Find the Least Common Denominator (LCD) of the fractions, multiply all terms by the LCD to get whole numbers, then simplify. For ½ : ¾, the LCD is 4: multiply to get 2 : 3 → already in simplest form → 2 : 3.
    Find the GCF of all three numbers and divide each term by it. For 12 : 18 : 24, the GCF is 6. Divide each: 2 : 3 : 4.
    A ratio A : B compares two quantities, while a fraction A/B represents a part of a whole. They are related: the ratio 3 : 4 corresponds to the fraction 3/4.
    The 1 : n form expresses a ratio with the first term as 1. Divide both terms by A. For 10 : 12, divide by 10 to get 1 : 1.2.
    The n : 1 form expresses a ratio with the second term as 1. Divide both terms by B. For 10 : 12, divide by 12 to get 0.833 : 1.
    Multiply all terms by the same number to scale up, or divide all terms by a common factor to scale down. For example, 2 : 3 × 5 = 10 : 15.
    A ratio compares two quantities (A : B). A proportion states that two ratios are equal (A : B = C : D). Ratios are building blocks; proportions are equations that use ratios.