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Ratio ↔ Fraction Conversion

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Introduction

Ratios and fractions are two ways to represent the same relationship between numbers. Converting between them is a basic but essential skill for solving many ratio problems.

In this lesson we learn how to convert a ratio into a fraction and how to express a fraction as a ratio, using clear explanations followed by the matching math steps.

Pattern: Ratio ↔ Fraction Conversion

Pattern: Ratio ↔ Fraction Conversion

Key rules:

Ratio a : b → Fraction = a/b
Fraction p/q → Ratio = p : q
If ratio has more than two terms (a : b : c), each pair can be written as fractions a/b, b/c, etc.

Always simplify after conversion by dividing numerator & denominator by GCD.

Step-by-Step Example

Question

Convert the ratio 18 : 24 into a fraction. Then convert the fraction 5/8 into a ratio.

Solution

  1. Step 1: Convert ratio to fraction.

    The ratio 18 : 24 means 18 parts to 24 parts. So, it can be written as the fraction 18/24.

  2. Step 2: Simplify the fraction.

    Both 18 and 24 can be divided by 6. 18 ÷ 6 = 3, 24 ÷ 6 = 4 → fraction = 3/4.

  3. Step 3: Convert fraction to ratio.

    The fraction 5/8 can be written as the ratio 5 : 8.

  4. Step 4: Simplify the ratio if possible.

    Since 5 and 8 have no common factor other than 1, the ratio remains 5 : 8.

  5. Step 5: Final Answer.

    18 : 24 → 3/4
    5/8 → 5 : 8

  6. Step 6: Quick Check.

    When we converted 18 : 24 into a fraction, we got 3/4. Decimal check: 18 ÷ 24 = 0.75 and 3 ÷ 4 = 0.75 → both match ✅ When we converted 5/8 into a ratio, we got 5 : 8. Decimal check: 5 ÷ 8 = 0.625 → same as the original fraction 5/8 = 0.625 ✅ So, the conversions are correct.

Quick Variations

Decimal → Ratio: Convert the decimal to a fraction first, then to ratio. Example: 0.6 → 60/100 → simplify to 3/5 → ratio = 3 : 5.

Mixed numbers: Convert a mixed number to an improper fraction, then to ratio. Example: 2 1/2 = 5/2 → ratio = 5 : 2.

Multiple-term ratios: For a : b : c = 4 : 6 : 10, you can form useful fractions such as a/(b+c) = 4/(6+10) = 4/16 = 1/4 in some problems.

Trick to Always Use

  • Step 1: Ratio → fraction by writing a/b, then simplify.
  • Step 2: Fraction → ratio by writing p : q, then simplify.
  • Step 3: For decimals, multiply to remove decimal places before simplifying.
  • Step 4: Verify by converting both forms to decimals for a quick check.

Summary

Converting between ratios and fractions is straightforward:

  • Ratio → Fraction: a : b → a/b
  • Fraction → Ratio: p/q → p : q
  • Decimals: Convert to fractions first, then to ratios
  • Always simplify: Divide by GCD if possible
  • Quick check: Convert to decimal form to confirm consistency

Once you master this, ratio ↔ fraction conversions become second nature in aptitude questions.

Practice

(1/5)
1. Convert the ratio 12 : 20 into a fraction in simplest form.
easy
A. 3/5
B. 12/20
C. 4/5
D. 2/5

Solution

  1. Step 1: Convert ratio to fraction

    Ratio = 12 : 20 → Fraction = 12/20.

  2. Step 2: Find GCD

    Simplify → GCD of 12 and 20 = 4.

  3. Step 3: Divide to simplify

    12 ÷ 4 = 3, 20 ÷ 4 = 5.

  4. Final Answer:

    3/5 → Option A

  5. Quick Check:

    12 ÷ 20 = 0.6, 3 ÷ 5 = 0.6 ✅
Hint: Always divide numerator and denominator by GCD.
Common Mistakes: Stopping at 12/20 without simplifying further.
2. Convert the fraction 7/8 into a ratio.
easy
A. 7 : 9
B. 7 : 8
C. 8 : 7
D. 14 : 16

Solution

  1. Step 1: Identify the fraction

    Fraction = 7/8.

  2. Step 2: Write numerator and denominator as a ratio

    Convert to ratio → 7 : 8.

  3. Final Answer:

    7 : 8 → Option B

  4. Quick Check:

    7 ÷ 8 = 0.875; ratio 7 : 8 → 7/8 = 0.875 ✅
Hint: Write numerator : denominator directly.
Common Mistakes: Inverting ratio as 8 : 7 instead of 7 : 8.
3. Convert the ratio 36 : 48 into a fraction in simplest form.
medium
A. 3/4
B. 4/3
C. 9/12
D. 6/8

Solution

  1. Step 1: Convert ratio to fraction

    Ratio = 36 : 48 → Fraction = 36/48.

  2. Step 2: Find GCD

    Simplify → GCD of 36 and 48 = 12.

  3. Step 3: Divide to simplify

    36 ÷ 12 = 3, 48 ÷ 12 = 4.

  4. Final Answer:

    3/4 → Option A

  5. Quick Check:

    36 ÷ 48 = 0.75, 3 ÷ 4 = 0.75 ✅
Hint: Reduce large ratios step by step using GCD.
Common Mistakes: Stopping at 9/12 instead of reducing to 3/4.
4. Express the fraction 11/22 as a ratio in simplest form.
medium
A. 11 : 22
B. 1 : 2
C. 2 : 1
D. 5 : 11

Solution

  1. Step 1: Identify the fraction

    Fraction = 11/22.

  2. Step 2: Write as ratio

    Write as ratio → 11 : 22.

  3. Step 3: Simplify using GCD

    Simplify by GCD 11 → (11 ÷ 11) : (22 ÷ 11) = 1 : 2.

  4. Final Answer:

    1 : 2 → Option B

  5. Quick Check:

    11 ÷ 22 = 0.5, ratio 1 : 2 → 1/2 = 0.5 ✅
Hint: Cancel numerator & denominator directly by common factors.
Common Mistakes: Leaving ratio as 11 : 22 without simplifying.
5. Convert the decimal 0.6 into a ratio.
medium
A. 6 : 100
B. 3 : 5
C. 5 : 3
D. 60 : 100

Solution

  1. Step 1: Express decimal as fraction

    Decimal = 0.6 → 0.6 = 60/100.

  2. Step 2: Simplify the fraction

    Simplify → divide numerator & denominator by 20 → 60/100 = 3/5.

  3. Step 3: Convert to ratio

    Convert fraction → ratio = 3 : 5.

  4. Final Answer:

    3 : 5 → Option B

  5. Quick Check:

    3 ÷ 5 = 0.6 ✅
Hint: For decimals, multiply by 10/100 to convert, then simplify.
Common Mistakes: Writing 60 : 100 without reducing to 3 : 5.