What is 3/9 plus 5/12? (Answer: 3/4)

Exact Answer

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Problem: What is 3/9 plus 5/12?
Formula / Expression: 3/9 + 5/12
Final Answer: 3/4
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 9 and 12 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 36 (which is smaller than their product 9 × 12 = 108, keeping the calculation simpler).
Working: LCD(9, 12) = 36

Step 2: Convert to Equivalent Fractions with Common Denominator 36
Multiply the numerator and denominator of 3/9 by 4, and multiply the numerator and denominator of 5/12 by 3 so both fractions share the common base 36.
Working: 3 × 4/9 × 4 = 12/36 and 5 × 3/12 × 3 = 15/36

Step 3: Add the Numerators
Now add the numerators (12 + 15 = 27) and keep the common denominator 36 unchanged.
Working: 12 + 15/36 = 27/36

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 27 and 36, which is 9. Divide both the numerator and denominator by 9.
Working: 27 ÷ 9/36 ÷ 9 = 3/4

Step 5: Decimal & Percentage Representation
Dividing the numerator 3 by denominator 4 yields an exact terminating decimal of 0.75 (or 75%).
Working: 3 ÷ 4 = 0.75 (75%)

Key Values:
- Simplified Fraction: 3/4
- Mixed Number Form: 3/4
- Decimal Value: 0.75
- Percentage: 75%

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Solved with FractionsCalc:
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3/9 + 5/12 = 3/4

Simplified Fraction

3/4

Mixed Number

Proper (3/4)

Decimal Value

0.75

Percentage

75%

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Step-by-Step Solution: 3/9 + 5/12

Step 1

Find the Least Common Denominator (LCD)

The denominators 9 and 12 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 36 (which is smaller than their product 9 × 12 = 108, keeping the calculation simpler).

LCD(9, 12) = 36

Step 2

Convert to Equivalent Fractions with Common Denominator 36

Multiply the numerator and denominator of 3/9 by 4, and multiply the numerator and denominator of 5/12 by 3 so both fractions share the common base 36.

3 × 4/9 × 4 = 12/36 and 5 × 3/12 × 3 = 15/36

Step 3

Add the Numerators

Now add the numerators (12 + 15 = 27) and keep the common denominator 36 unchanged.

12 + 15/36 = 27/36

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 27 and 36, which is 9. Divide both the numerator and denominator by 9.

27 ÷ 9/36 ÷ 9 = 3/4

Step 5

Decimal & Percentage Representation

Dividing the numerator 3 by denominator 4 yields an exact terminating decimal of 0.75 (or 75%).

3 ÷ 4 = 0.75 (75%)

Visual Representation

The diagram below illustrates 3/9 plus 5/12 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`3/4`
Mixed Number Form	`3/4`
Decimal Form	`0.75`
Percentage	`75%`

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Frequently Asked Questions

What is 3/9 plus 5/12 as a fraction?

3/9 + 5/12 in simplest fraction form is 3/4.

What is 3/9 plus 5/12 as a decimal?

3/9 + 5/12 converted to a decimal is 0.75.

What is 3/9 plus 5/12 as a percentage?

3/9 + 5/12 expressed as a percentage is 75%.

Does 3/9 plus 5/12 result in a terminating or repeating decimal?

It results in an exact terminating decimal (0.75) because the denominator in simplest terms contains only prime factors 2 and/or 5.