What is 8/12 plus 3/4? (Answer: 17/12)

Exact Answer

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Problem: What is 8/12 plus 3/4?
Formula / Expression: 8/12 + 3/4
Final Answer: 1 5/12 (17/12)
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
Notice that 12 is an exact multiple of 4 (4 × 3 = 12). The Least Common Denominator (LCD) is simply 12, meaning we only need to scale one fraction.
Working: LCD(12, 4) = 12

Step 2: Convert to Equivalent Fractions with Common Denominator 12
Multiply the numerator and denominator of 8/12 by 1, and multiply the numerator and denominator of 3/4 by 3 so both fractions share the common base 12.
Working: 8 × 1/12 × 1 = 8/12 and 3 × 3/4 × 3 = 9/12

Step 3: Add the Numerators
Now add the numerators (8 + 9 = 17) and keep the common denominator 12 unchanged.
Working: 8 + 9/12 = 17/12

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 17 and 12 is 1, confirming that 17/12 cannot be reduced further—it is already in its simplest irreducible form.
Working: 17/12

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (17) is greater than the denominator (12), divide 17 by 12: it goes in 1 whole time(s) with a remainder of 5, giving the mixed number 1 5/12.
Working: 17/12 = 1 5/12

Step 6: Decimal & Percentage Representation
Dividing the numerator 17 by denominator 12 produces a repeating decimal (approximately 1.416667, or 141.6667%).
Working: 17 ÷ 12 = 1.416667 (141.6667%)

Key Values:
- Simplified Fraction: 17/12
- Mixed Number Form: 1 5/12
- Decimal Value: 1.416667
- Percentage: 141.6667%

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Solved with FractionsCalc:
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8/12 + 3/4 = 17/12

Simplified Fraction

17/12

Mixed Number

1 5/12

Decimal Value

1.416667

Percentage

141.6667%

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Step-by-Step Solution: 8/12 + 3/4

Step 1

Find the Least Common Denominator (LCD)

Notice that 12 is an exact multiple of 4 (4 × 3 = 12). The Least Common Denominator (LCD) is simply 12, meaning we only need to scale one fraction.

LCD(12, 4) = 12

Step 2

Convert to Equivalent Fractions with Common Denominator 12

Multiply the numerator and denominator of 8/12 by 1, and multiply the numerator and denominator of 3/4 by 3 so both fractions share the common base 12.

8 × 1/12 × 1 = 8/12 and 3 × 3/4 × 3 = 9/12

Step 3

Add the Numerators

Now add the numerators (8 + 9 = 17) and keep the common denominator 12 unchanged.

8 + 9/12 = 17/12

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 17 and 12 is 1, confirming that 17/12 cannot be reduced further—it is already in its simplest irreducible form.

17/12

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (17) is greater than the denominator (12), divide 17 by 12: it goes in 1 whole time(s) with a remainder of 5, giving the mixed number 1 5/12.

17/12 = 15/12

Step 6

Decimal & Percentage Representation

Dividing the numerator 17 by denominator 12 produces a repeating decimal (approximately 1.416667, or 141.6667%).

17 ÷ 12 = 1.416667 (141.6667%)

Visual Representation

The diagram below illustrates 8/12 plus 3/4 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`17/12`
Mixed Number Form	`1 5/12`
Decimal Form	`1.416667`
Percentage	`141.6667%`

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Frequently Asked Questions

What is 8/12 plus 3/4 as a fraction?

8/12 + 3/4 in simplest fraction form is 17/12 (or 1 5/12 as a mixed number).

What is 8/12 plus 3/4 as a decimal?

8/12 + 3/4 converted to a decimal is 1.416667.

What is 8/12 plus 3/4 as a percentage?

8/12 + 3/4 expressed as a percentage is 141.6667%.

How do you write 8/12 plus 3/4 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 17/12 can be written as the mixed number 1 5/12.

Does 8/12 plus 3/4 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.416667...) because the denominator contains prime factors other than 2 and 5.