What is 1/12 plus 2/3? (Answer: 3/4)

Exact Answer

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Problem: What is 1/12 plus 2/3?
Formula / Expression: 1/12 + 2/3
Final Answer: 3/4
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Step-by-Step Solution:

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

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

Step 3: Add the Numerators
Now add the numerators (1 + 8 = 9) and keep the common denominator 12 unchanged.
Working: 1 + 8/12 = 9/12

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 9 and 12, which is 3. Divide both the numerator and denominator by 3.
Working: 9 ÷ 3/12 ÷ 3 = 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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1/12 + 2/3 = 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: 1/12 + 2/3

Step 1

Find the Least Common Denominator (LCD)

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

LCD(12, 3) = 12

Step 2

Convert to Equivalent Fractions with Common Denominator 12

Multiply the numerator and denominator of 1/12 by 1, and multiply the numerator and denominator of 2/3 by 4 so both fractions share the common base 12.

1 × 1/12 × 1 = 1/12 and 2 × 4/3 × 4 = 8/12

Step 3

Add the Numerators

Now add the numerators (1 + 8 = 9) and keep the common denominator 12 unchanged.

1 + 8/12 = 9/12

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 9 and 12, which is 3. Divide both the numerator and denominator by 3.

9 ÷ 3/12 ÷ 3 = 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 1/12 plus 2/3 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 1/12 plus 2/3 as a fraction?

1/12 + 2/3 in simplest fraction form is 3/4.

What is 1/12 plus 2/3 as a decimal?

1/12 + 2/3 converted to a decimal is 0.75.

What is 1/12 plus 2/3 as a percentage?

1/12 + 2/3 expressed as a percentage is 75%.

Does 1/12 plus 2/3 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.