What is 2/3 plus 10/12? (Answer: 3/2)

Exact Answer

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Problem: What is 2/3 plus 10/12?
Formula / Expression: 2/3 + 10/12
Final Answer: 1 1/2 (3/2)
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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(3, 12) = 12

Step 2: Convert to Equivalent Fractions with Common Denominator 12
Multiply the numerator and denominator of 2/3 by 4, and multiply the numerator and denominator of 10/12 by 1 so both fractions share the common base 12.
Working: 2 × 4/3 × 4 = 8/12 and 10 × 1/12 × 1 = 10/12

Step 3: Add the Numerators
Now add the numerators (8 + 10 = 18) and keep the common denominator 12 unchanged.
Working: 8 + 10/12 = 18/12

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 18 and 12, which is 6. Divide both the numerator and denominator by 6.
Working: 18 ÷ 6/12 ÷ 6 = 3/2

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (3) is greater than the denominator (2), divide 3 by 2: it goes in 1 whole time(s) with a remainder of 1, giving the mixed number 1 1/2.
Working: 3/2 = 1 1/2

Step 6: Decimal & Percentage Representation
Dividing the numerator 3 by denominator 2 yields an exact terminating decimal of 1.5 (or 150%).
Working: 3 ÷ 2 = 1.5 (150%)

Key Values:
- Simplified Fraction: 3/2
- Mixed Number Form: 1 1/2
- Decimal Value: 1.5
- Percentage: 150%

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2/3 + 10/12 = 3/2

Simplified Fraction

3/2

Mixed Number

1 1/2

Decimal Value

1.5

Percentage

150%

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Step-by-Step Solution: 2/3 + 10/12

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(3, 12) = 12

Step 2

Convert to Equivalent Fractions with Common Denominator 12

Multiply the numerator and denominator of 2/3 by 4, and multiply the numerator and denominator of 10/12 by 1 so both fractions share the common base 12.

2 × 4/3 × 4 = 8/12 and 10 × 1/12 × 1 = 10/12

Step 3

Add the Numerators

Now add the numerators (8 + 10 = 18) and keep the common denominator 12 unchanged.

8 + 10/12 = 18/12

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 18 and 12, which is 6. Divide both the numerator and denominator by 6.

18 ÷ 6/12 ÷ 6 = 3/2

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (3) is greater than the denominator (2), divide 3 by 2: it goes in 1 whole time(s) with a remainder of 1, giving the mixed number 1 1/2.

3/2 = 11/2

Step 6

Decimal & Percentage Representation

Dividing the numerator 3 by denominator 2 yields an exact terminating decimal of 1.5 (or 150%).

3 ÷ 2 = 1.5 (150%)

Visual Representation

The diagram below illustrates 2/3 plus 10/12 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`3/2`
Mixed Number Form	`1 1/2`
Decimal Form	`1.5`
Percentage	`150%`

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Frequently Asked Questions

What is 2/3 plus 10/12 as a fraction?

2/3 + 10/12 in simplest fraction form is 3/2 (or 1 1/2 as a mixed number).

What is 2/3 plus 10/12 as a decimal?

2/3 + 10/12 converted to a decimal is 1.5.

What is 2/3 plus 10/12 as a percentage?

2/3 + 10/12 expressed as a percentage is 150%.

How do you write 2/3 plus 10/12 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 3/2 can be written as the mixed number 1 1/2.

Does 2/3 plus 10/12 result in a terminating or repeating decimal?

It results in an exact terminating decimal (1.5) because the denominator in simplest terms contains only prime factors 2 and/or 5.