What is 7/12 plus 2/3? (Answer: 5/4)

Exact Answer

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Problem: What is 7/12 plus 2/3?
Formula / Expression: 7/12 + 2/3
Final Answer: 1 1/4 (5/4)
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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 7/12 by 1, and multiply the numerator and denominator of 2/3 by 4 so both fractions share the common base 12.
Working: 7 × 1/12 × 1 = 7/12 and 2 × 4/3 × 4 = 8/12

Step 3: Add the Numerators
Now add the numerators (7 + 8 = 15) and keep the common denominator 12 unchanged.
Working: 7 + 8/12 = 15/12

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 15 and 12, which is 3. Divide both the numerator and denominator by 3.
Working: 15 ÷ 3/12 ÷ 3 = 5/4

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (5) is greater than the denominator (4), divide 5 by 4: it goes in 1 whole time(s) with a remainder of 1, giving the mixed number 1 1/4.
Working: 5/4 = 1 1/4

Step 6: Decimal & Percentage Representation
Dividing the numerator 5 by denominator 4 yields an exact terminating decimal of 1.25 (or 125%).
Working: 5 ÷ 4 = 1.25 (125%)

Key Values:
- Simplified Fraction: 5/4
- Mixed Number Form: 1 1/4
- Decimal Value: 1.25
- Percentage: 125%

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7/12 + 2/3 = 5/4

Simplified Fraction

5/4

Mixed Number

1 1/4

Decimal Value

1.25

Percentage

125%

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Step-by-Step Solution: 7/12 + 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 7/12 by 1, and multiply the numerator and denominator of 2/3 by 4 so both fractions share the common base 12.

7 × 1/12 × 1 = 7/12 and 2 × 4/3 × 4 = 8/12

Step 3

Add the Numerators

Now add the numerators (7 + 8 = 15) and keep the common denominator 12 unchanged.

7 + 8/12 = 15/12

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 15 and 12, which is 3. Divide both the numerator and denominator by 3.

15 ÷ 3/12 ÷ 3 = 5/4

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (5) is greater than the denominator (4), divide 5 by 4: it goes in 1 whole time(s) with a remainder of 1, giving the mixed number 1 1/4.

5/4 = 11/4

Step 6

Decimal & Percentage Representation

Dividing the numerator 5 by denominator 4 yields an exact terminating decimal of 1.25 (or 125%).

5 ÷ 4 = 1.25 (125%)

Visual Representation

The diagram below illustrates 7/12 plus 2/3 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`5/4`
Mixed Number Form	`1 1/4`
Decimal Form	`1.25`
Percentage	`125%`

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Frequently Asked Questions

What is 7/12 plus 2/3 as a fraction?

7/12 + 2/3 in simplest fraction form is 5/4 (or 1 1/4 as a mixed number).

What is 7/12 plus 2/3 as a decimal?

7/12 + 2/3 converted to a decimal is 1.25.

What is 7/12 plus 2/3 as a percentage?

7/12 + 2/3 expressed as a percentage is 125%.

How do you write 7/12 plus 2/3 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 5/4 can be written as the mixed number 1 1/4.

Does 7/12 plus 2/3 result in a terminating or repeating decimal?

It results in an exact terminating decimal (1.25) because the denominator in simplest terms contains only prime factors 2 and/or 5.