What is 2/9 plus 10/12? (Answer: 19/18)

Exact Answer

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Problem: What is 2/9 plus 10/12?
Formula / Expression: 2/9 + 10/12
Final Answer: 1 1/18 (19/18)
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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 2/9 by 4, and multiply the numerator and denominator of 10/12 by 3 so both fractions share the common base 36.
Working: 2 × 4/9 × 4 = 8/36 and 10 × 3/12 × 3 = 30/36

Step 3: Add the Numerators
Now add the numerators (8 + 30 = 38) and keep the common denominator 36 unchanged.
Working: 8 + 30/36 = 38/36

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 38 and 36, which is 2. Divide both the numerator and denominator by 2.
Working: 38 ÷ 2/36 ÷ 2 = 19/18

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (19) is greater than the denominator (18), divide 19 by 18: it goes in 1 whole time(s) with a remainder of 1, giving the mixed number 1 1/18.
Working: 19/18 = 1 1/18

Step 6: Decimal & Percentage Representation
Dividing the numerator 19 by denominator 18 produces a repeating decimal (approximately 1.055556, or 105.5556%).
Working: 19 ÷ 18 = 1.055556 (105.5556%)

Key Values:
- Simplified Fraction: 19/18
- Mixed Number Form: 1 1/18
- Decimal Value: 1.055556
- Percentage: 105.5556%

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Solved with FractionsCalc:
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2/9 + 10/12 = 19/18

Simplified Fraction

19/18

Mixed Number

1 1/18

Decimal Value

1.055556

Percentage

105.5556%

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Step-by-Step Solution: 2/9 + 10/12

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 2/9 by 4, and multiply the numerator and denominator of 10/12 by 3 so both fractions share the common base 36.

2 × 4/9 × 4 = 8/36 and 10 × 3/12 × 3 = 30/36

Step 3

Add the Numerators

Now add the numerators (8 + 30 = 38) and keep the common denominator 36 unchanged.

8 + 30/36 = 38/36

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 38 and 36, which is 2. Divide both the numerator and denominator by 2.

38 ÷ 2/36 ÷ 2 = 19/18

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (19) is greater than the denominator (18), divide 19 by 18: it goes in 1 whole time(s) with a remainder of 1, giving the mixed number 1 1/18.

19/18 = 11/18

Step 6

Decimal & Percentage Representation

Dividing the numerator 19 by denominator 18 produces a repeating decimal (approximately 1.055556, or 105.5556%).

19 ÷ 18 = 1.055556 (105.5556%)

Visual Representation

The diagram below illustrates 2/9 plus 10/12 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`19/18`
Mixed Number Form	`1 1/18`
Decimal Form	`1.055556`
Percentage	`105.5556%`

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Frequently Asked Questions

What is 2/9 plus 10/12 as a fraction?

2/9 + 10/12 in simplest fraction form is 19/18 (or 1 1/18 as a mixed number).

What is 2/9 plus 10/12 as a decimal?

2/9 + 10/12 converted to a decimal is 1.055556.

What is 2/9 plus 10/12 as a percentage?

2/9 + 10/12 expressed as a percentage is 105.5556%.

How do you write 2/9 plus 10/12 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 19/18 can be written as the mixed number 1 1/18.

Does 2/9 plus 10/12 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.055556...) because the denominator contains prime factors other than 2 and 5.