What is 2/9 plus 12/16? (Answer: 35/36)

Exact Answer

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Problem: What is 2/9 plus 12/16?
Formula / Expression: 2/9 + 12/16
Final Answer: 35/36
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 9 and 16 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 9 × 16 = 144.
Working: LCD(9, 16) = 144

Step 2: Convert to Equivalent Fractions with Common Denominator 144
Multiply the numerator and denominator of 2/9 by 16, and multiply the numerator and denominator of 12/16 by 9 so both fractions share the common base 144.
Working: 2 × 16/9 × 16 = 32/144 and 12 × 9/16 × 9 = 108/144

Step 3: Add the Numerators
Now add the numerators (32 + 108 = 140) and keep the common denominator 144 unchanged.
Working: 32 + 108/144 = 140/144

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 140 and 144, which is 4. Divide both the numerator and denominator by 4.
Working: 140 ÷ 4/144 ÷ 4 = 35/36

Step 5: Decimal & Percentage Representation
Dividing the numerator 35 by denominator 36 produces a repeating decimal (approximately 0.972222, or 97.2222%).
Working: 35 ÷ 36 = 0.972222 (97.2222%)

Key Values:
- Simplified Fraction: 35/36
- Mixed Number Form: 35/36
- Decimal Value: 0.972222
- Percentage: 97.2222%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-9-plus-12-16/
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2/9 + 12/16 = 35/36

Simplified Fraction

35/36

Mixed Number

Proper (35/36)

Decimal Value

0.972222

Percentage

97.2222%

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Step-by-Step Solution: 2/9 + 12/16

Step 1

Find the Least Common Denominator (LCD)

The denominators 9 and 16 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 9 × 16 = 144.

LCD(9, 16) = 144

Step 2

Convert to Equivalent Fractions with Common Denominator 144

Multiply the numerator and denominator of 2/9 by 16, and multiply the numerator and denominator of 12/16 by 9 so both fractions share the common base 144.

2 × 16/9 × 16 = 32/144 and 12 × 9/16 × 9 = 108/144

Step 3

Add the Numerators

Now add the numerators (32 + 108 = 140) and keep the common denominator 144 unchanged.

32 + 108/144 = 140/144

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 140 and 144, which is 4. Divide both the numerator and denominator by 4.

140 ÷ 4/144 ÷ 4 = 35/36

Step 5

Decimal & Percentage Representation

Dividing the numerator 35 by denominator 36 produces a repeating decimal (approximately 0.972222, or 97.2222%).

35 ÷ 36 = 0.972222 (97.2222%)

Visual Representation

The diagram below illustrates 2/9 plus 12/16 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`35/36`
Mixed Number Form	`35/36`
Decimal Form	`0.972222`
Percentage	`97.2222%`

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Frequently Asked Questions

What is 2/9 plus 12/16 as a fraction?

2/9 + 12/16 in simplest fraction form is 35/36.

What is 2/9 plus 12/16 as a decimal?

2/9 + 12/16 converted to a decimal is 0.972222.

What is 2/9 plus 12/16 as a percentage?

2/9 + 12/16 expressed as a percentage is 97.2222%.

Does 2/9 plus 12/16 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.972222...) because the denominator contains prime factors other than 2 and 5.