What is 3/16 plus 2/9? (Answer: 59/144)

Exact Answer

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Problem: What is 3/16 plus 2/9?
Formula / Expression: 3/16 + 2/9
Final Answer: 59/144
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Step-by-Step Solution:

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

Step 2: Convert to Equivalent Fractions with Common Denominator 144
Multiply the numerator and denominator of 3/16 by 9, and multiply the numerator and denominator of 2/9 by 16 so both fractions share the common base 144.
Working: 3 × 9/16 × 9 = 27/144 and 2 × 16/9 × 16 = 32/144

Step 3: Add the Numerators
Now add the numerators (27 + 32 = 59) and keep the common denominator 144 unchanged.
Working: 27 + 32/144 = 59/144

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 59 and 144 is 1, confirming that 59/144 cannot be reduced further—it is already in its simplest irreducible form.
Working: 59/144

Step 5: Decimal & Percentage Representation
Dividing the numerator 59 by denominator 144 produces a repeating decimal (approximately 0.409722, or 40.9722%).
Working: 59 ÷ 144 = 0.409722 (40.9722%)

Key Values:
- Simplified Fraction: 59/144
- Mixed Number Form: 59/144
- Decimal Value: 0.409722
- Percentage: 40.9722%

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Solved with FractionsCalc:
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3/16 + 2/9 = 59/144

Simplified Fraction

59/144

Mixed Number

Proper (59/144)

Decimal Value

0.409722

Percentage

40.9722%

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Step-by-Step Solution: 3/16 + 2/9

Step 1

Find the Least Common Denominator (LCD)

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

LCD(16, 9) = 144

Step 2

Convert to Equivalent Fractions with Common Denominator 144

Multiply the numerator and denominator of 3/16 by 9, and multiply the numerator and denominator of 2/9 by 16 so both fractions share the common base 144.

3 × 9/16 × 9 = 27/144 and 2 × 16/9 × 16 = 32/144

Step 3

Add the Numerators

Now add the numerators (27 + 32 = 59) and keep the common denominator 144 unchanged.

27 + 32/144 = 59/144

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 59 and 144 is 1, confirming that 59/144 cannot be reduced further—it is already in its simplest irreducible form.

59/144

Step 5

Decimal & Percentage Representation

Dividing the numerator 59 by denominator 144 produces a repeating decimal (approximately 0.409722, or 40.9722%).

59 ÷ 144 = 0.409722 (40.9722%)

Visual Representation

The diagram below illustrates 3/16 plus 2/9 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`59/144`
Mixed Number Form	`59/144`
Decimal Form	`0.409722`
Percentage	`40.9722%`

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Frequently Asked Questions

What is 3/16 plus 2/9 as a fraction?

3/16 + 2/9 in simplest fraction form is 59/144.

What is 3/16 plus 2/9 as a decimal?

3/16 + 2/9 converted to a decimal is 0.409722.

What is 3/16 plus 2/9 as a percentage?

3/16 + 2/9 expressed as a percentage is 40.9722%.

Does 3/16 plus 2/9 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.409722...) because the denominator contains prime factors other than 2 and 5.