What is 3/16 plus 5/9? (Answer: 107/144)

Exact Answer

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Problem: What is 3/16 plus 5/9?
Formula / Expression: 3/16 + 5/9
Final Answer: 107/144
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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 5/9 by 16 so both fractions share the common base 144.
Working: 3 × 9/16 × 9 = 27/144 and 5 × 16/9 × 16 = 80/144

Step 3: Add the Numerators
Now add the numerators (27 + 80 = 107) and keep the common denominator 144 unchanged.
Working: 27 + 80/144 = 107/144

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 107 and 144 is 1, confirming that 107/144 cannot be reduced further—it is already in its simplest irreducible form.
Working: 107/144

Step 5: Decimal & Percentage Representation
Dividing the numerator 107 by denominator 144 produces a repeating decimal (approximately 0.743056, or 74.3056%).
Working: 107 ÷ 144 = 0.743056 (74.3056%)

Key Values:
- Simplified Fraction: 107/144
- Mixed Number Form: 107/144
- Decimal Value: 0.743056
- Percentage: 74.3056%

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Solved with FractionsCalc:
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3/16 + 5/9 = 107/144

Simplified Fraction

107/144

Mixed Number

Proper (107/144)

Decimal Value

0.743056

Percentage

74.3056%

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Step-by-Step Solution: 3/16 + 5/9

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 5/9 by 16 so both fractions share the common base 144.

3 × 9/16 × 9 = 27/144 and 5 × 16/9 × 16 = 80/144

Step 3

Add the Numerators

Now add the numerators (27 + 80 = 107) and keep the common denominator 144 unchanged.

27 + 80/144 = 107/144

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 107 and 144 is 1, confirming that 107/144 cannot be reduced further—it is already in its simplest irreducible form.

107/144

Step 5

Decimal & Percentage Representation

Dividing the numerator 107 by denominator 144 produces a repeating decimal (approximately 0.743056, or 74.3056%).

107 ÷ 144 = 0.743056 (74.3056%)

Visual Representation

The diagram below illustrates 3/16 plus 5/9 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`107/144`
Mixed Number Form	`107/144`
Decimal Form	`0.743056`
Percentage	`74.3056%`

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Frequently Asked Questions

What is 3/16 plus 5/9 as a fraction?

3/16 + 5/9 in simplest fraction form is 107/144.

What is 3/16 plus 5/9 as a decimal?

3/16 + 5/9 converted to a decimal is 0.743056.

What is 3/16 plus 5/9 as a percentage?

3/16 + 5/9 expressed as a percentage is 74.3056%.

Does 3/16 plus 5/9 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.743056...) because the denominator contains prime factors other than 2 and 5.