What is 3/16 plus 7/9? (Answer: 139/144)

Exact Answer

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Problem: What is 3/16 plus 7/9?
Formula / Expression: 3/16 + 7/9
Final Answer: 139/144
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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 7/9 by 16 so both fractions share the common base 144.
Working: 3 × 9/16 × 9 = 27/144 and 7 × 16/9 × 16 = 112/144

Step 3: Add the Numerators
Now add the numerators (27 + 112 = 139) and keep the common denominator 144 unchanged.
Working: 27 + 112/144 = 139/144

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 139 and 144 is 1, confirming that 139/144 cannot be reduced further—it is already in its simplest irreducible form.
Working: 139/144

Step 5: Decimal & Percentage Representation
Dividing the numerator 139 by denominator 144 produces a repeating decimal (approximately 0.965278, or 96.5278%).
Working: 139 ÷ 144 = 0.965278 (96.5278%)

Key Values:
- Simplified Fraction: 139/144
- Mixed Number Form: 139/144
- Decimal Value: 0.965278
- Percentage: 96.5278%

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Solved with FractionsCalc:
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3/16 + 7/9 = 139/144

Simplified Fraction

139/144

Mixed Number

Proper (139/144)

Decimal Value

0.965278

Percentage

96.5278%

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Step-by-Step Solution: 3/16 + 7/9

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 7/9 by 16 so both fractions share the common base 144.

3 × 9/16 × 9 = 27/144 and 7 × 16/9 × 16 = 112/144

Step 3

Add the Numerators

Now add the numerators (27 + 112 = 139) and keep the common denominator 144 unchanged.

27 + 112/144 = 139/144

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 139 and 144 is 1, confirming that 139/144 cannot be reduced further—it is already in its simplest irreducible form.

139/144

Step 5

Decimal & Percentage Representation

Dividing the numerator 139 by denominator 144 produces a repeating decimal (approximately 0.965278, or 96.5278%).

139 ÷ 144 = 0.965278 (96.5278%)

Visual Representation

The diagram below illustrates 3/16 plus 7/9 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`139/144`
Mixed Number Form	`139/144`
Decimal Form	`0.965278`
Percentage	`96.5278%`

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Frequently Asked Questions

What is 3/16 plus 7/9 as a fraction?

3/16 + 7/9 in simplest fraction form is 139/144.

What is 3/16 plus 7/9 as a decimal?

3/16 + 7/9 converted to a decimal is 0.965278.

What is 3/16 plus 7/9 as a percentage?

3/16 + 7/9 expressed as a percentage is 96.5278%.

Does 3/16 plus 7/9 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.965278...) because the denominator contains prime factors other than 2 and 5.