What is 1/9 plus 9/16? (Answer: 97/144)

Exact Answer

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Problem: What is 1/9 plus 9/16?
Formula / Expression: 1/9 + 9/16
Final Answer: 97/144
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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 1/9 by 16, and multiply the numerator and denominator of 9/16 by 9 so both fractions share the common base 144.
Working: 1 × 16/9 × 16 = 16/144 and 9 × 9/16 × 9 = 81/144

Step 3: Add the Numerators
Now add the numerators (16 + 81 = 97) and keep the common denominator 144 unchanged.
Working: 16 + 81/144 = 97/144

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 97 and 144 is 1, confirming that 97/144 cannot be reduced further—it is already in its simplest irreducible form.
Working: 97/144

Step 5: Decimal & Percentage Representation
Dividing the numerator 97 by denominator 144 produces a repeating decimal (approximately 0.673611, or 67.3611%).
Working: 97 ÷ 144 = 0.673611 (67.3611%)

Key Values:
- Simplified Fraction: 97/144
- Mixed Number Form: 97/144
- Decimal Value: 0.673611
- Percentage: 67.3611%

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Solved with FractionsCalc:
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1/9 + 9/16 = 97/144

Simplified Fraction

97/144

Mixed Number

Proper (97/144)

Decimal Value

0.673611

Percentage

67.3611%

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Step-by-Step Solution: 1/9 + 9/16

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 1/9 by 16, and multiply the numerator and denominator of 9/16 by 9 so both fractions share the common base 144.

1 × 16/9 × 16 = 16/144 and 9 × 9/16 × 9 = 81/144

Step 3

Add the Numerators

Now add the numerators (16 + 81 = 97) and keep the common denominator 144 unchanged.

16 + 81/144 = 97/144

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 97 and 144 is 1, confirming that 97/144 cannot be reduced further—it is already in its simplest irreducible form.

97/144

Step 5

Decimal & Percentage Representation

Dividing the numerator 97 by denominator 144 produces a repeating decimal (approximately 0.673611, or 67.3611%).

97 ÷ 144 = 0.673611 (67.3611%)

Visual Representation

The diagram below illustrates 1/9 plus 9/16 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`97/144`
Mixed Number Form	`97/144`
Decimal Form	`0.673611`
Percentage	`67.3611%`

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Frequently Asked Questions

What is 1/9 plus 9/16 as a fraction?

1/9 + 9/16 in simplest fraction form is 97/144.

What is 1/9 plus 9/16 as a decimal?

1/9 + 9/16 converted to a decimal is 0.673611.

What is 1/9 plus 9/16 as a percentage?

1/9 + 9/16 expressed as a percentage is 67.3611%.

Does 1/9 plus 9/16 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.673611...) because the denominator contains prime factors other than 2 and 5.