What is 9/16 plus 7/9? (Answer: 193/144)

Exact Answer

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Problem: What is 9/16 plus 7/9?
Formula / Expression: 9/16 + 7/9
Final Answer: 1 49/144 (193/144)
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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 9/16 by 9, and multiply the numerator and denominator of 7/9 by 16 so both fractions share the common base 144.
Working: 9 × 9/16 × 9 = 81/144 and 7 × 16/9 × 16 = 112/144

Step 3: Add the Numerators
Now add the numerators (81 + 112 = 193) and keep the common denominator 144 unchanged.
Working: 81 + 112/144 = 193/144

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 193 and 144 is 1, confirming that 193/144 cannot be reduced further—it is already in its simplest irreducible form.
Working: 193/144

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (193) is greater than the denominator (144), divide 193 by 144: it goes in 1 whole time(s) with a remainder of 49, giving the mixed number 1 49/144.
Working: 193/144 = 1 49/144

Step 6: Decimal & Percentage Representation
Dividing the numerator 193 by denominator 144 produces a repeating decimal (approximately 1.340278, or 134.0278%).
Working: 193 ÷ 144 = 1.340278 (134.0278%)

Key Values:
- Simplified Fraction: 193/144
- Mixed Number Form: 1 49/144
- Decimal Value: 1.340278
- Percentage: 134.0278%

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Solved with FractionsCalc:
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9/16 + 7/9 = 193/144

Simplified Fraction

193/144

Mixed Number

1 49/144

Decimal Value

1.340278

Percentage

134.0278%

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Step-by-Step Solution: 9/16 + 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 9/16 by 9, and multiply the numerator and denominator of 7/9 by 16 so both fractions share the common base 144.

9 × 9/16 × 9 = 81/144 and 7 × 16/9 × 16 = 112/144

Step 3

Add the Numerators

Now add the numerators (81 + 112 = 193) and keep the common denominator 144 unchanged.

81 + 112/144 = 193/144

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 193 and 144 is 1, confirming that 193/144 cannot be reduced further—it is already in its simplest irreducible form.

193/144

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (193) is greater than the denominator (144), divide 193 by 144: it goes in 1 whole time(s) with a remainder of 49, giving the mixed number 1 49/144.

193/144 = 149/144

Step 6

Decimal & Percentage Representation

Dividing the numerator 193 by denominator 144 produces a repeating decimal (approximately 1.340278, or 134.0278%).

193 ÷ 144 = 1.340278 (134.0278%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`193/144`
Mixed Number Form	`1 49/144`
Decimal Form	`1.340278`
Percentage	`134.0278%`

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Frequently Asked Questions

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

9/16 + 7/9 in simplest fraction form is 193/144 (or 1 49/144 as a mixed number).

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

9/16 + 7/9 converted to a decimal is 1.340278.

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

9/16 + 7/9 expressed as a percentage is 134.0278%.

How do you write 9/16 plus 7/9 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 193/144 can be written as the mixed number 1 49/144.

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

It results in a repeating decimal (approximately 1.340278...) because the denominator contains prime factors other than 2 and 5.