What is 9/12 plus 7/9? (Answer: 55/36)

Exact Answer

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Problem: What is 9/12 plus 7/9?
Formula / Expression: 9/12 + 7/9
Final Answer: 1 19/36 (55/36)
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 12 and 9 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 36 (which is smaller than their product 12 × 9 = 108, keeping the calculation simpler).
Working: LCD(12, 9) = 36

Step 2: Convert to Equivalent Fractions with Common Denominator 36
Multiply the numerator and denominator of 9/12 by 3, and multiply the numerator and denominator of 7/9 by 4 so both fractions share the common base 36.
Working: 9 × 3/12 × 3 = 27/36 and 7 × 4/9 × 4 = 28/36

Step 3: Add the Numerators
Now add the numerators (27 + 28 = 55) and keep the common denominator 36 unchanged.
Working: 27 + 28/36 = 55/36

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 55 and 36 is 1, confirming that 55/36 cannot be reduced further—it is already in its simplest irreducible form.
Working: 55/36

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (55) is greater than the denominator (36), divide 55 by 36: it goes in 1 whole time(s) with a remainder of 19, giving the mixed number 1 19/36.
Working: 55/36 = 1 19/36

Step 6: Decimal & Percentage Representation
Dividing the numerator 55 by denominator 36 produces a repeating decimal (approximately 1.527778, or 152.7778%).
Working: 55 ÷ 36 = 1.527778 (152.7778%)

Key Values:
- Simplified Fraction: 55/36
- Mixed Number Form: 1 19/36
- Decimal Value: 1.527778
- Percentage: 152.7778%

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Solved with FractionsCalc:
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9/12 + 7/9 = 55/36

Simplified Fraction

55/36

Mixed Number

1 19/36

Decimal Value

1.527778

Percentage

152.7778%

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Step-by-Step Solution: 9/12 + 7/9

Step 1

Find the Least Common Denominator (LCD)

The denominators 12 and 9 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 36 (which is smaller than their product 12 × 9 = 108, keeping the calculation simpler).

LCD(12, 9) = 36

Step 2

Convert to Equivalent Fractions with Common Denominator 36

Multiply the numerator and denominator of 9/12 by 3, and multiply the numerator and denominator of 7/9 by 4 so both fractions share the common base 36.

9 × 3/12 × 3 = 27/36 and 7 × 4/9 × 4 = 28/36

Step 3

Add the Numerators

Now add the numerators (27 + 28 = 55) and keep the common denominator 36 unchanged.

27 + 28/36 = 55/36

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 55 and 36 is 1, confirming that 55/36 cannot be reduced further—it is already in its simplest irreducible form.

55/36

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (55) is greater than the denominator (36), divide 55 by 36: it goes in 1 whole time(s) with a remainder of 19, giving the mixed number 1 19/36.

55/36 = 119/36

Step 6

Decimal & Percentage Representation

Dividing the numerator 55 by denominator 36 produces a repeating decimal (approximately 1.527778, or 152.7778%).

55 ÷ 36 = 1.527778 (152.7778%)

Visual Representation

The diagram below illustrates 9/12 plus 7/9 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`55/36`
Mixed Number Form	`1 19/36`
Decimal Form	`1.527778`
Percentage	`152.7778%`

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Frequently Asked Questions

What is 9/12 plus 7/9 as a fraction?

9/12 + 7/9 in simplest fraction form is 55/36 (or 1 19/36 as a mixed number).

What is 9/12 plus 7/9 as a decimal?

9/12 + 7/9 converted to a decimal is 1.527778.

What is 9/12 plus 7/9 as a percentage?

9/12 + 7/9 expressed as a percentage is 152.7778%.

How do you write 9/12 plus 7/9 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 55/36 can be written as the mixed number 1 19/36.

Does 9/12 plus 7/9 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.527778...) because the denominator contains prime factors other than 2 and 5.