What is 7/9 plus 5/6? (Answer: 29/18)

Exact Answer

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Problem: What is 7/9 plus 5/6?
Formula / Expression: 7/9 + 5/6
Final Answer: 1 11/18 (29/18)
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 9 and 6 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 18 (which is smaller than their product 9 × 6 = 54, keeping the calculation simpler).
Working: LCD(9, 6) = 18

Step 2: Convert to Equivalent Fractions with Common Denominator 18
Multiply the numerator and denominator of 7/9 by 2, and multiply the numerator and denominator of 5/6 by 3 so both fractions share the common base 18.
Working: 7 × 2/9 × 2 = 14/18 and 5 × 3/6 × 3 = 15/18

Step 3: Add the Numerators
Now add the numerators (14 + 15 = 29) and keep the common denominator 18 unchanged.
Working: 14 + 15/18 = 29/18

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 29 and 18 is 1, confirming that 29/18 cannot be reduced further—it is already in its simplest irreducible form.
Working: 29/18

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (29) is greater than the denominator (18), divide 29 by 18: it goes in 1 whole time(s) with a remainder of 11, giving the mixed number 1 11/18.
Working: 29/18 = 1 11/18

Step 6: Decimal & Percentage Representation
Dividing the numerator 29 by denominator 18 produces a repeating decimal (approximately 1.611111, or 161.1111%).
Working: 29 ÷ 18 = 1.611111 (161.1111%)

Key Values:
- Simplified Fraction: 29/18
- Mixed Number Form: 1 11/18
- Decimal Value: 1.611111
- Percentage: 161.1111%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-7-9-plus-5-6/
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7/9 + 5/6 = 29/18

Simplified Fraction

29/18

Mixed Number

1 11/18

Decimal Value

1.611111

Percentage

161.1111%

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Step-by-Step Solution: 7/9 + 5/6

Step 1

Find the Least Common Denominator (LCD)

The denominators 9 and 6 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 18 (which is smaller than their product 9 × 6 = 54, keeping the calculation simpler).

LCD(9, 6) = 18

Step 2

Convert to Equivalent Fractions with Common Denominator 18

Multiply the numerator and denominator of 7/9 by 2, and multiply the numerator and denominator of 5/6 by 3 so both fractions share the common base 18.

7 × 2/9 × 2 = 14/18 and 5 × 3/6 × 3 = 15/18

Step 3

Add the Numerators

Now add the numerators (14 + 15 = 29) and keep the common denominator 18 unchanged.

14 + 15/18 = 29/18

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 29 and 18 is 1, confirming that 29/18 cannot be reduced further—it is already in its simplest irreducible form.

29/18

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (29) is greater than the denominator (18), divide 29 by 18: it goes in 1 whole time(s) with a remainder of 11, giving the mixed number 1 11/18.

29/18 = 111/18

Step 6

Decimal & Percentage Representation

Dividing the numerator 29 by denominator 18 produces a repeating decimal (approximately 1.611111, or 161.1111%).

29 ÷ 18 = 1.611111 (161.1111%)

Visual Representation

The diagram below illustrates 7/9 plus 5/6 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`29/18`
Mixed Number Form	`1 11/18`
Decimal Form	`1.611111`
Percentage	`161.1111%`

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Frequently Asked Questions

What is 7/9 plus 5/6 as a fraction?

7/9 + 5/6 in simplest fraction form is 29/18 (or 1 11/18 as a mixed number).

What is 7/9 plus 5/6 as a decimal?

7/9 + 5/6 converted to a decimal is 1.611111.

What is 7/9 plus 5/6 as a percentage?

7/9 + 5/6 expressed as a percentage is 161.1111%.

How do you write 7/9 plus 5/6 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 29/18 can be written as the mixed number 1 11/18.

Does 7/9 plus 5/6 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.611111...) because the denominator contains prime factors other than 2 and 5.