What is 3/9 plus 5/6? (Answer: 7/6)

Exact Answer

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Problem: What is 3/9 plus 5/6?
Formula / Expression: 3/9 + 5/6
Final Answer: 1 1/6 (7/6)
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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 3/9 by 2, and multiply the numerator and denominator of 5/6 by 3 so both fractions share the common base 18.
Working: 3 × 2/9 × 2 = 6/18 and 5 × 3/6 × 3 = 15/18

Step 3: Add the Numerators
Now add the numerators (6 + 15 = 21) and keep the common denominator 18 unchanged.
Working: 6 + 15/18 = 21/18

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 21 and 18, which is 3. Divide both the numerator and denominator by 3.
Working: 21 ÷ 3/18 ÷ 3 = 7/6

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (7) is greater than the denominator (6), divide 7 by 6: it goes in 1 whole time(s) with a remainder of 1, giving the mixed number 1 1/6.
Working: 7/6 = 1 1/6

Step 6: Decimal & Percentage Representation
Dividing the numerator 7 by denominator 6 produces a repeating decimal (approximately 1.166667, or 116.6667%).
Working: 7 ÷ 6 = 1.166667 (116.6667%)

Key Values:
- Simplified Fraction: 7/6
- Mixed Number Form: 1 1/6
- Decimal Value: 1.166667
- Percentage: 116.6667%

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3/9 + 5/6 = 7/6

Simplified Fraction

7/6

Mixed Number

1 1/6

Decimal Value

1.166667

Percentage

116.6667%

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Step-by-Step Solution: 3/9 + 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 3/9 by 2, and multiply the numerator and denominator of 5/6 by 3 so both fractions share the common base 18.

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

Step 3

Add the Numerators

Now add the numerators (6 + 15 = 21) and keep the common denominator 18 unchanged.

6 + 15/18 = 21/18

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 21 and 18, which is 3. Divide both the numerator and denominator by 3.

21 ÷ 3/18 ÷ 3 = 7/6

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (7) is greater than the denominator (6), divide 7 by 6: it goes in 1 whole time(s) with a remainder of 1, giving the mixed number 1 1/6.

7/6 = 11/6

Step 6

Decimal & Percentage Representation

Dividing the numerator 7 by denominator 6 produces a repeating decimal (approximately 1.166667, or 116.6667%).

7 ÷ 6 = 1.166667 (116.6667%)

Visual Representation

The diagram below illustrates 3/9 plus 5/6 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`7/6`
Mixed Number Form	`1 1/6`
Decimal Form	`1.166667`
Percentage	`116.6667%`

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Frequently Asked Questions

What is 3/9 plus 5/6 as a fraction?

3/9 + 5/6 in simplest fraction form is 7/6 (or 1 1/6 as a mixed number).

What is 3/9 plus 5/6 as a decimal?

3/9 + 5/6 converted to a decimal is 1.166667.

What is 3/9 plus 5/6 as a percentage?

3/9 + 5/6 expressed as a percentage is 116.6667%.

How do you write 3/9 plus 5/6 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 7/6 can be written as the mixed number 1 1/6.

Does 3/9 plus 5/6 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.166667...) because the denominator contains prime factors other than 2 and 5.