What is 1/2 plus 6/9? (Answer: 7/6)

Exact Answer

==================================================
Problem: What is 1/2 plus 6/9?
Formula / Expression: 1/2 + 6/9
Final Answer: 1 1/6 (7/6)
==================================================

Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 2 and 9 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 2 × 9 = 18.
Working: LCD(2, 9) = 18

Step 2: Convert to Equivalent Fractions with Common Denominator 18
Multiply the numerator and denominator of 1/2 by 9, and multiply the numerator and denominator of 6/9 by 2 so both fractions share the common base 18.
Working: 1 × 9/2 × 9 = 9/18 and 6 × 2/9 × 2 = 12/18

Step 3: Add the Numerators
Now add the numerators (9 + 12 = 21) and keep the common denominator 18 unchanged.
Working: 9 + 12/18 = 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%

--------------------------------------------------
Solved with FractionsCalc:
https://fractionscalc.com/what-is-1-2-plus-6-9/
==================================================

1/2 + 6/9 = 7/6

Simplified Fraction

7/6

Mixed Number

1 1/6

Decimal Value

1.166667

Percentage

116.6667%

Reduce / Convert Fraction:

Convert Fraction:

Enter Decimal Number:

Enter Percentage: %

What is % of

From Value: To Value:

Simplify Ratio: :

First Number: Second Number:

Find All Factors of:

Dividend: ÷ Divisor:

√ Square Root of: OR Power (x^y): ^{^}

x² + x + = 0

Number (n! & log):

Circle Radius (r):

Side a: Side b:

Angle (Degrees): °

Numbers (comma separated):

Total Items (n): Choose (r):

Decimal Number:

Number (1–3999):

Step-by-Step Solution: 1/2 + 6/9

Step 1

Find the Least Common Denominator (LCD)

The denominators 2 and 9 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 2 × 9 = 18.

LCD(2, 9) = 18

Step 2

Convert to Equivalent Fractions with Common Denominator 18

Multiply the numerator and denominator of 1/2 by 9, and multiply the numerator and denominator of 6/9 by 2 so both fractions share the common base 18.

1 × 9/2 × 9 = 9/18 and 6 × 2/9 × 2 = 12/18

Step 3

Add the Numerators

Now add the numerators (9 + 12 = 21) and keep the common denominator 18 unchanged.

9 + 12/18 = 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 1/2 plus 6/9 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%`

Was this solution helpful?

Help us improve our free step-by-step tools

Frequently Asked Questions

What is 1/2 plus 6/9 as a fraction?

1/2 + 6/9 in simplest fraction form is 7/6 (or 1 1/6 as a mixed number).

What is 1/2 plus 6/9 as a decimal?

1/2 + 6/9 converted to a decimal is 1.166667.

What is 1/2 plus 6/9 as a percentage?

1/2 + 6/9 expressed as a percentage is 116.6667%.

How do you write 1/2 plus 6/9 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 1/2 plus 6/9 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.