What is 6/8 plus 8/9? (Answer: 59/36)

Exact Answer

==================================================
Problem: What is 6/8 plus 8/9?
Formula / Expression: 6/8 + 8/9
Final Answer: 1 23/36 (59/36)
==================================================

Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 8 and 9 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 8 × 9 = 72.
Working: LCD(8, 9) = 72

Step 2: Convert to Equivalent Fractions with Common Denominator 72
Multiply the numerator and denominator of 6/8 by 9, and multiply the numerator and denominator of 8/9 by 8 so both fractions share the common base 72.
Working: 6 × 9/8 × 9 = 54/72 and 8 × 8/9 × 8 = 64/72

Step 3: Add the Numerators
Now add the numerators (54 + 64 = 118) and keep the common denominator 72 unchanged.
Working: 54 + 64/72 = 118/72

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 118 and 72, which is 2. Divide both the numerator and denominator by 2.
Working: 118 ÷ 2/72 ÷ 2 = 59/36

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (59) is greater than the denominator (36), divide 59 by 36: it goes in 1 whole time(s) with a remainder of 23, giving the mixed number 1 23/36.
Working: 59/36 = 1 23/36

Step 6: Decimal & Percentage Representation
Dividing the numerator 59 by denominator 36 produces a repeating decimal (approximately 1.638889, or 163.8889%).
Working: 59 ÷ 36 = 1.638889 (163.8889%)

Key Values:
- Simplified Fraction: 59/36
- Mixed Number Form: 1 23/36
- Decimal Value: 1.638889
- Percentage: 163.8889%

--------------------------------------------------
Solved with FractionsCalc:
https://fractionscalc.com/what-is-6-8-plus-8-9/
==================================================

6/8 + 8/9 = 59/36

Simplified Fraction

59/36

Mixed Number

1 23/36

Decimal Value

1.638889

Percentage

163.8889%

Reduce / Convert Fraction:

Convert Fraction:

Enter Decimal Number:

Enter Percentage: %

What is % of

From Value: To Value:

Simplify Ratio: :

Switch to Proportion / Missing X Solver (A/B = C/D) →

Enter 3 known numbers and leave 1 empty (or type x) to solve:

← Switch to Ratio Simplifier (A:B)

Provide any 2 values below to calculate the remaining:

Price before discount

Discount

Price after discount

You saved

+ Add Sales Tax & Extra Coupon (Optional)

Sales Tax: % Extra Off: %

Provide any 2 values below to calculate the remaining:

Cost

Markup

REVENUE

Gross Profit

Profit Margin

Bill Subtotal

Tip Percentage

Split (People)

👥

Quick Tip:

Total Bill

Split Between

👥

Tip % (Optional)

Include Tip:

Total Price

Quantity

Unit of Measure

← Discount & Sales Tax • Ratio Simplifier (A:B) →

First Number: Second Number:

Find All Factors of:

Dividend: ÷ Divisor:

Number to Round: To Nearest:

Method: Standard (5+ ↑) Always Up (Ceil) Always Down (Floor)

Presets:

√ 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: 6/8 + 8/9

Step 1

Find the Least Common Denominator (LCD)

The denominators 8 and 9 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 8 × 9 = 72.

LCD(8, 9) = 72

Step 2

Convert to Equivalent Fractions with Common Denominator 72

Multiply the numerator and denominator of 6/8 by 9, and multiply the numerator and denominator of 8/9 by 8 so both fractions share the common base 72.

6 × 9/8 × 9 = 54/72 and 8 × 8/9 × 8 = 64/72

Step 3

Add the Numerators

Now add the numerators (54 + 64 = 118) and keep the common denominator 72 unchanged.

54 + 64/72 = 118/72

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 118 and 72, which is 2. Divide both the numerator and denominator by 2.

118 ÷ 2/72 ÷ 2 = 59/36

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (59) is greater than the denominator (36), divide 59 by 36: it goes in 1 whole time(s) with a remainder of 23, giving the mixed number 1 23/36.

59/36 = 123/36

Step 6

Decimal & Percentage Representation

Dividing the numerator 59 by denominator 36 produces a repeating decimal (approximately 1.638889, or 163.8889%).

59 ÷ 36 = 1.638889 (163.8889%)

Visual Representation

The diagram below illustrates 6/8 plus 8/9 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`59/36`
Mixed Number Form	`1 23/36`
Decimal Form	`1.638889`
Percentage	`163.8889%`

Was this solution helpful?

Help us improve our free step-by-step tools

Frequently Asked Questions

What is 6/8 plus 8/9 as a fraction?

6/8 + 8/9 in simplest fraction form is 59/36 (or 1 23/36 as a mixed number).

What is 6/8 plus 8/9 as a decimal?

6/8 + 8/9 converted to a decimal is 1.638889.

What is 6/8 plus 8/9 as a percentage?

6/8 + 8/9 expressed as a percentage is 163.8889%.

How do you write 6/8 plus 8/9 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 59/36 can be written as the mixed number 1 23/36.

Does 6/8 plus 8/9 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.638889...) because the denominator contains prime factors other than 2 and 5.