What is 1/6 plus 9/13? (Answer: 67/78)

Exact Answer

==================================================
Problem: What is 1/6 plus 9/13?
Formula / Expression: 1/6 + 9/13
Final Answer: 67/78
==================================================

Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 6 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 6 × 13 = 78.
Working: LCD(6, 13) = 78

Step 2: Convert to Equivalent Fractions with Common Denominator 78
Multiply the numerator and denominator of 1/6 by 13, and multiply the numerator and denominator of 9/13 by 6 so both fractions share the common base 78.
Working: 1 × 13/6 × 13 = 13/78 and 9 × 6/13 × 6 = 54/78

Step 3: Add the Numerators
Now add the numerators (13 + 54 = 67) and keep the common denominator 78 unchanged.
Working: 13 + 54/78 = 67/78

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 67 and 78 is 1, confirming that 67/78 cannot be reduced further—it is already in its simplest irreducible form.
Working: 67/78

Step 5: Decimal & Percentage Representation
Dividing the numerator 67 by denominator 78 produces a repeating decimal (approximately 0.858974, or 85.8974%).
Working: 67 ÷ 78 = 0.858974 (85.8974%)

Key Values:
- Simplified Fraction: 67/78
- Mixed Number Form: 67/78
- Decimal Value: 0.858974
- Percentage: 85.8974%

--------------------------------------------------
Solved with FractionsCalc:
https://fractionscalc.com/what-is-1-6-plus-9-13/
==================================================

1/6 + 9/13 = 67/78

Simplified Fraction

67/78

Mixed Number

Proper (67/78)

Decimal Value

0.858974

Percentage

85.8974%

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: 1/6 + 9/13

Step 1

Find the Least Common Denominator (LCD)

The denominators 6 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 6 × 13 = 78.

LCD(6, 13) = 78

Step 2

Convert to Equivalent Fractions with Common Denominator 78

Multiply the numerator and denominator of 1/6 by 13, and multiply the numerator and denominator of 9/13 by 6 so both fractions share the common base 78.

1 × 13/6 × 13 = 13/78 and 9 × 6/13 × 6 = 54/78

Step 3

Add the Numerators

Now add the numerators (13 + 54 = 67) and keep the common denominator 78 unchanged.

13 + 54/78 = 67/78

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 67 and 78 is 1, confirming that 67/78 cannot be reduced further—it is already in its simplest irreducible form.

67/78

Step 5

Decimal & Percentage Representation

Dividing the numerator 67 by denominator 78 produces a repeating decimal (approximately 0.858974, or 85.8974%).

67 ÷ 78 = 0.858974 (85.8974%)

Visual Representation

The diagram below illustrates 1/6 plus 9/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`67/78`
Mixed Number Form	`67/78`
Decimal Form	`0.858974`
Percentage	`85.8974%`

Was this solution helpful?

Help us improve our free step-by-step tools

Frequently Asked Questions

What is 1/6 plus 9/13 as a fraction?

1/6 + 9/13 in simplest fraction form is 67/78.

What is 1/6 plus 9/13 as a decimal?

1/6 + 9/13 converted to a decimal is 0.858974.

What is 1/6 plus 9/13 as a percentage?

1/6 + 9/13 expressed as a percentage is 85.8974%.

Does 1/6 plus 9/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.858974...) because the denominator contains prime factors other than 2 and 5.