What is 1/5 plus 5/6? (Answer: 31/30)

Exact Answer

==================================================
Problem: What is 1/5 plus 5/6?
Formula / Expression: 1/5 + 5/6
Final Answer: 1 1/30 (31/30)
==================================================

Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 5 and 6 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 5 × 6 = 30.
Working: LCD(5, 6) = 30

Step 2: Convert to Equivalent Fractions with Common Denominator 30
Multiply the numerator and denominator of 1/5 by 6, and multiply the numerator and denominator of 5/6 by 5 so both fractions share the common base 30.
Working: 1 × 6/5 × 6 = 6/30 and 5 × 5/6 × 5 = 25/30

Step 3: Add the Numerators
Now add the numerators (6 + 25 = 31) and keep the common denominator 30 unchanged.
Working: 6 + 25/30 = 31/30

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 31 and 30 is 1, confirming that 31/30 cannot be reduced further—it is already in its simplest irreducible form.
Working: 31/30

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (31) is greater than the denominator (30), divide 31 by 30: it goes in 1 whole time(s) with a remainder of 1, giving the mixed number 1 1/30.
Working: 31/30 = 1 1/30

Step 6: Decimal & Percentage Representation
Dividing the numerator 31 by denominator 30 produces a repeating decimal (approximately 1.033333, or 103.3333%).
Working: 31 ÷ 30 = 1.033333 (103.3333%)

Key Values:
- Simplified Fraction: 31/30
- Mixed Number Form: 1 1/30
- Decimal Value: 1.033333
- Percentage: 103.3333%

--------------------------------------------------
Solved with FractionsCalc:
https://fractionscalc.com/what-is-1-5-plus-5-6/
==================================================

1/5 + 5/6 = 31/30

Simplified Fraction

31/30

Mixed Number

1 1/30

Decimal Value

1.033333

Percentage

103.3333%

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: 1/5 + 5/6

Step 1

Find the Least Common Denominator (LCD)

The denominators 5 and 6 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 5 × 6 = 30.

LCD(5, 6) = 30

Step 2

Convert to Equivalent Fractions with Common Denominator 30

Multiply the numerator and denominator of 1/5 by 6, and multiply the numerator and denominator of 5/6 by 5 so both fractions share the common base 30.

1 × 6/5 × 6 = 6/30 and 5 × 5/6 × 5 = 25/30

Step 3

Add the Numerators

Now add the numerators (6 + 25 = 31) and keep the common denominator 30 unchanged.

6 + 25/30 = 31/30

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 31 and 30 is 1, confirming that 31/30 cannot be reduced further—it is already in its simplest irreducible form.

31/30

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (31) is greater than the denominator (30), divide 31 by 30: it goes in 1 whole time(s) with a remainder of 1, giving the mixed number 1 1/30.

31/30 = 11/30

Step 6

Decimal & Percentage Representation

Dividing the numerator 31 by denominator 30 produces a repeating decimal (approximately 1.033333, or 103.3333%).

31 ÷ 30 = 1.033333 (103.3333%)

Visual Representation

The diagram below illustrates 1/5 plus 5/6 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`31/30`
Mixed Number Form	`1 1/30`
Decimal Form	`1.033333`
Percentage	`103.3333%`

Was this solution helpful?

Help us improve our free step-by-step tools

Frequently Asked Questions

What is 1/5 plus 5/6 as a fraction?

1/5 + 5/6 in simplest fraction form is 31/30 (or 1 1/30 as a mixed number).

What is 1/5 plus 5/6 as a decimal?

1/5 + 5/6 converted to a decimal is 1.033333.

What is 1/5 plus 5/6 as a percentage?

1/5 + 5/6 expressed as a percentage is 103.3333%.

How do you write 1/5 plus 5/6 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 31/30 can be written as the mixed number 1 1/30.

Does 1/5 plus 5/6 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.033333...) because the denominator contains prime factors other than 2 and 5.