What is 2/31 plus 3/8? (Answer: 109/248)

Exact Answer

==================================================
Problem: What is 2/31 plus 3/8?
Formula / Expression: 2/31 + 3/8
Final Answer: 109/248
==================================================

Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 31 and 8 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 31 × 8 = 248.
Working: LCD(31, 8) = 248

Step 2: Convert to Equivalent Fractions with Common Denominator 248
Multiply the numerator and denominator of 2/31 by 8, and multiply the numerator and denominator of 3/8 by 31 so both fractions share the common base 248.
Working: 2 × 8/31 × 8 = 16/248 and 3 × 31/8 × 31 = 93/248

Step 3: Add the Numerators
Now add the numerators (16 + 93 = 109) and keep the common denominator 248 unchanged.
Working: 16 + 93/248 = 109/248

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 109 and 248 is 1, confirming that 109/248 cannot be reduced further—it is already in its simplest irreducible form.
Working: 109/248

Step 5: Decimal & Percentage Representation
Dividing the numerator 109 by denominator 248 produces a repeating decimal (approximately 0.439516, or 43.9516%).
Working: 109 ÷ 248 = 0.439516 (43.9516%)

Key Values:
- Simplified Fraction: 109/248
- Mixed Number Form: 109/248
- Decimal Value: 0.439516
- Percentage: 43.9516%

--------------------------------------------------
Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-31-plus-3-8/
==================================================

2/31 + 3/8 = 109/248

Simplified Fraction

109/248

Mixed Number

Proper (109/248)

Decimal Value

0.439516

Percentage

43.9516%

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: 2/31 + 3/8

Step 1

Find the Least Common Denominator (LCD)

The denominators 31 and 8 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 31 × 8 = 248.

LCD(31, 8) = 248

Step 2

Convert to Equivalent Fractions with Common Denominator 248

Multiply the numerator and denominator of 2/31 by 8, and multiply the numerator and denominator of 3/8 by 31 so both fractions share the common base 248.

2 × 8/31 × 8 = 16/248 and 3 × 31/8 × 31 = 93/248

Step 3

Add the Numerators

Now add the numerators (16 + 93 = 109) and keep the common denominator 248 unchanged.

16 + 93/248 = 109/248

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 109 and 248 is 1, confirming that 109/248 cannot be reduced further—it is already in its simplest irreducible form.

109/248

Step 5

Decimal & Percentage Representation

Dividing the numerator 109 by denominator 248 produces a repeating decimal (approximately 0.439516, or 43.9516%).

109 ÷ 248 = 0.439516 (43.9516%)

Visual Representation

The diagram below illustrates 2/31 plus 3/8 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`109/248`
Mixed Number Form	`109/248`
Decimal Form	`0.439516`
Percentage	`43.9516%`

Was this solution helpful?

Help us improve our free step-by-step tools

Frequently Asked Questions

What is 2/31 plus 3/8 as a fraction?

2/31 + 3/8 in simplest fraction form is 109/248.

What is 2/31 plus 3/8 as a decimal?

2/31 + 3/8 converted to a decimal is 0.439516.

What is 2/31 plus 3/8 as a percentage?

2/31 + 3/8 expressed as a percentage is 43.9516%.

Does 2/31 plus 3/8 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.439516...) because the denominator contains prime factors other than 2 and 5.