What is 3/19 plus 2/8? (Answer: 31/76)

Exact Answer

==================================================
Problem: What is 3/19 plus 2/8?
Formula / Expression: 3/19 + 2/8
Final Answer: 31/76
==================================================

Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 19 and 8 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 19 × 8 = 152.
Working: LCD(19, 8) = 152

Step 2: Convert to Equivalent Fractions with Common Denominator 152
Multiply the numerator and denominator of 3/19 by 8, and multiply the numerator and denominator of 2/8 by 19 so both fractions share the common base 152.
Working: 3 × 8/19 × 8 = 24/152 and 2 × 19/8 × 19 = 38/152

Step 3: Add the Numerators
Now add the numerators (24 + 38 = 62) and keep the common denominator 152 unchanged.
Working: 24 + 38/152 = 62/152

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 62 and 152, which is 2. Divide both the numerator and denominator by 2.
Working: 62 ÷ 2/152 ÷ 2 = 31/76

Step 5: Decimal & Percentage Representation
Dividing the numerator 31 by denominator 76 produces a repeating decimal (approximately 0.407895, or 40.7895%).
Working: 31 ÷ 76 = 0.407895 (40.7895%)

Key Values:
- Simplified Fraction: 31/76
- Mixed Number Form: 31/76
- Decimal Value: 0.407895
- Percentage: 40.7895%

--------------------------------------------------
Solved with FractionsCalc:
https://fractionscalc.com/what-is-3-19-plus-2-8/
==================================================

3/19 + 2/8 = 31/76

Simplified Fraction

31/76

Mixed Number

Proper (31/76)

Decimal Value

0.407895

Percentage

40.7895%

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: 3/19 + 2/8

Step 1

Find the Least Common Denominator (LCD)

The denominators 19 and 8 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 19 × 8 = 152.

LCD(19, 8) = 152

Step 2

Convert to Equivalent Fractions with Common Denominator 152

Multiply the numerator and denominator of 3/19 by 8, and multiply the numerator and denominator of 2/8 by 19 so both fractions share the common base 152.

3 × 8/19 × 8 = 24/152 and 2 × 19/8 × 19 = 38/152

Step 3

Add the Numerators

Now add the numerators (24 + 38 = 62) and keep the common denominator 152 unchanged.

24 + 38/152 = 62/152

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 62 and 152, which is 2. Divide both the numerator and denominator by 2.

62 ÷ 2/152 ÷ 2 = 31/76

Step 5

Decimal & Percentage Representation

Dividing the numerator 31 by denominator 76 produces a repeating decimal (approximately 0.407895, or 40.7895%).

31 ÷ 76 = 0.407895 (40.7895%)

Visual Representation

The diagram below illustrates 3/19 plus 2/8 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`31/76`
Mixed Number Form	`31/76`
Decimal Form	`0.407895`
Percentage	`40.7895%`

Was this solution helpful?

Help us improve our free step-by-step tools

Frequently Asked Questions

What is 3/19 plus 2/8 as a fraction?

3/19 + 2/8 in simplest fraction form is 31/76.

What is 3/19 plus 2/8 as a decimal?

3/19 + 2/8 converted to a decimal is 0.407895.

What is 3/19 plus 2/8 as a percentage?

3/19 + 2/8 expressed as a percentage is 40.7895%.

Does 3/19 plus 2/8 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.407895...) because the denominator contains prime factors other than 2 and 5.