What is 8/31 plus 12/21? (Answer: 180/217)

Exact Answer

==================================================
Problem: What is 8/31 plus 12/21?
Formula / Expression: 8/31 + 12/21
Final Answer: 180/217
==================================================

Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 31 and 21 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 31 × 21 = 651.
Working: LCD(31, 21) = 651

Step 2: Convert to Equivalent Fractions with Common Denominator 651
Multiply the numerator and denominator of 8/31 by 21, and multiply the numerator and denominator of 12/21 by 31 so both fractions share the common base 651.
Working: 8 × 21/31 × 21 = 168/651 and 12 × 31/21 × 31 = 372/651

Step 3: Add the Numerators
Now add the numerators (168 + 372 = 540) and keep the common denominator 651 unchanged.
Working: 168 + 372/651 = 540/651

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 540 and 651, which is 3. Divide both the numerator and denominator by 3.
Working: 540 ÷ 3/651 ÷ 3 = 180/217

Step 5: Decimal & Percentage Representation
Dividing the numerator 180 by denominator 217 produces a repeating decimal (approximately 0.829493, or 82.9493%).
Working: 180 ÷ 217 = 0.829493 (82.9493%)

Key Values:
- Simplified Fraction: 180/217
- Mixed Number Form: 180/217
- Decimal Value: 0.829493
- Percentage: 82.9493%

--------------------------------------------------
Solved with FractionsCalc:
https://fractionscalc.com/what-is-8-31-plus-12-21/
==================================================

8/31 + 12/21 = 180/217

Simplified Fraction

180/217

Mixed Number

Proper (180/217)

Decimal Value

0.829493

Percentage

82.9493%

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: 8/31 + 12/21

Step 1

Find the Least Common Denominator (LCD)

The denominators 31 and 21 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 31 × 21 = 651.

LCD(31, 21) = 651

Step 2

Convert to Equivalent Fractions with Common Denominator 651

Multiply the numerator and denominator of 8/31 by 21, and multiply the numerator and denominator of 12/21 by 31 so both fractions share the common base 651.

8 × 21/31 × 21 = 168/651 and 12 × 31/21 × 31 = 372/651

Step 3

Add the Numerators

Now add the numerators (168 + 372 = 540) and keep the common denominator 651 unchanged.

168 + 372/651 = 540/651

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 540 and 651, which is 3. Divide both the numerator and denominator by 3.

540 ÷ 3/651 ÷ 3 = 180/217

Step 5

Decimal & Percentage Representation

Dividing the numerator 180 by denominator 217 produces a repeating decimal (approximately 0.829493, or 82.9493%).

180 ÷ 217 = 0.829493 (82.9493%)

Visual Representation

The diagram below illustrates 8/31 plus 12/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`180/217`
Mixed Number Form	`180/217`
Decimal Form	`0.829493`
Percentage	`82.9493%`

Was this solution helpful?

Help us improve our free step-by-step tools

Frequently Asked Questions

What is 8/31 plus 12/21 as a fraction?

8/31 + 12/21 in simplest fraction form is 180/217.

What is 8/31 plus 12/21 as a decimal?

8/31 + 12/21 converted to a decimal is 0.829493.

What is 8/31 plus 12/21 as a percentage?

8/31 + 12/21 expressed as a percentage is 82.9493%.

Does 8/31 plus 12/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.829493...) because the denominator contains prime factors other than 2 and 5.