What is 12/57 plus 9/21? (Answer: 85/133)

Exact Answer

==================================================
Problem: What is 12/57 plus 9/21?
Formula / Expression: 12/57 + 9/21
Final Answer: 85/133
==================================================

Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 57 and 21 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 399 (which is smaller than their product 57 × 21 = 1197, keeping the calculation simpler).
Working: LCD(57, 21) = 399

Step 2: Convert to Equivalent Fractions with Common Denominator 399
Multiply the numerator and denominator of 12/57 by 7, and multiply the numerator and denominator of 9/21 by 19 so both fractions share the common base 399.
Working: 12 × 7/57 × 7 = 84/399 and 9 × 19/21 × 19 = 171/399

Step 3: Add the Numerators
Now add the numerators (84 + 171 = 255) and keep the common denominator 399 unchanged.
Working: 84 + 171/399 = 255/399

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 255 and 399, which is 3. Divide both the numerator and denominator by 3.
Working: 255 ÷ 3/399 ÷ 3 = 85/133

Step 5: Decimal & Percentage Representation
Dividing the numerator 85 by denominator 133 produces a repeating decimal (approximately 0.639098, or 63.9098%).
Working: 85 ÷ 133 = 0.639098 (63.9098%)

Key Values:
- Simplified Fraction: 85/133
- Mixed Number Form: 85/133
- Decimal Value: 0.639098
- Percentage: 63.9098%

--------------------------------------------------
Solved with FractionsCalc:
https://fractionscalc.com/what-is-12-57-plus-9-21/
==================================================

12/57 + 9/21 = 85/133

Simplified Fraction

85/133

Mixed Number

Proper (85/133)

Decimal Value

0.639098

Percentage

63.9098%

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: 12/57 + 9/21

Step 1

Find the Least Common Denominator (LCD)

The denominators 57 and 21 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 399 (which is smaller than their product 57 × 21 = 1197, keeping the calculation simpler).

LCD(57, 21) = 399

Step 2

Convert to Equivalent Fractions with Common Denominator 399

Multiply the numerator and denominator of 12/57 by 7, and multiply the numerator and denominator of 9/21 by 19 so both fractions share the common base 399.

12 × 7/57 × 7 = 84/399 and 9 × 19/21 × 19 = 171/399

Step 3

Add the Numerators

Now add the numerators (84 + 171 = 255) and keep the common denominator 399 unchanged.

84 + 171/399 = 255/399

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 255 and 399, which is 3. Divide both the numerator and denominator by 3.

255 ÷ 3/399 ÷ 3 = 85/133

Step 5

Decimal & Percentage Representation

Dividing the numerator 85 by denominator 133 produces a repeating decimal (approximately 0.639098, or 63.9098%).

85 ÷ 133 = 0.639098 (63.9098%)

Visual Representation

The diagram below illustrates 12/57 plus 9/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`85/133`
Mixed Number Form	`85/133`
Decimal Form	`0.639098`
Percentage	`63.9098%`

Was this solution helpful?

Help us improve our free step-by-step tools

Frequently Asked Questions

What is 12/57 plus 9/21 as a fraction?

12/57 + 9/21 in simplest fraction form is 85/133.

What is 12/57 plus 9/21 as a decimal?

12/57 + 9/21 converted to a decimal is 0.639098.

What is 12/57 plus 9/21 as a percentage?

12/57 + 9/21 expressed as a percentage is 63.9098%.

Does 12/57 plus 9/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.639098...) because the denominator contains prime factors other than 2 and 5.