What is 3/20 plus 9/21? (Answer: 81/140)

Exact Answer

==================================================
Problem: What is 3/20 plus 9/21?
Formula / Expression: 3/20 + 9/21
Final Answer: 81/140
==================================================

Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 20 and 21 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 20 × 21 = 420.
Working: LCD(20, 21) = 420

Step 2: Convert to Equivalent Fractions with Common Denominator 420
Multiply the numerator and denominator of 3/20 by 21, and multiply the numerator and denominator of 9/21 by 20 so both fractions share the common base 420.
Working: 3 × 21/20 × 21 = 63/420 and 9 × 20/21 × 20 = 180/420

Step 3: Add the Numerators
Now add the numerators (63 + 180 = 243) and keep the common denominator 420 unchanged.
Working: 63 + 180/420 = 243/420

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 243 and 420, which is 3. Divide both the numerator and denominator by 3.
Working: 243 ÷ 3/420 ÷ 3 = 81/140

Step 5: Decimal & Percentage Representation
Dividing the numerator 81 by denominator 140 produces a repeating decimal (approximately 0.578571, or 57.8571%).
Working: 81 ÷ 140 = 0.578571 (57.8571%)

Key Values:
- Simplified Fraction: 81/140
- Mixed Number Form: 81/140
- Decimal Value: 0.578571
- Percentage: 57.8571%

--------------------------------------------------
Solved with FractionsCalc:
https://fractionscalc.com/what-is-3-20-plus-9-21/
==================================================

3/20 + 9/21 = 81/140

Simplified Fraction

81/140

Mixed Number

Proper (81/140)

Decimal Value

0.578571

Percentage

57.8571%

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: 3/20 + 9/21

Step 1

Find the Least Common Denominator (LCD)

The denominators 20 and 21 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 20 × 21 = 420.

LCD(20, 21) = 420

Step 2

Convert to Equivalent Fractions with Common Denominator 420

Multiply the numerator and denominator of 3/20 by 21, and multiply the numerator and denominator of 9/21 by 20 so both fractions share the common base 420.

3 × 21/20 × 21 = 63/420 and 9 × 20/21 × 20 = 180/420

Step 3

Add the Numerators

Now add the numerators (63 + 180 = 243) and keep the common denominator 420 unchanged.

63 + 180/420 = 243/420

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 243 and 420, which is 3. Divide both the numerator and denominator by 3.

243 ÷ 3/420 ÷ 3 = 81/140

Step 5

Decimal & Percentage Representation

Dividing the numerator 81 by denominator 140 produces a repeating decimal (approximately 0.578571, or 57.8571%).

81 ÷ 140 = 0.578571 (57.8571%)

Visual Representation

The diagram below illustrates 3/20 plus 9/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`81/140`
Mixed Number Form	`81/140`
Decimal Form	`0.578571`
Percentage	`57.8571%`

Was this solution helpful?

Help us improve our free step-by-step tools

Frequently Asked Questions

What is 3/20 plus 9/21 as a fraction?

3/20 + 9/21 in simplest fraction form is 81/140.

What is 3/20 plus 9/21 as a decimal?

3/20 + 9/21 converted to a decimal is 0.578571.

What is 3/20 plus 9/21 as a percentage?

3/20 + 9/21 expressed as a percentage is 57.8571%.

Does 3/20 plus 9/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.578571...) because the denominator contains prime factors other than 2 and 5.