What is 3/21 plus 9/60? (Answer: 41/140)

Exact Answer

==================================================
Problem: What is 3/21 plus 9/60?
Formula / Expression: 3/21 + 9/60
Final Answer: 41/140
==================================================

Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 21 and 60 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 420 (which is smaller than their product 21 × 60 = 1260, keeping the calculation simpler).
Working: LCD(21, 60) = 420

Step 2: Convert to Equivalent Fractions with Common Denominator 420
Multiply the numerator and denominator of 3/21 by 20, and multiply the numerator and denominator of 9/60 by 7 so both fractions share the common base 420.
Working: 3 × 20/21 × 20 = 60/420 and 9 × 7/60 × 7 = 63/420

Step 3: Add the Numerators
Now add the numerators (60 + 63 = 123) and keep the common denominator 420 unchanged.
Working: 60 + 63/420 = 123/420

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 123 and 420, which is 3. Divide both the numerator and denominator by 3.
Working: 123 ÷ 3/420 ÷ 3 = 41/140

Step 5: Decimal & Percentage Representation
Dividing the numerator 41 by denominator 140 produces a repeating decimal (approximately 0.292857, or 29.2857%).
Working: 41 ÷ 140 = 0.292857 (29.2857%)

Key Values:
- Simplified Fraction: 41/140
- Mixed Number Form: 41/140
- Decimal Value: 0.292857
- Percentage: 29.2857%

--------------------------------------------------
Solved with FractionsCalc:
https://fractionscalc.com/what-is-3-21-plus-9-60/
==================================================

3/21 + 9/60 = 41/140

Simplified Fraction

41/140

Mixed Number

Proper (41/140)

Decimal Value

0.292857

Percentage

29.2857%

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: 3/21 + 9/60

Step 1

Find the Least Common Denominator (LCD)

The denominators 21 and 60 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 420 (which is smaller than their product 21 × 60 = 1260, keeping the calculation simpler).

LCD(21, 60) = 420

Step 2

Convert to Equivalent Fractions with Common Denominator 420

Multiply the numerator and denominator of 3/21 by 20, and multiply the numerator and denominator of 9/60 by 7 so both fractions share the common base 420.

3 × 20/21 × 20 = 60/420 and 9 × 7/60 × 7 = 63/420

Step 3

Add the Numerators

Now add the numerators (60 + 63 = 123) and keep the common denominator 420 unchanged.

60 + 63/420 = 123/420

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 123 and 420, which is 3. Divide both the numerator and denominator by 3.

123 ÷ 3/420 ÷ 3 = 41/140

Step 5

Decimal & Percentage Representation

Dividing the numerator 41 by denominator 140 produces a repeating decimal (approximately 0.292857, or 29.2857%).

41 ÷ 140 = 0.292857 (29.2857%)

Visual Representation

The diagram below illustrates 3/21 plus 9/60 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`41/140`
Mixed Number Form	`41/140`
Decimal Form	`0.292857`
Percentage	`29.2857%`

Was this solution helpful?

Help us improve our free step-by-step tools

Frequently Asked Questions

What is 3/21 plus 9/60 as a fraction?

3/21 + 9/60 in simplest fraction form is 41/140.

What is 3/21 plus 9/60 as a decimal?

3/21 + 9/60 converted to a decimal is 0.292857.

What is 3/21 plus 9/60 as a percentage?

3/21 + 9/60 expressed as a percentage is 29.2857%.

Does 3/21 plus 9/60 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.292857...) because the denominator contains prime factors other than 2 and 5.