What is 3/60 plus 2/21? (Answer: 61/420)

Exact Answer

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Problem: What is 3/60 plus 2/21?
Formula / Expression: 3/60 + 2/21
Final Answer: 61/420
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Step-by-Step Solution:

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

Step 2: Convert to Equivalent Fractions with Common Denominator 420
Multiply the numerator and denominator of 3/60 by 7, and multiply the numerator and denominator of 2/21 by 20 so both fractions share the common base 420.
Working: 3 × 7/60 × 7 = 21/420 and 2 × 20/21 × 20 = 40/420

Step 3: Add the Numerators
Now add the numerators (21 + 40 = 61) and keep the common denominator 420 unchanged.
Working: 21 + 40/420 = 61/420

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 61 and 420 is 1, confirming that 61/420 cannot be reduced further—it is already in its simplest irreducible form.
Working: 61/420

Step 5: Decimal & Percentage Representation
Dividing the numerator 61 by denominator 420 produces a repeating decimal (approximately 0.145238, or 14.5238%).
Working: 61 ÷ 420 = 0.145238 (14.5238%)

Key Values:
- Simplified Fraction: 61/420
- Mixed Number Form: 61/420
- Decimal Value: 0.145238
- Percentage: 14.5238%

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3/60 + 2/21 = 61/420

Simplified Fraction

61/420

Mixed Number

Proper (61/420)

Decimal Value

0.145238

Percentage

14.5238%

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Step-by-Step Solution: 3/60 + 2/21

Step 1

Find the Least Common Denominator (LCD)

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

LCD(60, 21) = 420

Step 2

Convert to Equivalent Fractions with Common Denominator 420

Multiply the numerator and denominator of 3/60 by 7, and multiply the numerator and denominator of 2/21 by 20 so both fractions share the common base 420.

3 × 7/60 × 7 = 21/420 and 2 × 20/21 × 20 = 40/420

Step 3

Add the Numerators

Now add the numerators (21 + 40 = 61) and keep the common denominator 420 unchanged.

21 + 40/420 = 61/420

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 61 and 420 is 1, confirming that 61/420 cannot be reduced further—it is already in its simplest irreducible form.

61/420

Step 5

Decimal & Percentage Representation

Dividing the numerator 61 by denominator 420 produces a repeating decimal (approximately 0.145238, or 14.5238%).

61 ÷ 420 = 0.145238 (14.5238%)

Visual Representation

The diagram below illustrates 3/60 plus 2/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`61/420`
Mixed Number Form	`61/420`
Decimal Form	`0.145238`
Percentage	`14.5238%`

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Frequently Asked Questions

What is 3/60 plus 2/21 as a fraction?

3/60 + 2/21 in simplest fraction form is 61/420.

What is 3/60 plus 2/21 as a decimal?

3/60 + 2/21 converted to a decimal is 0.145238.

What is 3/60 plus 2/21 as a percentage?

3/60 + 2/21 expressed as a percentage is 14.5238%.

Does 3/60 plus 2/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.145238...) because the denominator contains prime factors other than 2 and 5.