What is 2/60 plus 3/21? (Answer: 37/210)

Exact Answer

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Problem: What is 2/60 plus 3/21?
Formula / Expression: 2/60 + 3/21
Final Answer: 37/210
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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 2/60 by 7, and multiply the numerator and denominator of 3/21 by 20 so both fractions share the common base 420.
Working: 2 × 7/60 × 7 = 14/420 and 3 × 20/21 × 20 = 60/420

Step 3: Add the Numerators
Now add the numerators (14 + 60 = 74) and keep the common denominator 420 unchanged.
Working: 14 + 60/420 = 74/420

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 74 and 420, which is 2. Divide both the numerator and denominator by 2.
Working: 74 ÷ 2/420 ÷ 2 = 37/210

Step 5: Decimal & Percentage Representation
Dividing the numerator 37 by denominator 210 produces a repeating decimal (approximately 0.17619, or 17.619%).
Working: 37 ÷ 210 = 0.17619 (17.619%)

Key Values:
- Simplified Fraction: 37/210
- Mixed Number Form: 37/210
- Decimal Value: 0.17619
- Percentage: 17.619%

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Solved with FractionsCalc:
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2/60 + 3/21 = 37/210

Simplified Fraction

37/210

Mixed Number

Proper (37/210)

Decimal Value

0.17619

Percentage

17.619%

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

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

2 × 7/60 × 7 = 14/420 and 3 × 20/21 × 20 = 60/420

Step 3

Add the Numerators

Now add the numerators (14 + 60 = 74) and keep the common denominator 420 unchanged.

14 + 60/420 = 74/420

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 74 and 420, which is 2. Divide both the numerator and denominator by 2.

74 ÷ 2/420 ÷ 2 = 37/210

Step 5

Decimal & Percentage Representation

Dividing the numerator 37 by denominator 210 produces a repeating decimal (approximately 0.17619, or 17.619%).

37 ÷ 210 = 0.17619 (17.619%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`37/210`
Mixed Number Form	`37/210`
Decimal Form	`0.17619`
Percentage	`17.619%`

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Frequently Asked Questions

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

2/60 + 3/21 in simplest fraction form is 37/210.

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

2/60 + 3/21 converted to a decimal is 0.17619.

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

2/60 + 3/21 expressed as a percentage is 17.619%.

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

It results in a repeating decimal (approximately 0.17619...) because the denominator contains prime factors other than 2 and 5.