What is 6/60 plus 5/21? (Answer: 71/210)

Exact Answer

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Problem: What is 6/60 plus 5/21?
Formula / Expression: 6/60 + 5/21
Final Answer: 71/210
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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 6/60 by 7, and multiply the numerator and denominator of 5/21 by 20 so both fractions share the common base 420.
Working: 6 × 7/60 × 7 = 42/420 and 5 × 20/21 × 20 = 100/420

Step 3: Add the Numerators
Now add the numerators (42 + 100 = 142) and keep the common denominator 420 unchanged.
Working: 42 + 100/420 = 142/420

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 142 and 420, which is 2. Divide both the numerator and denominator by 2.
Working: 142 ÷ 2/420 ÷ 2 = 71/210

Step 5: Decimal & Percentage Representation
Dividing the numerator 71 by denominator 210 produces a repeating decimal (approximately 0.338095, or 33.8095%).
Working: 71 ÷ 210 = 0.338095 (33.8095%)

Key Values:
- Simplified Fraction: 71/210
- Mixed Number Form: 71/210
- Decimal Value: 0.338095
- Percentage: 33.8095%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-6-60-plus-5-21/
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6/60 + 5/21 = 71/210

Simplified Fraction

71/210

Mixed Number

Proper (71/210)

Decimal Value

0.338095

Percentage

33.8095%

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Step-by-Step Solution: 6/60 + 5/21

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 6/60 by 7, and multiply the numerator and denominator of 5/21 by 20 so both fractions share the common base 420.

6 × 7/60 × 7 = 42/420 and 5 × 20/21 × 20 = 100/420

Step 3

Add the Numerators

Now add the numerators (42 + 100 = 142) and keep the common denominator 420 unchanged.

42 + 100/420 = 142/420

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 142 and 420, which is 2. Divide both the numerator and denominator by 2.

142 ÷ 2/420 ÷ 2 = 71/210

Step 5

Decimal & Percentage Representation

Dividing the numerator 71 by denominator 210 produces a repeating decimal (approximately 0.338095, or 33.8095%).

71 ÷ 210 = 0.338095 (33.8095%)

Visual Representation

The diagram below illustrates 6/60 plus 5/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`71/210`
Mixed Number Form	`71/210`
Decimal Form	`0.338095`
Percentage	`33.8095%`

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Frequently Asked Questions

What is 6/60 plus 5/21 as a fraction?

6/60 + 5/21 in simplest fraction form is 71/210.

What is 6/60 plus 5/21 as a decimal?

6/60 + 5/21 converted to a decimal is 0.338095.

What is 6/60 plus 5/21 as a percentage?

6/60 + 5/21 expressed as a percentage is 33.8095%.

Does 6/60 plus 5/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.338095...) because the denominator contains prime factors other than 2 and 5.