What is 6/60 plus 7/21? (Answer: 13/30)

Exact Answer

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Problem: What is 6/60 plus 7/21?
Formula / Expression: 6/60 + 7/21
Final Answer: 13/30
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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 7/21 by 20 so both fractions share the common base 420.
Working: 6 × 7/60 × 7 = 42/420 and 7 × 20/21 × 20 = 140/420

Step 3: Add the Numerators
Now add the numerators (42 + 140 = 182) and keep the common denominator 420 unchanged.
Working: 42 + 140/420 = 182/420

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 182 and 420, which is 14. Divide both the numerator and denominator by 14.
Working: 182 ÷ 14/420 ÷ 14 = 13/30

Step 5: Decimal & Percentage Representation
Dividing the numerator 13 by denominator 30 produces a repeating decimal (approximately 0.433333, or 43.3333%).
Working: 13 ÷ 30 = 0.433333 (43.3333%)

Key Values:
- Simplified Fraction: 13/30
- Mixed Number Form: 13/30
- Decimal Value: 0.433333
- Percentage: 43.3333%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-6-60-plus-7-21/
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6/60 + 7/21 = 13/30

Simplified Fraction

13/30

Mixed Number

Proper (13/30)

Decimal Value

0.433333

Percentage

43.3333%

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Step-by-Step Solution: 6/60 + 7/21

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 7/21 by 20 so both fractions share the common base 420.

6 × 7/60 × 7 = 42/420 and 7 × 20/21 × 20 = 140/420

Step 3

Add the Numerators

Now add the numerators (42 + 140 = 182) and keep the common denominator 420 unchanged.

42 + 140/420 = 182/420

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 182 and 420, which is 14. Divide both the numerator and denominator by 14.

182 ÷ 14/420 ÷ 14 = 13/30

Step 5

Decimal & Percentage Representation

Dividing the numerator 13 by denominator 30 produces a repeating decimal (approximately 0.433333, or 43.3333%).

13 ÷ 30 = 0.433333 (43.3333%)

Visual Representation

The diagram below illustrates 6/60 plus 7/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`13/30`
Mixed Number Form	`13/30`
Decimal Form	`0.433333`
Percentage	`43.3333%`

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Frequently Asked Questions

What is 6/60 plus 7/21 as a fraction?

6/60 + 7/21 in simplest fraction form is 13/30.

What is 6/60 plus 7/21 as a decimal?

6/60 + 7/21 converted to a decimal is 0.433333.

What is 6/60 plus 7/21 as a percentage?

6/60 + 7/21 expressed as a percentage is 43.3333%.

Does 6/60 plus 7/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.433333...) because the denominator contains prime factors other than 2 and 5.