What is 13/60 plus 9/21? (Answer: 271/420)

Exact Answer

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Problem: What is 13/60 plus 9/21?
Formula / Expression: 13/60 + 9/21
Final Answer: 271/420
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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 13/60 by 7, and multiply the numerator and denominator of 9/21 by 20 so both fractions share the common base 420.
Working: 13 × 7/60 × 7 = 91/420 and 9 × 20/21 × 20 = 180/420

Step 3: Add the Numerators
Now add the numerators (91 + 180 = 271) and keep the common denominator 420 unchanged.
Working: 91 + 180/420 = 271/420

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 271 and 420 is 1, confirming that 271/420 cannot be reduced further—it is already in its simplest irreducible form.
Working: 271/420

Step 5: Decimal & Percentage Representation
Dividing the numerator 271 by denominator 420 produces a repeating decimal (approximately 0.645238, or 64.5238%).
Working: 271 ÷ 420 = 0.645238 (64.5238%)

Key Values:
- Simplified Fraction: 271/420
- Mixed Number Form: 271/420
- Decimal Value: 0.645238
- Percentage: 64.5238%

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Solved with FractionsCalc:
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13/60 + 9/21 = 271/420

Simplified Fraction

271/420

Mixed Number

Proper (271/420)

Decimal Value

0.645238

Percentage

64.5238%

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Step-by-Step Solution: 13/60 + 9/21

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 13/60 by 7, and multiply the numerator and denominator of 9/21 by 20 so both fractions share the common base 420.

13 × 7/60 × 7 = 91/420 and 9 × 20/21 × 20 = 180/420

Step 3

Add the Numerators

Now add the numerators (91 + 180 = 271) and keep the common denominator 420 unchanged.

91 + 180/420 = 271/420

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 271 and 420 is 1, confirming that 271/420 cannot be reduced further—it is already in its simplest irreducible form.

271/420

Step 5

Decimal & Percentage Representation

Dividing the numerator 271 by denominator 420 produces a repeating decimal (approximately 0.645238, or 64.5238%).

271 ÷ 420 = 0.645238 (64.5238%)

Visual Representation

The diagram below illustrates 13/60 plus 9/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`271/420`
Mixed Number Form	`271/420`
Decimal Form	`0.645238`
Percentage	`64.5238%`

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Frequently Asked Questions

What is 13/60 plus 9/21 as a fraction?

13/60 + 9/21 in simplest fraction form is 271/420.

What is 13/60 plus 9/21 as a decimal?

13/60 + 9/21 converted to a decimal is 0.645238.

What is 13/60 plus 9/21 as a percentage?

13/60 + 9/21 expressed as a percentage is 64.5238%.

Does 13/60 plus 9/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.645238...) because the denominator contains prime factors other than 2 and 5.