What is 13/30 plus 15/21? (Answer: 241/210)

Exact Answer

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Problem: What is 13/30 plus 15/21?
Formula / Expression: 13/30 + 15/21
Final Answer: 1 31/210 (241/210)
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 30 and 21 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 210 (which is smaller than their product 30 × 21 = 630, keeping the calculation simpler).
Working: LCD(30, 21) = 210

Step 2: Convert to Equivalent Fractions with Common Denominator 210
Multiply the numerator and denominator of 13/30 by 7, and multiply the numerator and denominator of 15/21 by 10 so both fractions share the common base 210.
Working: 13 × 7/30 × 7 = 91/210 and 15 × 10/21 × 10 = 150/210

Step 3: Add the Numerators
Now add the numerators (91 + 150 = 241) and keep the common denominator 210 unchanged.
Working: 91 + 150/210 = 241/210

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 241 and 210 is 1, confirming that 241/210 cannot be reduced further—it is already in its simplest irreducible form.
Working: 241/210

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (241) is greater than the denominator (210), divide 241 by 210: it goes in 1 whole time(s) with a remainder of 31, giving the mixed number 1 31/210.
Working: 241/210 = 1 31/210

Step 6: Decimal & Percentage Representation
Dividing the numerator 241 by denominator 210 produces a repeating decimal (approximately 1.147619, or 114.7619%).
Working: 241 ÷ 210 = 1.147619 (114.7619%)

Key Values:
- Simplified Fraction: 241/210
- Mixed Number Form: 1 31/210
- Decimal Value: 1.147619
- Percentage: 114.7619%

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13/30 + 15/21 = 241/210

Simplified Fraction

241/210

Mixed Number

1 31/210

Decimal Value

1.147619

Percentage

114.7619%

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Step-by-Step Solution: 13/30 + 15/21

Step 1

Find the Least Common Denominator (LCD)

The denominators 30 and 21 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 210 (which is smaller than their product 30 × 21 = 630, keeping the calculation simpler).

LCD(30, 21) = 210

Step 2

Convert to Equivalent Fractions with Common Denominator 210

Multiply the numerator and denominator of 13/30 by 7, and multiply the numerator and denominator of 15/21 by 10 so both fractions share the common base 210.

13 × 7/30 × 7 = 91/210 and 15 × 10/21 × 10 = 150/210

Step 3

Add the Numerators

Now add the numerators (91 + 150 = 241) and keep the common denominator 210 unchanged.

91 + 150/210 = 241/210

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 241 and 210 is 1, confirming that 241/210 cannot be reduced further—it is already in its simplest irreducible form.

241/210

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (241) is greater than the denominator (210), divide 241 by 210: it goes in 1 whole time(s) with a remainder of 31, giving the mixed number 1 31/210.

241/210 = 131/210

Step 6

Decimal & Percentage Representation

Dividing the numerator 241 by denominator 210 produces a repeating decimal (approximately 1.147619, or 114.7619%).

241 ÷ 210 = 1.147619 (114.7619%)

Visual Representation

The diagram below illustrates 13/30 plus 15/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`241/210`
Mixed Number Form	`1 31/210`
Decimal Form	`1.147619`
Percentage	`114.7619%`

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Frequently Asked Questions

What is 13/30 plus 15/21 as a fraction?

13/30 + 15/21 in simplest fraction form is 241/210 (or 1 31/210 as a mixed number).

What is 13/30 plus 15/21 as a decimal?

13/30 + 15/21 converted to a decimal is 1.147619.

What is 13/30 plus 15/21 as a percentage?

13/30 + 15/21 expressed as a percentage is 114.7619%.

How do you write 13/30 plus 15/21 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 241/210 can be written as the mixed number 1 31/210.

Does 13/30 plus 15/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.147619...) because the denominator contains prime factors other than 2 and 5.