What is 13/30 plus 12/21? (Answer: 211/210)

Exact Answer

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Problem: What is 13/30 plus 12/21?
Formula / Expression: 13/30 + 12/21
Final Answer: 1 1/210 (211/210)
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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 12/21 by 10 so both fractions share the common base 210.
Working: 13 × 7/30 × 7 = 91/210 and 12 × 10/21 × 10 = 120/210

Step 3: Add the Numerators
Now add the numerators (91 + 120 = 211) and keep the common denominator 210 unchanged.
Working: 91 + 120/210 = 211/210

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 211 and 210 is 1, confirming that 211/210 cannot be reduced further—it is already in its simplest irreducible form.
Working: 211/210

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (211) is greater than the denominator (210), divide 211 by 210: it goes in 1 whole time(s) with a remainder of 1, giving the mixed number 1 1/210.
Working: 211/210 = 1 1/210

Step 6: Decimal & Percentage Representation
Dividing the numerator 211 by denominator 210 produces a repeating decimal (approximately 1.004762, or 100.4762%).
Working: 211 ÷ 210 = 1.004762 (100.4762%)

Key Values:
- Simplified Fraction: 211/210
- Mixed Number Form: 1 1/210
- Decimal Value: 1.004762
- Percentage: 100.4762%

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Solved with FractionsCalc:
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13/30 + 12/21 = 211/210

Simplified Fraction

211/210

Mixed Number

1 1/210

Decimal Value

1.004762

Percentage

100.4762%

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Step-by-Step Solution: 13/30 + 12/21

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 12/21 by 10 so both fractions share the common base 210.

13 × 7/30 × 7 = 91/210 and 12 × 10/21 × 10 = 120/210

Step 3

Add the Numerators

Now add the numerators (91 + 120 = 211) and keep the common denominator 210 unchanged.

91 + 120/210 = 211/210

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 211 and 210 is 1, confirming that 211/210 cannot be reduced further—it is already in its simplest irreducible form.

211/210

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (211) is greater than the denominator (210), divide 211 by 210: it goes in 1 whole time(s) with a remainder of 1, giving the mixed number 1 1/210.

211/210 = 11/210

Step 6

Decimal & Percentage Representation

Dividing the numerator 211 by denominator 210 produces a repeating decimal (approximately 1.004762, or 100.4762%).

211 ÷ 210 = 1.004762 (100.4762%)

Visual Representation

The diagram below illustrates 13/30 plus 12/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`211/210`
Mixed Number Form	`1 1/210`
Decimal Form	`1.004762`
Percentage	`100.4762%`

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Frequently Asked Questions

What is 13/30 plus 12/21 as a fraction?

13/30 + 12/21 in simplest fraction form is 211/210 (or 1 1/210 as a mixed number).

What is 13/30 plus 12/21 as a decimal?

13/30 + 12/21 converted to a decimal is 1.004762.

What is 13/30 plus 12/21 as a percentage?

13/30 + 12/21 expressed as a percentage is 100.4762%.

How do you write 13/30 plus 12/21 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 211/210 can be written as the mixed number 1 1/210.

Does 13/30 plus 12/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.004762...) because the denominator contains prime factors other than 2 and 5.