What is 11/30 plus 15/21? (Answer: 227/210)

Exact Answer

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Problem: What is 11/30 plus 15/21?
Formula / Expression: 11/30 + 15/21
Final Answer: 1 17/210 (227/210)
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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 11/30 by 7, and multiply the numerator and denominator of 15/21 by 10 so both fractions share the common base 210.
Working: 11 × 7/30 × 7 = 77/210 and 15 × 10/21 × 10 = 150/210

Step 3: Add the Numerators
Now add the numerators (77 + 150 = 227) and keep the common denominator 210 unchanged.
Working: 77 + 150/210 = 227/210

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 227 and 210 is 1, confirming that 227/210 cannot be reduced further—it is already in its simplest irreducible form.
Working: 227/210

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (227) is greater than the denominator (210), divide 227 by 210: it goes in 1 whole time(s) with a remainder of 17, giving the mixed number 1 17/210.
Working: 227/210 = 1 17/210

Step 6: Decimal & Percentage Representation
Dividing the numerator 227 by denominator 210 produces a repeating decimal (approximately 1.080952, or 108.0952%).
Working: 227 ÷ 210 = 1.080952 (108.0952%)

Key Values:
- Simplified Fraction: 227/210
- Mixed Number Form: 1 17/210
- Decimal Value: 1.080952
- Percentage: 108.0952%

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11/30 + 15/21 = 227/210

Simplified Fraction

227/210

Mixed Number

1 17/210

Decimal Value

1.080952

Percentage

108.0952%

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Step-by-Step Solution: 11/30 + 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 11/30 by 7, and multiply the numerator and denominator of 15/21 by 10 so both fractions share the common base 210.

11 × 7/30 × 7 = 77/210 and 15 × 10/21 × 10 = 150/210

Step 3

Add the Numerators

Now add the numerators (77 + 150 = 227) and keep the common denominator 210 unchanged.

77 + 150/210 = 227/210

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 227 and 210 is 1, confirming that 227/210 cannot be reduced further—it is already in its simplest irreducible form.

227/210

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (227) is greater than the denominator (210), divide 227 by 210: it goes in 1 whole time(s) with a remainder of 17, giving the mixed number 1 17/210.

227/210 = 117/210

Step 6

Decimal & Percentage Representation

Dividing the numerator 227 by denominator 210 produces a repeating decimal (approximately 1.080952, or 108.0952%).

227 ÷ 210 = 1.080952 (108.0952%)

Visual Representation

The diagram below illustrates 11/30 plus 15/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`227/210`
Mixed Number Form	`1 17/210`
Decimal Form	`1.080952`
Percentage	`108.0952%`

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Frequently Asked Questions

What is 11/30 plus 15/21 as a fraction?

11/30 + 15/21 in simplest fraction form is 227/210 (or 1 17/210 as a mixed number).

What is 11/30 plus 15/21 as a decimal?

11/30 + 15/21 converted to a decimal is 1.080952.

What is 11/30 plus 15/21 as a percentage?

11/30 + 15/21 expressed as a percentage is 108.0952%.

How do you write 11/30 plus 15/21 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 227/210 can be written as the mixed number 1 17/210.

Does 11/30 plus 15/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.080952...) because the denominator contains prime factors other than 2 and 5.