What is 12/30 plus 11/21? (Answer: 97/105)

Exact Answer

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Problem: What is 12/30 plus 11/21?
Formula / Expression: 12/30 + 11/21
Final Answer: 97/105
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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 12/30 by 7, and multiply the numerator and denominator of 11/21 by 10 so both fractions share the common base 210.
Working: 12 × 7/30 × 7 = 84/210 and 11 × 10/21 × 10 = 110/210

Step 3: Add the Numerators
Now add the numerators (84 + 110 = 194) and keep the common denominator 210 unchanged.
Working: 84 + 110/210 = 194/210

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 194 and 210, which is 2. Divide both the numerator and denominator by 2.
Working: 194 ÷ 2/210 ÷ 2 = 97/105

Step 5: Decimal & Percentage Representation
Dividing the numerator 97 by denominator 105 produces a repeating decimal (approximately 0.92381, or 92.381%).
Working: 97 ÷ 105 = 0.92381 (92.381%)

Key Values:
- Simplified Fraction: 97/105
- Mixed Number Form: 97/105
- Decimal Value: 0.92381
- Percentage: 92.381%

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Solved with FractionsCalc:
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12/30 + 11/21 = 97/105

Simplified Fraction

97/105

Mixed Number

Proper (97/105)

Decimal Value

0.92381

Percentage

92.381%

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Step-by-Step Solution: 12/30 + 11/21

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 12/30 by 7, and multiply the numerator and denominator of 11/21 by 10 so both fractions share the common base 210.

12 × 7/30 × 7 = 84/210 and 11 × 10/21 × 10 = 110/210

Step 3

Add the Numerators

Now add the numerators (84 + 110 = 194) and keep the common denominator 210 unchanged.

84 + 110/210 = 194/210

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 194 and 210, which is 2. Divide both the numerator and denominator by 2.

194 ÷ 2/210 ÷ 2 = 97/105

Step 5

Decimal & Percentage Representation

Dividing the numerator 97 by denominator 105 produces a repeating decimal (approximately 0.92381, or 92.381%).

97 ÷ 105 = 0.92381 (92.381%)

Visual Representation

The diagram below illustrates 12/30 plus 11/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`97/105`
Mixed Number Form	`97/105`
Decimal Form	`0.92381`
Percentage	`92.381%`

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Frequently Asked Questions

What is 12/30 plus 11/21 as a fraction?

12/30 + 11/21 in simplest fraction form is 97/105.

What is 12/30 plus 11/21 as a decimal?

12/30 + 11/21 converted to a decimal is 0.92381.

What is 12/30 plus 11/21 as a percentage?

12/30 + 11/21 expressed as a percentage is 92.381%.

Does 12/30 plus 11/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.92381...) because the denominator contains prime factors other than 2 and 5.