What is 8/21 plus 12/30? (Answer: 82/105)

Exact Answer

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Problem: What is 8/21 plus 12/30?
Formula / Expression: 8/21 + 12/30
Final Answer: 82/105
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Step-by-Step Solution:

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

Step 2: Convert to Equivalent Fractions with Common Denominator 210
Multiply the numerator and denominator of 8/21 by 10, and multiply the numerator and denominator of 12/30 by 7 so both fractions share the common base 210.
Working: 8 × 10/21 × 10 = 80/210 and 12 × 7/30 × 7 = 84/210

Step 3: Add the Numerators
Now add the numerators (80 + 84 = 164) and keep the common denominator 210 unchanged.
Working: 80 + 84/210 = 164/210

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 164 and 210, which is 2. Divide both the numerator and denominator by 2.
Working: 164 ÷ 2/210 ÷ 2 = 82/105

Step 5: Decimal & Percentage Representation
Dividing the numerator 82 by denominator 105 produces a repeating decimal (approximately 0.780952, or 78.0952%).
Working: 82 ÷ 105 = 0.780952 (78.0952%)

Key Values:
- Simplified Fraction: 82/105
- Mixed Number Form: 82/105
- Decimal Value: 0.780952
- Percentage: 78.0952%

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Solved with FractionsCalc:
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8/21 + 12/30 = 82/105

Simplified Fraction

82/105

Mixed Number

Proper (82/105)

Decimal Value

0.780952

Percentage

78.0952%

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Step-by-Step Solution: 8/21 + 12/30

Step 1

Find the Least Common Denominator (LCD)

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

LCD(21, 30) = 210

Step 2

Convert to Equivalent Fractions with Common Denominator 210

Multiply the numerator and denominator of 8/21 by 10, and multiply the numerator and denominator of 12/30 by 7 so both fractions share the common base 210.

8 × 10/21 × 10 = 80/210 and 12 × 7/30 × 7 = 84/210

Step 3

Add the Numerators

Now add the numerators (80 + 84 = 164) and keep the common denominator 210 unchanged.

80 + 84/210 = 164/210

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 164 and 210, which is 2. Divide both the numerator and denominator by 2.

164 ÷ 2/210 ÷ 2 = 82/105

Step 5

Decimal & Percentage Representation

Dividing the numerator 82 by denominator 105 produces a repeating decimal (approximately 0.780952, or 78.0952%).

82 ÷ 105 = 0.780952 (78.0952%)

Visual Representation

The diagram below illustrates 8/21 plus 12/30 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`82/105`
Mixed Number Form	`82/105`
Decimal Form	`0.780952`
Percentage	`78.0952%`

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Frequently Asked Questions

What is 8/21 plus 12/30 as a fraction?

8/21 + 12/30 in simplest fraction form is 82/105.

What is 8/21 plus 12/30 as a decimal?

8/21 + 12/30 converted to a decimal is 0.780952.

What is 8/21 plus 12/30 as a percentage?

8/21 + 12/30 expressed as a percentage is 78.0952%.

Does 8/21 plus 12/30 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.780952...) because the denominator contains prime factors other than 2 and 5.