What is 2/49 plus 12/21? (Answer: 30/49)

Exact Answer

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Problem: What is 2/49 plus 12/21?
Formula / Expression: 2/49 + 12/21
Final Answer: 30/49
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 49 and 21 share a common factor (GCD = 7). Finding their Least Common Multiple gives an LCD of 147 (which is smaller than their product 49 × 21 = 1029, keeping the calculation simpler).
Working: LCD(49, 21) = 147

Step 2: Convert to Equivalent Fractions with Common Denominator 147
Multiply the numerator and denominator of 2/49 by 3, and multiply the numerator and denominator of 12/21 by 7 so both fractions share the common base 147.
Working: 2 × 3/49 × 3 = 6/147 and 12 × 7/21 × 7 = 84/147

Step 3: Add the Numerators
Now add the numerators (6 + 84 = 90) and keep the common denominator 147 unchanged.
Working: 6 + 84/147 = 90/147

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 90 and 147, which is 3. Divide both the numerator and denominator by 3.
Working: 90 ÷ 3/147 ÷ 3 = 30/49

Step 5: Decimal & Percentage Representation
Dividing the numerator 30 by denominator 49 produces a repeating decimal (approximately 0.612245, or 61.2245%).
Working: 30 ÷ 49 = 0.612245 (61.2245%)

Key Values:
- Simplified Fraction: 30/49
- Mixed Number Form: 30/49
- Decimal Value: 0.612245
- Percentage: 61.2245%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-49-plus-12-21/
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2/49 + 12/21 = 30/49

Simplified Fraction

30/49

Mixed Number

Proper (30/49)

Decimal Value

0.612245

Percentage

61.2245%

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Step-by-Step Solution: 2/49 + 12/21

Step 1

Find the Least Common Denominator (LCD)

The denominators 49 and 21 share a common factor (GCD = 7). Finding their Least Common Multiple gives an LCD of 147 (which is smaller than their product 49 × 21 = 1029, keeping the calculation simpler).

LCD(49, 21) = 147

Step 2

Convert to Equivalent Fractions with Common Denominator 147

Multiply the numerator and denominator of 2/49 by 3, and multiply the numerator and denominator of 12/21 by 7 so both fractions share the common base 147.

2 × 3/49 × 3 = 6/147 and 12 × 7/21 × 7 = 84/147

Step 3

Add the Numerators

Now add the numerators (6 + 84 = 90) and keep the common denominator 147 unchanged.

6 + 84/147 = 90/147

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 90 and 147, which is 3. Divide both the numerator and denominator by 3.

90 ÷ 3/147 ÷ 3 = 30/49

Step 5

Decimal & Percentage Representation

Dividing the numerator 30 by denominator 49 produces a repeating decimal (approximately 0.612245, or 61.2245%).

30 ÷ 49 = 0.612245 (61.2245%)

Visual Representation

The diagram below illustrates 2/49 plus 12/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`30/49`
Mixed Number Form	`30/49`
Decimal Form	`0.612245`
Percentage	`61.2245%`

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Frequently Asked Questions

What is 2/49 plus 12/21 as a fraction?

2/49 + 12/21 in simplest fraction form is 30/49.

What is 2/49 plus 12/21 as a decimal?

2/49 + 12/21 converted to a decimal is 0.612245.

What is 2/49 plus 12/21 as a percentage?

2/49 + 12/21 expressed as a percentage is 61.2245%.

Does 2/49 plus 12/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.612245...) because the denominator contains prime factors other than 2 and 5.