What is 2/49 plus 2/21? (Answer: 20/147)

Exact Answer

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Problem: What is 2/49 plus 2/21?
Formula / Expression: 2/49 + 2/21
Final Answer: 20/147
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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 2/21 by 7 so both fractions share the common base 147.
Working: 2 × 3/49 × 3 = 6/147 and 2 × 7/21 × 7 = 14/147

Step 3: Add the Numerators
Now add the numerators (6 + 14 = 20) and keep the common denominator 147 unchanged.
Working: 6 + 14/147 = 20/147

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 20 and 147 is 1, confirming that 20/147 cannot be reduced further—it is already in its simplest irreducible form.
Working: 20/147

Step 5: Decimal & Percentage Representation
Dividing the numerator 20 by denominator 147 produces a repeating decimal (approximately 0.136054, or 13.6054%).
Working: 20 ÷ 147 = 0.136054 (13.6054%)

Key Values:
- Simplified Fraction: 20/147
- Mixed Number Form: 20/147
- Decimal Value: 0.136054
- Percentage: 13.6054%

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Solved with FractionsCalc:
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2/49 + 2/21 = 20/147

Simplified Fraction

20/147

Mixed Number

Proper (20/147)

Decimal Value

0.136054

Percentage

13.6054%

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

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 2/21 by 7 so both fractions share the common base 147.

2 × 3/49 × 3 = 6/147 and 2 × 7/21 × 7 = 14/147

Step 3

Add the Numerators

Now add the numerators (6 + 14 = 20) and keep the common denominator 147 unchanged.

6 + 14/147 = 20/147

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 20 and 147 is 1, confirming that 20/147 cannot be reduced further—it is already in its simplest irreducible form.

20/147

Step 5

Decimal & Percentage Representation

Dividing the numerator 20 by denominator 147 produces a repeating decimal (approximately 0.136054, or 13.6054%).

20 ÷ 147 = 0.136054 (13.6054%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`20/147`
Mixed Number Form	`20/147`
Decimal Form	`0.136054`
Percentage	`13.6054%`

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Frequently Asked Questions

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

2/49 + 2/21 in simplest fraction form is 20/147.

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

2/49 + 2/21 converted to a decimal is 0.136054.

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

2/49 + 2/21 expressed as a percentage is 13.6054%.

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

It results in a repeating decimal (approximately 0.136054...) because the denominator contains prime factors other than 2 and 5.