What is 2/21 plus 5/49? (Answer: 29/147)

Exact Answer

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Problem: What is 2/21 plus 5/49?
Formula / Expression: 2/21 + 5/49
Final Answer: 29/147
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Step-by-Step Solution:

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

Step 2: Convert to Equivalent Fractions with Common Denominator 147
Multiply the numerator and denominator of 2/21 by 7, and multiply the numerator and denominator of 5/49 by 3 so both fractions share the common base 147.
Working: 2 × 7/21 × 7 = 14/147 and 5 × 3/49 × 3 = 15/147

Step 3: Add the Numerators
Now add the numerators (14 + 15 = 29) and keep the common denominator 147 unchanged.
Working: 14 + 15/147 = 29/147

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 29 and 147 is 1, confirming that 29/147 cannot be reduced further—it is already in its simplest irreducible form.
Working: 29/147

Step 5: Decimal & Percentage Representation
Dividing the numerator 29 by denominator 147 produces a repeating decimal (approximately 0.197279, or 19.7279%).
Working: 29 ÷ 147 = 0.197279 (19.7279%)

Key Values:
- Simplified Fraction: 29/147
- Mixed Number Form: 29/147
- Decimal Value: 0.197279
- Percentage: 19.7279%

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Solved with FractionsCalc:
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2/21 + 5/49 = 29/147

Simplified Fraction

29/147

Mixed Number

Proper (29/147)

Decimal Value

0.197279

Percentage

19.7279%

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Step-by-Step Solution: 2/21 + 5/49

Step 1

Find the Least Common Denominator (LCD)

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

LCD(21, 49) = 147

Step 2

Convert to Equivalent Fractions with Common Denominator 147

Multiply the numerator and denominator of 2/21 by 7, and multiply the numerator and denominator of 5/49 by 3 so both fractions share the common base 147.

2 × 7/21 × 7 = 14/147 and 5 × 3/49 × 3 = 15/147

Step 3

Add the Numerators

Now add the numerators (14 + 15 = 29) and keep the common denominator 147 unchanged.

14 + 15/147 = 29/147

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 29 and 147 is 1, confirming that 29/147 cannot be reduced further—it is already in its simplest irreducible form.

29/147

Step 5

Decimal & Percentage Representation

Dividing the numerator 29 by denominator 147 produces a repeating decimal (approximately 0.197279, or 19.7279%).

29 ÷ 147 = 0.197279 (19.7279%)

Visual Representation

The diagram below illustrates 2/21 plus 5/49 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`29/147`
Mixed Number Form	`29/147`
Decimal Form	`0.197279`
Percentage	`19.7279%`

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Frequently Asked Questions

What is 2/21 plus 5/49 as a fraction?

2/21 + 5/49 in simplest fraction form is 29/147.

What is 2/21 plus 5/49 as a decimal?

2/21 + 5/49 converted to a decimal is 0.197279.

What is 2/21 plus 5/49 as a percentage?

2/21 + 5/49 expressed as a percentage is 19.7279%.

Does 2/21 plus 5/49 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.197279...) because the denominator contains prime factors other than 2 and 5.