What is 13/49 plus 8/21? (Answer: 95/147)

Exact Answer

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Problem: What is 13/49 plus 8/21?
Formula / Expression: 13/49 + 8/21
Final Answer: 95/147
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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 13/49 by 3, and multiply the numerator and denominator of 8/21 by 7 so both fractions share the common base 147.
Working: 13 × 3/49 × 3 = 39/147 and 8 × 7/21 × 7 = 56/147

Step 3: Add the Numerators
Now add the numerators (39 + 56 = 95) and keep the common denominator 147 unchanged.
Working: 39 + 56/147 = 95/147

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 95 and 147 is 1, confirming that 95/147 cannot be reduced further—it is already in its simplest irreducible form.
Working: 95/147

Step 5: Decimal & Percentage Representation
Dividing the numerator 95 by denominator 147 produces a repeating decimal (approximately 0.646259, or 64.6259%).
Working: 95 ÷ 147 = 0.646259 (64.6259%)

Key Values:
- Simplified Fraction: 95/147
- Mixed Number Form: 95/147
- Decimal Value: 0.646259
- Percentage: 64.6259%

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Solved with FractionsCalc:
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13/49 + 8/21 = 95/147

Simplified Fraction

95/147

Mixed Number

Proper (95/147)

Decimal Value

0.646259

Percentage

64.6259%

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Step-by-Step Solution: 13/49 + 8/21

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 13/49 by 3, and multiply the numerator and denominator of 8/21 by 7 so both fractions share the common base 147.

13 × 3/49 × 3 = 39/147 and 8 × 7/21 × 7 = 56/147

Step 3

Add the Numerators

Now add the numerators (39 + 56 = 95) and keep the common denominator 147 unchanged.

39 + 56/147 = 95/147

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 95 and 147 is 1, confirming that 95/147 cannot be reduced further—it is already in its simplest irreducible form.

95/147

Step 5

Decimal & Percentage Representation

Dividing the numerator 95 by denominator 147 produces a repeating decimal (approximately 0.646259, or 64.6259%).

95 ÷ 147 = 0.646259 (64.6259%)

Visual Representation

The diagram below illustrates 13/49 plus 8/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`95/147`
Mixed Number Form	`95/147`
Decimal Form	`0.646259`
Percentage	`64.6259%`

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Frequently Asked Questions

What is 13/49 plus 8/21 as a fraction?

13/49 + 8/21 in simplest fraction form is 95/147.

What is 13/49 plus 8/21 as a decimal?

13/49 + 8/21 converted to a decimal is 0.646259.

What is 13/49 plus 8/21 as a percentage?

13/49 + 8/21 expressed as a percentage is 64.6259%.

Does 13/49 plus 8/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.646259...) because the denominator contains prime factors other than 2 and 5.