What is 6/49 plus 5/21? (Answer: 53/147)

Exact Answer

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Problem: What is 6/49 plus 5/21?
Formula / Expression: 6/49 + 5/21
Final Answer: 53/147
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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 6/49 by 3, and multiply the numerator and denominator of 5/21 by 7 so both fractions share the common base 147.
Working: 6 × 3/49 × 3 = 18/147 and 5 × 7/21 × 7 = 35/147

Step 3: Add the Numerators
Now add the numerators (18 + 35 = 53) and keep the common denominator 147 unchanged.
Working: 18 + 35/147 = 53/147

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 53 and 147 is 1, confirming that 53/147 cannot be reduced further—it is already in its simplest irreducible form.
Working: 53/147

Step 5: Decimal & Percentage Representation
Dividing the numerator 53 by denominator 147 produces a repeating decimal (approximately 0.360544, or 36.0544%).
Working: 53 ÷ 147 = 0.360544 (36.0544%)

Key Values:
- Simplified Fraction: 53/147
- Mixed Number Form: 53/147
- Decimal Value: 0.360544
- Percentage: 36.0544%

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Solved with FractionsCalc:
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6/49 + 5/21 = 53/147

Simplified Fraction

53/147

Mixed Number

Proper (53/147)

Decimal Value

0.360544

Percentage

36.0544%

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Step-by-Step Solution: 6/49 + 5/21

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 6/49 by 3, and multiply the numerator and denominator of 5/21 by 7 so both fractions share the common base 147.

6 × 3/49 × 3 = 18/147 and 5 × 7/21 × 7 = 35/147

Step 3

Add the Numerators

Now add the numerators (18 + 35 = 53) and keep the common denominator 147 unchanged.

18 + 35/147 = 53/147

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 53 and 147 is 1, confirming that 53/147 cannot be reduced further—it is already in its simplest irreducible form.

53/147

Step 5

Decimal & Percentage Representation

Dividing the numerator 53 by denominator 147 produces a repeating decimal (approximately 0.360544, or 36.0544%).

53 ÷ 147 = 0.360544 (36.0544%)

Visual Representation

The diagram below illustrates 6/49 plus 5/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`53/147`
Mixed Number Form	`53/147`
Decimal Form	`0.360544`
Percentage	`36.0544%`

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Frequently Asked Questions

What is 6/49 plus 5/21 as a fraction?

6/49 + 5/21 in simplest fraction form is 53/147.

What is 6/49 plus 5/21 as a decimal?

6/49 + 5/21 converted to a decimal is 0.360544.

What is 6/49 plus 5/21 as a percentage?

6/49 + 5/21 expressed as a percentage is 36.0544%.

Does 6/49 plus 5/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.360544...) because the denominator contains prime factors other than 2 and 5.