What is 5/49 plus 5/21? (Answer: 50/147)

Exact Answer

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Problem: What is 5/49 plus 5/21?
Formula / Expression: 5/49 + 5/21
Final Answer: 50/147
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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 5/49 by 3, and multiply the numerator and denominator of 5/21 by 7 so both fractions share the common base 147.
Working: 5 × 3/49 × 3 = 15/147 and 5 × 7/21 × 7 = 35/147

Step 3: Add the Numerators
Now add the numerators (15 + 35 = 50) and keep the common denominator 147 unchanged.
Working: 15 + 35/147 = 50/147

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 50 and 147 is 1, confirming that 50/147 cannot be reduced further—it is already in its simplest irreducible form.
Working: 50/147

Step 5: Decimal & Percentage Representation
Dividing the numerator 50 by denominator 147 produces a repeating decimal (approximately 0.340136, or 34.0136%).
Working: 50 ÷ 147 = 0.340136 (34.0136%)

Key Values:
- Simplified Fraction: 50/147
- Mixed Number Form: 50/147
- Decimal Value: 0.340136
- Percentage: 34.0136%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-5-49-plus-5-21/
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5/49 + 5/21 = 50/147

Simplified Fraction

50/147

Mixed Number

Proper (50/147)

Decimal Value

0.340136

Percentage

34.0136%

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Step-by-Step Solution: 5/49 + 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 5/49 by 3, and multiply the numerator and denominator of 5/21 by 7 so both fractions share the common base 147.

5 × 3/49 × 3 = 15/147 and 5 × 7/21 × 7 = 35/147

Step 3

Add the Numerators

Now add the numerators (15 + 35 = 50) and keep the common denominator 147 unchanged.

15 + 35/147 = 50/147

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 50 and 147 is 1, confirming that 50/147 cannot be reduced further—it is already in its simplest irreducible form.

50/147

Step 5

Decimal & Percentage Representation

Dividing the numerator 50 by denominator 147 produces a repeating decimal (approximately 0.340136, or 34.0136%).

50 ÷ 147 = 0.340136 (34.0136%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`50/147`
Mixed Number Form	`50/147`
Decimal Form	`0.340136`
Percentage	`34.0136%`

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Frequently Asked Questions

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

5/49 + 5/21 in simplest fraction form is 50/147.

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

5/49 + 5/21 converted to a decimal is 0.340136.

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

5/49 + 5/21 expressed as a percentage is 34.0136%.

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

It results in a repeating decimal (approximately 0.340136...) because the denominator contains prime factors other than 2 and 5.