What is 5/49 plus 7/21? (Answer: 64/147)

Exact Answer

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Problem: What is 5/49 plus 7/21?
Formula / Expression: 5/49 + 7/21
Final Answer: 64/147
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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 7/21 by 7 so both fractions share the common base 147.
Working: 5 × 3/49 × 3 = 15/147 and 7 × 7/21 × 7 = 49/147

Step 3: Add the Numerators
Now add the numerators (15 + 49 = 64) and keep the common denominator 147 unchanged.
Working: 15 + 49/147 = 64/147

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 64 and 147 is 1, confirming that 64/147 cannot be reduced further—it is already in its simplest irreducible form.
Working: 64/147

Step 5: Decimal & Percentage Representation
Dividing the numerator 64 by denominator 147 produces a repeating decimal (approximately 0.435374, or 43.5374%).
Working: 64 ÷ 147 = 0.435374 (43.5374%)

Key Values:
- Simplified Fraction: 64/147
- Mixed Number Form: 64/147
- Decimal Value: 0.435374
- Percentage: 43.5374%

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Solved with FractionsCalc:
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5/49 + 7/21 = 64/147

Simplified Fraction

64/147

Mixed Number

Proper (64/147)

Decimal Value

0.435374

Percentage

43.5374%

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Step-by-Step Solution: 5/49 + 7/21

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

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

Step 3

Add the Numerators

Now add the numerators (15 + 49 = 64) and keep the common denominator 147 unchanged.

15 + 49/147 = 64/147

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 64 and 147 is 1, confirming that 64/147 cannot be reduced further—it is already in its simplest irreducible form.

64/147

Step 5

Decimal & Percentage Representation

Dividing the numerator 64 by denominator 147 produces a repeating decimal (approximately 0.435374, or 43.5374%).

64 ÷ 147 = 0.435374 (43.5374%)

Visual Representation

The diagram below illustrates 5/49 plus 7/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`64/147`
Mixed Number Form	`64/147`
Decimal Form	`0.435374`
Percentage	`43.5374%`

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Frequently Asked Questions

What is 5/49 plus 7/21 as a fraction?

5/49 + 7/21 in simplest fraction form is 64/147.

What is 5/49 plus 7/21 as a decimal?

5/49 + 7/21 converted to a decimal is 0.435374.

What is 5/49 plus 7/21 as a percentage?

5/49 + 7/21 expressed as a percentage is 43.5374%.

Does 5/49 plus 7/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.435374...) because the denominator contains prime factors other than 2 and 5.