What is 8/49 plus 8/21? (Answer: 80/147)

Exact Answer

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Problem: What is 8/49 plus 8/21?
Formula / Expression: 8/49 + 8/21
Final Answer: 80/147
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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 8/49 by 3, and multiply the numerator and denominator of 8/21 by 7 so both fractions share the common base 147.
Working: 8 × 3/49 × 3 = 24/147 and 8 × 7/21 × 7 = 56/147

Step 3: Add the Numerators
Now add the numerators (24 + 56 = 80) and keep the common denominator 147 unchanged.
Working: 24 + 56/147 = 80/147

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 80 and 147 is 1, confirming that 80/147 cannot be reduced further—it is already in its simplest irreducible form.
Working: 80/147

Step 5: Decimal & Percentage Representation
Dividing the numerator 80 by denominator 147 produces a repeating decimal (approximately 0.544218, or 54.4218%).
Working: 80 ÷ 147 = 0.544218 (54.4218%)

Key Values:
- Simplified Fraction: 80/147
- Mixed Number Form: 80/147
- Decimal Value: 0.544218
- Percentage: 54.4218%

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Solved with FractionsCalc:
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8/49 + 8/21 = 80/147

Simplified Fraction

80/147

Mixed Number

Proper (80/147)

Decimal Value

0.544218

Percentage

54.4218%

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Step-by-Step Solution: 8/49 + 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 8/49 by 3, and multiply the numerator and denominator of 8/21 by 7 so both fractions share the common base 147.

8 × 3/49 × 3 = 24/147 and 8 × 7/21 × 7 = 56/147

Step 3

Add the Numerators

Now add the numerators (24 + 56 = 80) and keep the common denominator 147 unchanged.

24 + 56/147 = 80/147

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 80 and 147 is 1, confirming that 80/147 cannot be reduced further—it is already in its simplest irreducible form.

80/147

Step 5

Decimal & Percentage Representation

Dividing the numerator 80 by denominator 147 produces a repeating decimal (approximately 0.544218, or 54.4218%).

80 ÷ 147 = 0.544218 (54.4218%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`80/147`
Mixed Number Form	`80/147`
Decimal Form	`0.544218`
Percentage	`54.4218%`

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Frequently Asked Questions

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

8/49 + 8/21 in simplest fraction form is 80/147.

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

8/49 + 8/21 converted to a decimal is 0.544218.

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

8/49 + 8/21 expressed as a percentage is 54.4218%.

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

It results in a repeating decimal (approximately 0.544218...) because the denominator contains prime factors other than 2 and 5.