What is 8/21 plus 19/49? (Answer: 113/147)

Exact Answer

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Problem: What is 8/21 plus 19/49?
Formula / Expression: 8/21 + 19/49
Final Answer: 113/147
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 21 and 49 share a common factor (GCD = 7). Finding their Least Common Multiple gives an LCD of 147 (which is smaller than their product 21 × 49 = 1029, keeping the calculation simpler).
Working: LCD(21, 49) = 147

Step 2: Convert to Equivalent Fractions with Common Denominator 147
Multiply the numerator and denominator of 8/21 by 7, and multiply the numerator and denominator of 19/49 by 3 so both fractions share the common base 147.
Working: 8 × 7/21 × 7 = 56/147 and 19 × 3/49 × 3 = 57/147

Step 3: Add the Numerators
Now add the numerators (56 + 57 = 113) and keep the common denominator 147 unchanged.
Working: 56 + 57/147 = 113/147

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 113 and 147 is 1, confirming that 113/147 cannot be reduced further—it is already in its simplest irreducible form.
Working: 113/147

Step 5: Decimal & Percentage Representation
Dividing the numerator 113 by denominator 147 produces a repeating decimal (approximately 0.768707, or 76.8707%).
Working: 113 ÷ 147 = 0.768707 (76.8707%)

Key Values:
- Simplified Fraction: 113/147
- Mixed Number Form: 113/147
- Decimal Value: 0.768707
- Percentage: 76.8707%

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Solved with FractionsCalc:
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8/21 + 19/49 = 113/147

Simplified Fraction

113/147

Mixed Number

Proper (113/147)

Decimal Value

0.768707

Percentage

76.8707%

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Step-by-Step Solution: 8/21 + 19/49

Step 1

Find the Least Common Denominator (LCD)

The denominators 21 and 49 share a common factor (GCD = 7). Finding their Least Common Multiple gives an LCD of 147 (which is smaller than their product 21 × 49 = 1029, keeping the calculation simpler).

LCD(21, 49) = 147

Step 2

Convert to Equivalent Fractions with Common Denominator 147

Multiply the numerator and denominator of 8/21 by 7, and multiply the numerator and denominator of 19/49 by 3 so both fractions share the common base 147.

8 × 7/21 × 7 = 56/147 and 19 × 3/49 × 3 = 57/147

Step 3

Add the Numerators

Now add the numerators (56 + 57 = 113) and keep the common denominator 147 unchanged.

56 + 57/147 = 113/147

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 113 and 147 is 1, confirming that 113/147 cannot be reduced further—it is already in its simplest irreducible form.

113/147

Step 5

Decimal & Percentage Representation

Dividing the numerator 113 by denominator 147 produces a repeating decimal (approximately 0.768707, or 76.8707%).

113 ÷ 147 = 0.768707 (76.8707%)

Visual Representation

The diagram below illustrates 8/21 plus 19/49 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`113/147`
Mixed Number Form	`113/147`
Decimal Form	`0.768707`
Percentage	`76.8707%`

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Frequently Asked Questions

What is 8/21 plus 19/49 as a fraction?

8/21 + 19/49 in simplest fraction form is 113/147.

What is 8/21 plus 19/49 as a decimal?

8/21 + 19/49 converted to a decimal is 0.768707.

What is 8/21 plus 19/49 as a percentage?

8/21 + 19/49 expressed as a percentage is 76.8707%.

Does 8/21 plus 19/49 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.768707...) because the denominator contains prime factors other than 2 and 5.