What is 9/49 plus 8/21? (Answer: 83/147)

Exact Answer

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Problem: What is 9/49 plus 8/21?
Formula / Expression: 9/49 + 8/21
Final Answer: 83/147
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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 9/49 by 3, and multiply the numerator and denominator of 8/21 by 7 so both fractions share the common base 147.
Working: 9 × 3/49 × 3 = 27/147 and 8 × 7/21 × 7 = 56/147

Step 3: Add the Numerators
Now add the numerators (27 + 56 = 83) and keep the common denominator 147 unchanged.
Working: 27 + 56/147 = 83/147

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 83 and 147 is 1, confirming that 83/147 cannot be reduced further—it is already in its simplest irreducible form.
Working: 83/147

Step 5: Decimal & Percentage Representation
Dividing the numerator 83 by denominator 147 produces a repeating decimal (approximately 0.564626, or 56.4626%).
Working: 83 ÷ 147 = 0.564626 (56.4626%)

Key Values:
- Simplified Fraction: 83/147
- Mixed Number Form: 83/147
- Decimal Value: 0.564626
- Percentage: 56.4626%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-9-49-plus-8-21/
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9/49 + 8/21 = 83/147

Simplified Fraction

83/147

Mixed Number

Proper (83/147)

Decimal Value

0.564626

Percentage

56.4626%

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Step-by-Step Solution: 9/49 + 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 9/49 by 3, and multiply the numerator and denominator of 8/21 by 7 so both fractions share the common base 147.

9 × 3/49 × 3 = 27/147 and 8 × 7/21 × 7 = 56/147

Step 3

Add the Numerators

Now add the numerators (27 + 56 = 83) and keep the common denominator 147 unchanged.

27 + 56/147 = 83/147

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 83 and 147 is 1, confirming that 83/147 cannot be reduced further—it is already in its simplest irreducible form.

83/147

Step 5

Decimal & Percentage Representation

Dividing the numerator 83 by denominator 147 produces a repeating decimal (approximately 0.564626, or 56.4626%).

83 ÷ 147 = 0.564626 (56.4626%)

Visual Representation

The diagram below illustrates 9/49 plus 8/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`83/147`
Mixed Number Form	`83/147`
Decimal Form	`0.564626`
Percentage	`56.4626%`

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Frequently Asked Questions

What is 9/49 plus 8/21 as a fraction?

9/49 + 8/21 in simplest fraction form is 83/147.

What is 9/49 plus 8/21 as a decimal?

9/49 + 8/21 converted to a decimal is 0.564626.

What is 9/49 plus 8/21 as a percentage?

9/49 + 8/21 expressed as a percentage is 56.4626%.

Does 9/49 plus 8/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.564626...) because the denominator contains prime factors other than 2 and 5.