What is 8/21 plus 4/9? (Answer: 52/63)

Exact Answer

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Problem: What is 8/21 plus 4/9?
Formula / Expression: 8/21 + 4/9
Final Answer: 52/63
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 21 and 9 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 63 (which is smaller than their product 21 × 9 = 189, keeping the calculation simpler).
Working: LCD(21, 9) = 63

Step 2: Convert to Equivalent Fractions with Common Denominator 63
Multiply the numerator and denominator of 8/21 by 3, and multiply the numerator and denominator of 4/9 by 7 so both fractions share the common base 63.
Working: 8 × 3/21 × 3 = 24/63 and 4 × 7/9 × 7 = 28/63

Step 3: Add the Numerators
Now add the numerators (24 + 28 = 52) and keep the common denominator 63 unchanged.
Working: 24 + 28/63 = 52/63

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 52 and 63 is 1, confirming that 52/63 cannot be reduced further—it is already in its simplest irreducible form.
Working: 52/63

Step 5: Decimal & Percentage Representation
Dividing the numerator 52 by denominator 63 produces a repeating decimal (approximately 0.825397, or 82.5397%).
Working: 52 ÷ 63 = 0.825397 (82.5397%)

Key Values:
- Simplified Fraction: 52/63
- Mixed Number Form: 52/63
- Decimal Value: 0.825397
- Percentage: 82.5397%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-8-21-plus-4-9/
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8/21 + 4/9 = 52/63

Simplified Fraction

52/63

Mixed Number

Proper (52/63)

Decimal Value

0.825397

Percentage

82.5397%

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Step-by-Step Solution: 8/21 + 4/9

Step 1

Find the Least Common Denominator (LCD)

The denominators 21 and 9 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 63 (which is smaller than their product 21 × 9 = 189, keeping the calculation simpler).

LCD(21, 9) = 63

Step 2

Convert to Equivalent Fractions with Common Denominator 63

Multiply the numerator and denominator of 8/21 by 3, and multiply the numerator and denominator of 4/9 by 7 so both fractions share the common base 63.

8 × 3/21 × 3 = 24/63 and 4 × 7/9 × 7 = 28/63

Step 3

Add the Numerators

Now add the numerators (24 + 28 = 52) and keep the common denominator 63 unchanged.

24 + 28/63 = 52/63

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 52 and 63 is 1, confirming that 52/63 cannot be reduced further—it is already in its simplest irreducible form.

52/63

Step 5

Decimal & Percentage Representation

Dividing the numerator 52 by denominator 63 produces a repeating decimal (approximately 0.825397, or 82.5397%).

52 ÷ 63 = 0.825397 (82.5397%)

Visual Representation

The diagram below illustrates 8/21 plus 4/9 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`52/63`
Mixed Number Form	`52/63`
Decimal Form	`0.825397`
Percentage	`82.5397%`

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Frequently Asked Questions

What is 8/21 plus 4/9 as a fraction?

8/21 + 4/9 in simplest fraction form is 52/63.

What is 8/21 plus 4/9 as a decimal?

8/21 + 4/9 converted to a decimal is 0.825397.

What is 8/21 plus 4/9 as a percentage?

8/21 + 4/9 expressed as a percentage is 82.5397%.

Does 8/21 plus 4/9 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.825397...) because the denominator contains prime factors other than 2 and 5.