What is 4/21 plus 8/39? (Answer: 36/91)

Exact Answer

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Problem: What is 4/21 plus 8/39?
Formula / Expression: 4/21 + 8/39
Final Answer: 36/91
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 21 and 39 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 273 (which is smaller than their product 21 × 39 = 819, keeping the calculation simpler).
Working: LCD(21, 39) = 273

Step 2: Convert to Equivalent Fractions with Common Denominator 273
Multiply the numerator and denominator of 4/21 by 13, and multiply the numerator and denominator of 8/39 by 7 so both fractions share the common base 273.
Working: 4 × 13/21 × 13 = 52/273 and 8 × 7/39 × 7 = 56/273

Step 3: Add the Numerators
Now add the numerators (52 + 56 = 108) and keep the common denominator 273 unchanged.
Working: 52 + 56/273 = 108/273

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 108 and 273, which is 3. Divide both the numerator and denominator by 3.
Working: 108 ÷ 3/273 ÷ 3 = 36/91

Step 5: Decimal & Percentage Representation
Dividing the numerator 36 by denominator 91 produces a repeating decimal (approximately 0.395604, or 39.5604%).
Working: 36 ÷ 91 = 0.395604 (39.5604%)

Key Values:
- Simplified Fraction: 36/91
- Mixed Number Form: 36/91
- Decimal Value: 0.395604
- Percentage: 39.5604%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-4-21-plus-8-39/
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4/21 + 8/39 = 36/91

Simplified Fraction

36/91

Mixed Number

Proper (36/91)

Decimal Value

0.395604

Percentage

39.5604%

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Step-by-Step Solution: 4/21 + 8/39

Step 1

Find the Least Common Denominator (LCD)

The denominators 21 and 39 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 273 (which is smaller than their product 21 × 39 = 819, keeping the calculation simpler).

LCD(21, 39) = 273

Step 2

Convert to Equivalent Fractions with Common Denominator 273

Multiply the numerator and denominator of 4/21 by 13, and multiply the numerator and denominator of 8/39 by 7 so both fractions share the common base 273.

4 × 13/21 × 13 = 52/273 and 8 × 7/39 × 7 = 56/273

Step 3

Add the Numerators

Now add the numerators (52 + 56 = 108) and keep the common denominator 273 unchanged.

52 + 56/273 = 108/273

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 108 and 273, which is 3. Divide both the numerator and denominator by 3.

108 ÷ 3/273 ÷ 3 = 36/91

Step 5

Decimal & Percentage Representation

Dividing the numerator 36 by denominator 91 produces a repeating decimal (approximately 0.395604, or 39.5604%).

36 ÷ 91 = 0.395604 (39.5604%)

Visual Representation

The diagram below illustrates 4/21 plus 8/39 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`36/91`
Mixed Number Form	`36/91`
Decimal Form	`0.395604`
Percentage	`39.5604%`

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Frequently Asked Questions

What is 4/21 plus 8/39 as a fraction?

4/21 + 8/39 in simplest fraction form is 36/91.

What is 4/21 plus 8/39 as a decimal?

4/21 + 8/39 converted to a decimal is 0.395604.

What is 4/21 plus 8/39 as a percentage?

4/21 + 8/39 expressed as a percentage is 39.5604%.

Does 4/21 plus 8/39 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.395604...) because the denominator contains prime factors other than 2 and 5.