What is 4/39 plus 5/21? (Answer: 31/91)

Exact Answer

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Problem: What is 4/39 plus 5/21?
Formula / Expression: 4/39 + 5/21
Final Answer: 31/91
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Step-by-Step Solution:

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

Step 2: Convert to Equivalent Fractions with Common Denominator 273
Multiply the numerator and denominator of 4/39 by 7, and multiply the numerator and denominator of 5/21 by 13 so both fractions share the common base 273.
Working: 4 × 7/39 × 7 = 28/273 and 5 × 13/21 × 13 = 65/273

Step 3: Add the Numerators
Now add the numerators (28 + 65 = 93) and keep the common denominator 273 unchanged.
Working: 28 + 65/273 = 93/273

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 93 and 273, which is 3. Divide both the numerator and denominator by 3.
Working: 93 ÷ 3/273 ÷ 3 = 31/91

Step 5: Decimal & Percentage Representation
Dividing the numerator 31 by denominator 91 produces a repeating decimal (approximately 0.340659, or 34.0659%).
Working: 31 ÷ 91 = 0.340659 (34.0659%)

Key Values:
- Simplified Fraction: 31/91
- Mixed Number Form: 31/91
- Decimal Value: 0.340659
- Percentage: 34.0659%

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Solved with FractionsCalc:
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4/39 + 5/21 = 31/91

Simplified Fraction

31/91

Mixed Number

Proper (31/91)

Decimal Value

0.340659

Percentage

34.0659%

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Step-by-Step Solution: 4/39 + 5/21

Step 1

Find the Least Common Denominator (LCD)

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

LCD(39, 21) = 273

Step 2

Convert to Equivalent Fractions with Common Denominator 273

Multiply the numerator and denominator of 4/39 by 7, and multiply the numerator and denominator of 5/21 by 13 so both fractions share the common base 273.

4 × 7/39 × 7 = 28/273 and 5 × 13/21 × 13 = 65/273

Step 3

Add the Numerators

Now add the numerators (28 + 65 = 93) and keep the common denominator 273 unchanged.

28 + 65/273 = 93/273

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 93 and 273, which is 3. Divide both the numerator and denominator by 3.

93 ÷ 3/273 ÷ 3 = 31/91

Step 5

Decimal & Percentage Representation

Dividing the numerator 31 by denominator 91 produces a repeating decimal (approximately 0.340659, or 34.0659%).

31 ÷ 91 = 0.340659 (34.0659%)

Visual Representation

The diagram below illustrates 4/39 plus 5/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`31/91`
Mixed Number Form	`31/91`
Decimal Form	`0.340659`
Percentage	`34.0659%`

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Frequently Asked Questions

What is 4/39 plus 5/21 as a fraction?

4/39 + 5/21 in simplest fraction form is 31/91.

What is 4/39 plus 5/21 as a decimal?

4/39 + 5/21 converted to a decimal is 0.340659.

What is 4/39 plus 5/21 as a percentage?

4/39 + 5/21 expressed as a percentage is 34.0659%.

Does 4/39 plus 5/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.340659...) because the denominator contains prime factors other than 2 and 5.