What is 5/39 plus 7/21? (Answer: 6/13)

Exact Answer

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Problem: What is 5/39 plus 7/21?
Formula / Expression: 5/39 + 7/21
Final Answer: 6/13
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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 5/39 by 7, and multiply the numerator and denominator of 7/21 by 13 so both fractions share the common base 273.
Working: 5 × 7/39 × 7 = 35/273 and 7 × 13/21 × 13 = 91/273

Step 3: Add the Numerators
Now add the numerators (35 + 91 = 126) and keep the common denominator 273 unchanged.
Working: 35 + 91/273 = 126/273

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 126 and 273, which is 21. Divide both the numerator and denominator by 21.
Working: 126 ÷ 21/273 ÷ 21 = 6/13

Step 5: Decimal & Percentage Representation
Dividing the numerator 6 by denominator 13 produces a repeating decimal (approximately 0.461538, or 46.1538%).
Working: 6 ÷ 13 = 0.461538 (46.1538%)

Key Values:
- Simplified Fraction: 6/13
- Mixed Number Form: 6/13
- Decimal Value: 0.461538
- Percentage: 46.1538%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-5-39-plus-7-21/
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5/39 + 7/21 = 6/13

Simplified Fraction

6/13

Mixed Number

Proper (6/13)

Decimal Value

0.461538

Percentage

46.1538%

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Step-by-Step Solution: 5/39 + 7/21

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

5 × 7/39 × 7 = 35/273 and 7 × 13/21 × 13 = 91/273

Step 3

Add the Numerators

Now add the numerators (35 + 91 = 126) and keep the common denominator 273 unchanged.

35 + 91/273 = 126/273

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 126 and 273, which is 21. Divide both the numerator and denominator by 21.

126 ÷ 21/273 ÷ 21 = 6/13

Step 5

Decimal & Percentage Representation

Dividing the numerator 6 by denominator 13 produces a repeating decimal (approximately 0.461538, or 46.1538%).

6 ÷ 13 = 0.461538 (46.1538%)

Visual Representation

The diagram below illustrates 5/39 plus 7/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`6/13`
Mixed Number Form	`6/13`
Decimal Form	`0.461538`
Percentage	`46.1538%`

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Frequently Asked Questions

What is 5/39 plus 7/21 as a fraction?

5/39 + 7/21 in simplest fraction form is 6/13.

What is 5/39 plus 7/21 as a decimal?

5/39 + 7/21 converted to a decimal is 0.461538.

What is 5/39 plus 7/21 as a percentage?

5/39 + 7/21 expressed as a percentage is 46.1538%.

Does 5/39 plus 7/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.461538...) because the denominator contains prime factors other than 2 and 5.