What is 7/39 plus 7/21? (Answer: 20/39)

Exact Answer

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Problem: What is 7/39 plus 7/21?
Formula / Expression: 7/39 + 7/21
Final Answer: 20/39
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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 7/39 by 7, and multiply the numerator and denominator of 7/21 by 13 so both fractions share the common base 273.
Working: 7 × 7/39 × 7 = 49/273 and 7 × 13/21 × 13 = 91/273

Step 3: Add the Numerators
Now add the numerators (49 + 91 = 140) and keep the common denominator 273 unchanged.
Working: 49 + 91/273 = 140/273

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 140 and 273, which is 7. Divide both the numerator and denominator by 7.
Working: 140 ÷ 7/273 ÷ 7 = 20/39

Step 5: Decimal & Percentage Representation
Dividing the numerator 20 by denominator 39 produces a repeating decimal (approximately 0.512821, or 51.2821%).
Working: 20 ÷ 39 = 0.512821 (51.2821%)

Key Values:
- Simplified Fraction: 20/39
- Mixed Number Form: 20/39
- Decimal Value: 0.512821
- Percentage: 51.2821%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-7-39-plus-7-21/
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7/39 + 7/21 = 20/39

Simplified Fraction

20/39

Mixed Number

Proper (20/39)

Decimal Value

0.512821

Percentage

51.2821%

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Step-by-Step Solution: 7/39 + 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 7/39 by 7, and multiply the numerator and denominator of 7/21 by 13 so both fractions share the common base 273.

7 × 7/39 × 7 = 49/273 and 7 × 13/21 × 13 = 91/273

Step 3

Add the Numerators

Now add the numerators (49 + 91 = 140) and keep the common denominator 273 unchanged.

49 + 91/273 = 140/273

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 140 and 273, which is 7. Divide both the numerator and denominator by 7.

140 ÷ 7/273 ÷ 7 = 20/39

Step 5

Decimal & Percentage Representation

Dividing the numerator 20 by denominator 39 produces a repeating decimal (approximately 0.512821, or 51.2821%).

20 ÷ 39 = 0.512821 (51.2821%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`20/39`
Mixed Number Form	`20/39`
Decimal Form	`0.512821`
Percentage	`51.2821%`

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Frequently Asked Questions

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

7/39 + 7/21 in simplest fraction form is 20/39.

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

7/39 + 7/21 converted to a decimal is 0.512821.

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

7/39 + 7/21 expressed as a percentage is 51.2821%.

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

It results in a repeating decimal (approximately 0.512821...) because the denominator contains prime factors other than 2 and 5.