What is 8/39 plus 7/21? (Answer: 7/13)

Exact Answer

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Problem: What is 8/39 plus 7/21?
Formula / Expression: 8/39 + 7/21
Final Answer: 7/13
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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 8/39 by 7, and multiply the numerator and denominator of 7/21 by 13 so both fractions share the common base 273.
Working: 8 × 7/39 × 7 = 56/273 and 7 × 13/21 × 13 = 91/273

Step 3: Add the Numerators
Now add the numerators (56 + 91 = 147) and keep the common denominator 273 unchanged.
Working: 56 + 91/273 = 147/273

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 147 and 273, which is 21. Divide both the numerator and denominator by 21.
Working: 147 ÷ 21/273 ÷ 21 = 7/13

Step 5: Decimal & Percentage Representation
Dividing the numerator 7 by denominator 13 produces a repeating decimal (approximately 0.538462, or 53.8462%).
Working: 7 ÷ 13 = 0.538462 (53.8462%)

Key Values:
- Simplified Fraction: 7/13
- Mixed Number Form: 7/13
- Decimal Value: 0.538462
- Percentage: 53.8462%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-8-39-plus-7-21/
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8/39 + 7/21 = 7/13

Simplified Fraction

7/13

Mixed Number

Proper (7/13)

Decimal Value

0.538462

Percentage

53.8462%

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Step-by-Step Solution: 8/39 + 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 8/39 by 7, and multiply the numerator and denominator of 7/21 by 13 so both fractions share the common base 273.

8 × 7/39 × 7 = 56/273 and 7 × 13/21 × 13 = 91/273

Step 3

Add the Numerators

Now add the numerators (56 + 91 = 147) and keep the common denominator 273 unchanged.

56 + 91/273 = 147/273

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 147 and 273, which is 21. Divide both the numerator and denominator by 21.

147 ÷ 21/273 ÷ 21 = 7/13

Step 5

Decimal & Percentage Representation

Dividing the numerator 7 by denominator 13 produces a repeating decimal (approximately 0.538462, or 53.8462%).

7 ÷ 13 = 0.538462 (53.8462%)

Visual Representation

The diagram below illustrates 8/39 plus 7/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`7/13`
Mixed Number Form	`7/13`
Decimal Form	`0.538462`
Percentage	`53.8462%`

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Frequently Asked Questions

What is 8/39 plus 7/21 as a fraction?

8/39 + 7/21 in simplest fraction form is 7/13.

What is 8/39 plus 7/21 as a decimal?

8/39 + 7/21 converted to a decimal is 0.538462.

What is 8/39 plus 7/21 as a percentage?

8/39 + 7/21 expressed as a percentage is 53.8462%.

Does 8/39 plus 7/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.538462...) because the denominator contains prime factors other than 2 and 5.