What is 1/39 plus 8/21? (Answer: 37/91)

Exact Answer

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Problem: What is 1/39 plus 8/21?
Formula / Expression: 1/39 + 8/21
Final Answer: 37/91
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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 1/39 by 7, and multiply the numerator and denominator of 8/21 by 13 so both fractions share the common base 273.
Working: 1 × 7/39 × 7 = 7/273 and 8 × 13/21 × 13 = 104/273

Step 3: Add the Numerators
Now add the numerators (7 + 104 = 111) and keep the common denominator 273 unchanged.
Working: 7 + 104/273 = 111/273

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 111 and 273, which is 3. Divide both the numerator and denominator by 3.
Working: 111 ÷ 3/273 ÷ 3 = 37/91

Step 5: Decimal & Percentage Representation
Dividing the numerator 37 by denominator 91 produces a repeating decimal (approximately 0.406593, or 40.6593%).
Working: 37 ÷ 91 = 0.406593 (40.6593%)

Key Values:
- Simplified Fraction: 37/91
- Mixed Number Form: 37/91
- Decimal Value: 0.406593
- Percentage: 40.6593%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-1-39-plus-8-21/
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1/39 + 8/21 = 37/91

Simplified Fraction

37/91

Mixed Number

Proper (37/91)

Decimal Value

0.406593

Percentage

40.6593%

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Step-by-Step Solution: 1/39 + 8/21

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 1/39 by 7, and multiply the numerator and denominator of 8/21 by 13 so both fractions share the common base 273.

1 × 7/39 × 7 = 7/273 and 8 × 13/21 × 13 = 104/273

Step 3

Add the Numerators

Now add the numerators (7 + 104 = 111) and keep the common denominator 273 unchanged.

7 + 104/273 = 111/273

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 111 and 273, which is 3. Divide both the numerator and denominator by 3.

111 ÷ 3/273 ÷ 3 = 37/91

Step 5

Decimal & Percentage Representation

Dividing the numerator 37 by denominator 91 produces a repeating decimal (approximately 0.406593, or 40.6593%).

37 ÷ 91 = 0.406593 (40.6593%)

Visual Representation

The diagram below illustrates 1/39 plus 8/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`37/91`
Mixed Number Form	`37/91`
Decimal Form	`0.406593`
Percentage	`40.6593%`

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Frequently Asked Questions

What is 1/39 plus 8/21 as a fraction?

1/39 + 8/21 in simplest fraction form is 37/91.

What is 1/39 plus 8/21 as a decimal?

1/39 + 8/21 converted to a decimal is 0.406593.

What is 1/39 plus 8/21 as a percentage?

1/39 + 8/21 expressed as a percentage is 40.6593%.

Does 1/39 plus 8/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.406593...) because the denominator contains prime factors other than 2 and 5.