What is 5/39 plus 10/21? (Answer: 55/91)

Exact Answer

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Problem: What is 5/39 plus 10/21?
Formula / Expression: 5/39 + 10/21
Final Answer: 55/91
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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 5/39 by 7, and multiply the numerator and denominator of 10/21 by 13 so both fractions share the common base 273.
Working: 5 × 7/39 × 7 = 35/273 and 10 × 13/21 × 13 = 130/273

Step 3: Add the Numerators
Now add the numerators (35 + 130 = 165) and keep the common denominator 273 unchanged.
Working: 35 + 130/273 = 165/273

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 165 and 273, which is 3. Divide both the numerator and denominator by 3.
Working: 165 ÷ 3/273 ÷ 3 = 55/91

Step 5: Decimal & Percentage Representation
Dividing the numerator 55 by denominator 91 produces a repeating decimal (approximately 0.604396, or 60.4396%).
Working: 55 ÷ 91 = 0.604396 (60.4396%)

Key Values:
- Simplified Fraction: 55/91
- Mixed Number Form: 55/91
- Decimal Value: 0.604396
- Percentage: 60.4396%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-5-39-plus-10-21/
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5/39 + 10/21 = 55/91

Simplified Fraction

55/91

Mixed Number

Proper (55/91)

Decimal Value

0.604396

Percentage

60.4396%

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Step-by-Step Solution: 5/39 + 10/21

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 10/21 by 13 so both fractions share the common base 273.

5 × 7/39 × 7 = 35/273 and 10 × 13/21 × 13 = 130/273

Step 3

Add the Numerators

Now add the numerators (35 + 130 = 165) and keep the common denominator 273 unchanged.

35 + 130/273 = 165/273

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 165 and 273, which is 3. Divide both the numerator and denominator by 3.

165 ÷ 3/273 ÷ 3 = 55/91

Step 5

Decimal & Percentage Representation

Dividing the numerator 55 by denominator 91 produces a repeating decimal (approximately 0.604396, or 60.4396%).

55 ÷ 91 = 0.604396 (60.4396%)

Visual Representation

The diagram below illustrates 5/39 plus 10/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`55/91`
Mixed Number Form	`55/91`
Decimal Form	`0.604396`
Percentage	`60.4396%`

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Frequently Asked Questions

What is 5/39 plus 10/21 as a fraction?

5/39 + 10/21 in simplest fraction form is 55/91.

What is 5/39 plus 10/21 as a decimal?

5/39 + 10/21 converted to a decimal is 0.604396.

What is 5/39 plus 10/21 as a percentage?

5/39 + 10/21 expressed as a percentage is 60.4396%.

Does 5/39 plus 10/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.604396...) because the denominator contains prime factors other than 2 and 5.