What is 5/21 plus 10/39? (Answer: 45/91)

Exact Answer

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Problem: What is 5/21 plus 10/39?
Formula / Expression: 5/21 + 10/39
Final Answer: 45/91
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 21 and 39 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 273 (which is smaller than their product 21 × 39 = 819, keeping the calculation simpler).
Working: LCD(21, 39) = 273

Step 2: Convert to Equivalent Fractions with Common Denominator 273
Multiply the numerator and denominator of 5/21 by 13, and multiply the numerator and denominator of 10/39 by 7 so both fractions share the common base 273.
Working: 5 × 13/21 × 13 = 65/273 and 10 × 7/39 × 7 = 70/273

Step 3: Add the Numerators
Now add the numerators (65 + 70 = 135) and keep the common denominator 273 unchanged.
Working: 65 + 70/273 = 135/273

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 135 and 273, which is 3. Divide both the numerator and denominator by 3.
Working: 135 ÷ 3/273 ÷ 3 = 45/91

Step 5: Decimal & Percentage Representation
Dividing the numerator 45 by denominator 91 produces a repeating decimal (approximately 0.494505, or 49.4505%).
Working: 45 ÷ 91 = 0.494505 (49.4505%)

Key Values:
- Simplified Fraction: 45/91
- Mixed Number Form: 45/91
- Decimal Value: 0.494505
- Percentage: 49.4505%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-5-21-plus-10-39/
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5/21 + 10/39 = 45/91

Simplified Fraction

45/91

Mixed Number

Proper (45/91)

Decimal Value

0.494505

Percentage

49.4505%

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

Step 1

Find the Least Common Denominator (LCD)

The denominators 21 and 39 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 273 (which is smaller than their product 21 × 39 = 819, keeping the calculation simpler).

LCD(21, 39) = 273

Step 2

Convert to Equivalent Fractions with Common Denominator 273

Multiply the numerator and denominator of 5/21 by 13, and multiply the numerator and denominator of 10/39 by 7 so both fractions share the common base 273.

5 × 13/21 × 13 = 65/273 and 10 × 7/39 × 7 = 70/273

Step 3

Add the Numerators

Now add the numerators (65 + 70 = 135) and keep the common denominator 273 unchanged.

65 + 70/273 = 135/273

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 135 and 273, which is 3. Divide both the numerator and denominator by 3.

135 ÷ 3/273 ÷ 3 = 45/91

Step 5

Decimal & Percentage Representation

Dividing the numerator 45 by denominator 91 produces a repeating decimal (approximately 0.494505, or 49.4505%).

45 ÷ 91 = 0.494505 (49.4505%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`45/91`
Mixed Number Form	`45/91`
Decimal Form	`0.494505`
Percentage	`49.4505%`

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Frequently Asked Questions

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

5/21 + 10/39 in simplest fraction form is 45/91.

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

5/21 + 10/39 converted to a decimal is 0.494505.

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

5/21 + 10/39 expressed as a percentage is 49.4505%.

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

It results in a repeating decimal (approximately 0.494505...) because the denominator contains prime factors other than 2 and 5.