What is 3/13 plus 7/21? (Answer: 22/39)

Exact Answer

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Problem: What is 3/13 plus 7/21?
Formula / Expression: 3/13 + 7/21
Final Answer: 22/39
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 13 and 21 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 13 × 21 = 273.
Working: LCD(13, 21) = 273

Step 2: Convert to Equivalent Fractions with Common Denominator 273
Multiply the numerator and denominator of 3/13 by 21, and multiply the numerator and denominator of 7/21 by 13 so both fractions share the common base 273.
Working: 3 × 21/13 × 21 = 63/273 and 7 × 13/21 × 13 = 91/273

Step 3: Add the Numerators
Now add the numerators (63 + 91 = 154) and keep the common denominator 273 unchanged.
Working: 63 + 91/273 = 154/273

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 154 and 273, which is 7. Divide both the numerator and denominator by 7.
Working: 154 ÷ 7/273 ÷ 7 = 22/39

Step 5: Decimal & Percentage Representation
Dividing the numerator 22 by denominator 39 produces a repeating decimal (approximately 0.564103, or 56.4103%).
Working: 22 ÷ 39 = 0.564103 (56.4103%)

Key Values:
- Simplified Fraction: 22/39
- Mixed Number Form: 22/39
- Decimal Value: 0.564103
- Percentage: 56.4103%

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Solved with FractionsCalc:
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3/13 + 7/21 = 22/39

Simplified Fraction

22/39

Mixed Number

Proper (22/39)

Decimal Value

0.564103

Percentage

56.4103%

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Step-by-Step Solution: 3/13 + 7/21

Step 1

Find the Least Common Denominator (LCD)

The denominators 13 and 21 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 13 × 21 = 273.

LCD(13, 21) = 273

Step 2

Convert to Equivalent Fractions with Common Denominator 273

Multiply the numerator and denominator of 3/13 by 21, and multiply the numerator and denominator of 7/21 by 13 so both fractions share the common base 273.

3 × 21/13 × 21 = 63/273 and 7 × 13/21 × 13 = 91/273

Step 3

Add the Numerators

Now add the numerators (63 + 91 = 154) and keep the common denominator 273 unchanged.

63 + 91/273 = 154/273

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 154 and 273, which is 7. Divide both the numerator and denominator by 7.

154 ÷ 7/273 ÷ 7 = 22/39

Step 5

Decimal & Percentage Representation

Dividing the numerator 22 by denominator 39 produces a repeating decimal (approximately 0.564103, or 56.4103%).

22 ÷ 39 = 0.564103 (56.4103%)

Visual Representation

The diagram below illustrates 3/13 plus 7/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`22/39`
Mixed Number Form	`22/39`
Decimal Form	`0.564103`
Percentage	`56.4103%`

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Frequently Asked Questions

What is 3/13 plus 7/21 as a fraction?

3/13 + 7/21 in simplest fraction form is 22/39.

What is 3/13 plus 7/21 as a decimal?

3/13 + 7/21 converted to a decimal is 0.564103.

What is 3/13 plus 7/21 as a percentage?

3/13 + 7/21 expressed as a percentage is 56.4103%.

Does 3/13 plus 7/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.564103...) because the denominator contains prime factors other than 2 and 5.