What is 7/21 plus 13/38? (Answer: 77/114)

Exact Answer

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Problem: What is 7/21 plus 13/38?
Formula / Expression: 7/21 + 13/38
Final Answer: 77/114
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 21 and 38 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 21 × 38 = 798.
Working: LCD(21, 38) = 798

Step 2: Convert to Equivalent Fractions with Common Denominator 798
Multiply the numerator and denominator of 7/21 by 38, and multiply the numerator and denominator of 13/38 by 21 so both fractions share the common base 798.
Working: 7 × 38/21 × 38 = 266/798 and 13 × 21/38 × 21 = 273/798

Step 3: Add the Numerators
Now add the numerators (266 + 273 = 539) and keep the common denominator 798 unchanged.
Working: 266 + 273/798 = 539/798

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 539 and 798, which is 7. Divide both the numerator and denominator by 7.
Working: 539 ÷ 7/798 ÷ 7 = 77/114

Step 5: Decimal & Percentage Representation
Dividing the numerator 77 by denominator 114 produces a repeating decimal (approximately 0.675439, or 67.5439%).
Working: 77 ÷ 114 = 0.675439 (67.5439%)

Key Values:
- Simplified Fraction: 77/114
- Mixed Number Form: 77/114
- Decimal Value: 0.675439
- Percentage: 67.5439%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-7-21-plus-13-38/
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7/21 + 13/38 = 77/114

Simplified Fraction

77/114

Mixed Number

Proper (77/114)

Decimal Value

0.675439

Percentage

67.5439%

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Step-by-Step Solution: 7/21 + 13/38

Step 1

Find the Least Common Denominator (LCD)

The denominators 21 and 38 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 21 × 38 = 798.

LCD(21, 38) = 798

Step 2

Convert to Equivalent Fractions with Common Denominator 798

Multiply the numerator and denominator of 7/21 by 38, and multiply the numerator and denominator of 13/38 by 21 so both fractions share the common base 798.

7 × 38/21 × 38 = 266/798 and 13 × 21/38 × 21 = 273/798

Step 3

Add the Numerators

Now add the numerators (266 + 273 = 539) and keep the common denominator 798 unchanged.

266 + 273/798 = 539/798

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 539 and 798, which is 7. Divide both the numerator and denominator by 7.

539 ÷ 7/798 ÷ 7 = 77/114

Step 5

Decimal & Percentage Representation

Dividing the numerator 77 by denominator 114 produces a repeating decimal (approximately 0.675439, or 67.5439%).

77 ÷ 114 = 0.675439 (67.5439%)

Visual Representation

The diagram below illustrates 7/21 plus 13/38 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`77/114`
Mixed Number Form	`77/114`
Decimal Form	`0.675439`
Percentage	`67.5439%`

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Frequently Asked Questions

What is 7/21 plus 13/38 as a fraction?

7/21 + 13/38 in simplest fraction form is 77/114.

What is 7/21 plus 13/38 as a decimal?

7/21 + 13/38 converted to a decimal is 0.675439.

What is 7/21 plus 13/38 as a percentage?

7/21 + 13/38 expressed as a percentage is 67.5439%.

Does 7/21 plus 13/38 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.675439...) because the denominator contains prime factors other than 2 and 5.