What is 6/19 plus 7/21? (Answer: 37/57)

Exact Answer

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Problem: What is 6/19 plus 7/21?
Formula / Expression: 6/19 + 7/21
Final Answer: 37/57
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 19 and 21 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 19 × 21 = 399.
Working: LCD(19, 21) = 399

Step 2: Convert to Equivalent Fractions with Common Denominator 399
Multiply the numerator and denominator of 6/19 by 21, and multiply the numerator and denominator of 7/21 by 19 so both fractions share the common base 399.
Working: 6 × 21/19 × 21 = 126/399 and 7 × 19/21 × 19 = 133/399

Step 3: Add the Numerators
Now add the numerators (126 + 133 = 259) and keep the common denominator 399 unchanged.
Working: 126 + 133/399 = 259/399

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 259 and 399, which is 7. Divide both the numerator and denominator by 7.
Working: 259 ÷ 7/399 ÷ 7 = 37/57

Step 5: Decimal & Percentage Representation
Dividing the numerator 37 by denominator 57 produces a repeating decimal (approximately 0.649123, or 64.9123%).
Working: 37 ÷ 57 = 0.649123 (64.9123%)

Key Values:
- Simplified Fraction: 37/57
- Mixed Number Form: 37/57
- Decimal Value: 0.649123
- Percentage: 64.9123%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-6-19-plus-7-21/
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6/19 + 7/21 = 37/57

Simplified Fraction

37/57

Mixed Number

Proper (37/57)

Decimal Value

0.649123

Percentage

64.9123%

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Step-by-Step Solution: 6/19 + 7/21

Step 1

Find the Least Common Denominator (LCD)

The denominators 19 and 21 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 19 × 21 = 399.

LCD(19, 21) = 399

Step 2

Convert to Equivalent Fractions with Common Denominator 399

Multiply the numerator and denominator of 6/19 by 21, and multiply the numerator and denominator of 7/21 by 19 so both fractions share the common base 399.

6 × 21/19 × 21 = 126/399 and 7 × 19/21 × 19 = 133/399

Step 3

Add the Numerators

Now add the numerators (126 + 133 = 259) and keep the common denominator 399 unchanged.

126 + 133/399 = 259/399

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 259 and 399, which is 7. Divide both the numerator and denominator by 7.

259 ÷ 7/399 ÷ 7 = 37/57

Step 5

Decimal & Percentage Representation

Dividing the numerator 37 by denominator 57 produces a repeating decimal (approximately 0.649123, or 64.9123%).

37 ÷ 57 = 0.649123 (64.9123%)

Visual Representation

The diagram below illustrates 6/19 plus 7/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`37/57`
Mixed Number Form	`37/57`
Decimal Form	`0.649123`
Percentage	`64.9123%`

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Frequently Asked Questions

What is 6/19 plus 7/21 as a fraction?

6/19 + 7/21 in simplest fraction form is 37/57.

What is 6/19 plus 7/21 as a decimal?

6/19 + 7/21 converted to a decimal is 0.649123.

What is 6/19 plus 7/21 as a percentage?

6/19 + 7/21 expressed as a percentage is 64.9123%.

Does 6/19 plus 7/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.649123...) because the denominator contains prime factors other than 2 and 5.