What is 6/37 plus 5/21? (Answer: 311/777)

Exact Answer

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Problem: What is 6/37 plus 5/21?
Formula / Expression: 6/37 + 5/21
Final Answer: 311/777
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 37 and 21 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 37 × 21 = 777.
Working: LCD(37, 21) = 777

Step 2: Convert to Equivalent Fractions with Common Denominator 777
Multiply the numerator and denominator of 6/37 by 21, and multiply the numerator and denominator of 5/21 by 37 so both fractions share the common base 777.
Working: 6 × 21/37 × 21 = 126/777 and 5 × 37/21 × 37 = 185/777

Step 3: Add the Numerators
Now add the numerators (126 + 185 = 311) and keep the common denominator 777 unchanged.
Working: 126 + 185/777 = 311/777

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 311 and 777 is 1, confirming that 311/777 cannot be reduced further—it is already in its simplest irreducible form.
Working: 311/777

Step 5: Decimal & Percentage Representation
Dividing the numerator 311 by denominator 777 produces a repeating decimal (approximately 0.400257, or 40.0257%).
Working: 311 ÷ 777 = 0.400257 (40.0257%)

Key Values:
- Simplified Fraction: 311/777
- Mixed Number Form: 311/777
- Decimal Value: 0.400257
- Percentage: 40.0257%

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Solved with FractionsCalc:
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6/37 + 5/21 = 311/777

Simplified Fraction

311/777

Mixed Number

Proper (311/777)

Decimal Value

0.400257

Percentage

40.0257%

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Step-by-Step Solution: 6/37 + 5/21

Step 1

Find the Least Common Denominator (LCD)

The denominators 37 and 21 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 37 × 21 = 777.

LCD(37, 21) = 777

Step 2

Convert to Equivalent Fractions with Common Denominator 777

Multiply the numerator and denominator of 6/37 by 21, and multiply the numerator and denominator of 5/21 by 37 so both fractions share the common base 777.

6 × 21/37 × 21 = 126/777 and 5 × 37/21 × 37 = 185/777

Step 3

Add the Numerators

Now add the numerators (126 + 185 = 311) and keep the common denominator 777 unchanged.

126 + 185/777 = 311/777

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 311 and 777 is 1, confirming that 311/777 cannot be reduced further—it is already in its simplest irreducible form.

311/777

Step 5

Decimal & Percentage Representation

Dividing the numerator 311 by denominator 777 produces a repeating decimal (approximately 0.400257, or 40.0257%).

311 ÷ 777 = 0.400257 (40.0257%)

Visual Representation

The diagram below illustrates 6/37 plus 5/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`311/777`
Mixed Number Form	`311/777`
Decimal Form	`0.400257`
Percentage	`40.0257%`

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Frequently Asked Questions

What is 6/37 plus 5/21 as a fraction?

6/37 + 5/21 in simplest fraction form is 311/777.

What is 6/37 plus 5/21 as a decimal?

6/37 + 5/21 converted to a decimal is 0.400257.

What is 6/37 plus 5/21 as a percentage?

6/37 + 5/21 expressed as a percentage is 40.0257%.

Does 6/37 plus 5/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.400257...) because the denominator contains prime factors other than 2 and 5.