What is 1/3 plus 3/7? (Answer: 16/21)

Exact Answer

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Problem: What is 1/3 plus 3/7?
Formula / Expression: 1/3 + 3/7
Final Answer: 16/21
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 3 and 7 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 3 × 7 = 21.
Working: LCD(3, 7) = 21

Step 2: Convert to Equivalent Fractions with Common Denominator 21
Multiply the numerator and denominator of 1/3 by 7, and multiply the numerator and denominator of 3/7 by 3 so both fractions share the common base 21.
Working: 1 × 7/3 × 7 = 7/21 and 3 × 3/7 × 3 = 9/21

Step 3: Add the Numerators
Now add the numerators (7 + 9 = 16) and keep the common denominator 21 unchanged.
Working: 7 + 9/21 = 16/21

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 16 and 21 is 1, confirming that 16/21 cannot be reduced further—it is already in its simplest irreducible form.
Working: 16/21

Step 5: Decimal & Percentage Representation
Dividing the numerator 16 by denominator 21 produces a repeating decimal (approximately 0.761905, or 76.1905%).
Working: 16 ÷ 21 = 0.761905 (76.1905%)

Key Values:
- Simplified Fraction: 16/21
- Mixed Number Form: 16/21
- Decimal Value: 0.761905
- Percentage: 76.1905%

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1/3 + 3/7 = 16/21

Simplified Fraction

16/21

Mixed Number

Proper (16/21)

Decimal Value

0.761905

Percentage

76.1905%

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Step-by-Step Solution: 1/3 + 3/7

Step 1

Find the Least Common Denominator (LCD)

The denominators 3 and 7 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 3 × 7 = 21.

LCD(3, 7) = 21

Step 2

Convert to Equivalent Fractions with Common Denominator 21

Multiply the numerator and denominator of 1/3 by 7, and multiply the numerator and denominator of 3/7 by 3 so both fractions share the common base 21.

1 × 7/3 × 7 = 7/21 and 3 × 3/7 × 3 = 9/21

Step 3

Add the Numerators

Now add the numerators (7 + 9 = 16) and keep the common denominator 21 unchanged.

7 + 9/21 = 16/21

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 16 and 21 is 1, confirming that 16/21 cannot be reduced further—it is already in its simplest irreducible form.

16/21

Step 5

Decimal & Percentage Representation

Dividing the numerator 16 by denominator 21 produces a repeating decimal (approximately 0.761905, or 76.1905%).

16 ÷ 21 = 0.761905 (76.1905%)

Visual Representation

The diagram below illustrates 1/3 plus 3/7 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`16/21`
Mixed Number Form	`16/21`
Decimal Form	`0.761905`
Percentage	`76.1905%`

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Frequently Asked Questions

What is 1/3 plus 3/7 as a fraction?

1/3 + 3/7 in simplest fraction form is 16/21.

What is 1/3 plus 3/7 as a decimal?

1/3 + 3/7 converted to a decimal is 0.761905.

What is 1/3 plus 3/7 as a percentage?

1/3 + 3/7 expressed as a percentage is 76.1905%.

Does 1/3 plus 3/7 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.761905...) because the denominator contains prime factors other than 2 and 5.