What is 1/7 plus 6/21? (Answer: 3/7)

Exact Answer

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Problem: What is 1/7 plus 6/21?
Formula / Expression: 1/7 + 6/21
Final Answer: 3/7
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
Notice that 21 is an exact multiple of 7 (7 × 3 = 21). The Least Common Denominator (LCD) is simply 21, meaning we only need to scale one fraction.
Working: LCD(7, 21) = 21

Step 2: Convert to Equivalent Fractions with Common Denominator 21
Multiply the numerator and denominator of 1/7 by 3, and multiply the numerator and denominator of 6/21 by 1 so both fractions share the common base 21.
Working: 1 × 3/7 × 3 = 3/21 and 6 × 1/21 × 1 = 6/21

Step 3: Add the Numerators
Now add the numerators (3 + 6 = 9) and keep the common denominator 21 unchanged.
Working: 3 + 6/21 = 9/21

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 9 and 21, which is 3. Divide both the numerator and denominator by 3.
Working: 9 ÷ 3/21 ÷ 3 = 3/7

Step 5: Decimal & Percentage Representation
Dividing the numerator 3 by denominator 7 produces a repeating decimal (approximately 0.428571, or 42.8571%).
Working: 3 ÷ 7 = 0.428571 (42.8571%)

Key Values:
- Simplified Fraction: 3/7
- Mixed Number Form: 3/7
- Decimal Value: 0.428571
- Percentage: 42.8571%

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Solved with FractionsCalc:
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1/7 + 6/21 = 3/7

Simplified Fraction

3/7

Mixed Number

Proper (3/7)

Decimal Value

0.428571

Percentage

42.8571%

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Step-by-Step Solution: 1/7 + 6/21

Step 1

Find the Least Common Denominator (LCD)

Notice that 21 is an exact multiple of 7 (7 × 3 = 21). The Least Common Denominator (LCD) is simply 21, meaning we only need to scale one fraction.

LCD(7, 21) = 21

Step 2

Convert to Equivalent Fractions with Common Denominator 21

Multiply the numerator and denominator of 1/7 by 3, and multiply the numerator and denominator of 6/21 by 1 so both fractions share the common base 21.

1 × 3/7 × 3 = 3/21 and 6 × 1/21 × 1 = 6/21

Step 3

Add the Numerators

Now add the numerators (3 + 6 = 9) and keep the common denominator 21 unchanged.

3 + 6/21 = 9/21

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 9 and 21, which is 3. Divide both the numerator and denominator by 3.

9 ÷ 3/21 ÷ 3 = 3/7

Step 5

Decimal & Percentage Representation

Dividing the numerator 3 by denominator 7 produces a repeating decimal (approximately 0.428571, or 42.8571%).

3 ÷ 7 = 0.428571 (42.8571%)

Visual Representation

The diagram below illustrates 1/7 plus 6/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`3/7`
Mixed Number Form	`3/7`
Decimal Form	`0.428571`
Percentage	`42.8571%`

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Frequently Asked Questions

What is 1/7 plus 6/21 as a fraction?

1/7 + 6/21 in simplest fraction form is 3/7.

What is 1/7 plus 6/21 as a decimal?

1/7 + 6/21 converted to a decimal is 0.428571.

What is 1/7 plus 6/21 as a percentage?

1/7 + 6/21 expressed as a percentage is 42.8571%.

Does 1/7 plus 6/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.428571...) because the denominator contains prime factors other than 2 and 5.