What is 3/21 plus 6/42? (Answer: 2/7)

Exact Answer

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Problem: What is 3/21 plus 6/42?
Formula / Expression: 3/21 + 6/42
Final Answer: 2/7
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
Notice that 42 is an exact multiple of 21 (21 × 2 = 42). The Least Common Denominator (LCD) is simply 42, meaning we only need to scale one fraction.
Working: LCD(21, 42) = 42

Step 2: Convert to Equivalent Fractions with Common Denominator 42
Multiply the numerator and denominator of 3/21 by 2, and multiply the numerator and denominator of 6/42 by 1 so both fractions share the common base 42.
Working: 3 × 2/21 × 2 = 6/42 and 6 × 1/42 × 1 = 6/42

Step 3: Add the Numerators
Now add the numerators (6 + 6 = 12) and keep the common denominator 42 unchanged.
Working: 6 + 6/42 = 12/42

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 12 and 42, which is 6. Divide both the numerator and denominator by 6.
Working: 12 ÷ 6/42 ÷ 6 = 2/7

Step 5: Decimal & Percentage Representation
Dividing the numerator 2 by denominator 7 produces a repeating decimal (approximately 0.285714, or 28.5714%).
Working: 2 ÷ 7 = 0.285714 (28.5714%)

Key Values:
- Simplified Fraction: 2/7
- Mixed Number Form: 2/7
- Decimal Value: 0.285714
- Percentage: 28.5714%

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Solved with FractionsCalc:
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3/21 + 6/42 = 2/7

Simplified Fraction

2/7

Mixed Number

Proper (2/7)

Decimal Value

0.285714

Percentage

28.5714%

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Step-by-Step Solution: 3/21 + 6/42

Step 1

Find the Least Common Denominator (LCD)

Notice that 42 is an exact multiple of 21 (21 × 2 = 42). The Least Common Denominator (LCD) is simply 42, meaning we only need to scale one fraction.

LCD(21, 42) = 42

Step 2

Convert to Equivalent Fractions with Common Denominator 42

Multiply the numerator and denominator of 3/21 by 2, and multiply the numerator and denominator of 6/42 by 1 so both fractions share the common base 42.

3 × 2/21 × 2 = 6/42 and 6 × 1/42 × 1 = 6/42

Step 3

Add the Numerators

Now add the numerators (6 + 6 = 12) and keep the common denominator 42 unchanged.

6 + 6/42 = 12/42

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 12 and 42, which is 6. Divide both the numerator and denominator by 6.

12 ÷ 6/42 ÷ 6 = 2/7

Step 5

Decimal & Percentage Representation

Dividing the numerator 2 by denominator 7 produces a repeating decimal (approximately 0.285714, or 28.5714%).

2 ÷ 7 = 0.285714 (28.5714%)

Visual Representation

The diagram below illustrates 3/21 plus 6/42 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`2/7`
Mixed Number Form	`2/7`
Decimal Form	`0.285714`
Percentage	`28.5714%`

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Frequently Asked Questions

What is 3/21 plus 6/42 as a fraction?

3/21 + 6/42 in simplest fraction form is 2/7.

What is 3/21 plus 6/42 as a decimal?

3/21 + 6/42 converted to a decimal is 0.285714.

What is 3/21 plus 6/42 as a percentage?

3/21 + 6/42 expressed as a percentage is 28.5714%.

Does 3/21 plus 6/42 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.285714...) because the denominator contains prime factors other than 2 and 5.