What is 3/42 plus 6/21? (Answer: 5/14)

Exact Answer

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Problem: What is 3/42 plus 6/21?
Formula / Expression: 3/42 + 6/21
Final Answer: 5/14
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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(42, 21) = 42

Step 2: Convert to Equivalent Fractions with Common Denominator 42
Multiply the numerator and denominator of 3/42 by 1, and multiply the numerator and denominator of 6/21 by 2 so both fractions share the common base 42.
Working: 3 × 1/42 × 1 = 3/42 and 6 × 2/21 × 2 = 12/42

Step 3: Add the Numerators
Now add the numerators (3 + 12 = 15) and keep the common denominator 42 unchanged.
Working: 3 + 12/42 = 15/42

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 15 and 42, which is 3. Divide both the numerator and denominator by 3.
Working: 15 ÷ 3/42 ÷ 3 = 5/14

Step 5: Decimal & Percentage Representation
Dividing the numerator 5 by denominator 14 produces a repeating decimal (approximately 0.357143, or 35.7143%).
Working: 5 ÷ 14 = 0.357143 (35.7143%)

Key Values:
- Simplified Fraction: 5/14
- Mixed Number Form: 5/14
- Decimal Value: 0.357143
- Percentage: 35.7143%

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Solved with FractionsCalc:
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3/42 + 6/21 = 5/14

Simplified Fraction

5/14

Mixed Number

Proper (5/14)

Decimal Value

0.357143

Percentage

35.7143%

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

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(42, 21) = 42

Step 2

Convert to Equivalent Fractions with Common Denominator 42

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

3 × 1/42 × 1 = 3/42 and 6 × 2/21 × 2 = 12/42

Step 3

Add the Numerators

Now add the numerators (3 + 12 = 15) and keep the common denominator 42 unchanged.

3 + 12/42 = 15/42

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 15 and 42, which is 3. Divide both the numerator and denominator by 3.

15 ÷ 3/42 ÷ 3 = 5/14

Step 5

Decimal & Percentage Representation

Dividing the numerator 5 by denominator 14 produces a repeating decimal (approximately 0.357143, or 35.7143%).

5 ÷ 14 = 0.357143 (35.7143%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`5/14`
Mixed Number Form	`5/14`
Decimal Form	`0.357143`
Percentage	`35.7143%`

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Frequently Asked Questions

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

3/42 + 6/21 in simplest fraction form is 5/14.

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

3/42 + 6/21 converted to a decimal is 0.357143.

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

3/42 + 6/21 expressed as a percentage is 35.7143%.

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

It results in a repeating decimal (approximately 0.357143...) because the denominator contains prime factors other than 2 and 5.