What is 1/42 plus 2/21? (Answer: 5/42)

Exact Answer

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Problem: What is 1/42 plus 2/21?
Formula / Expression: 1/42 + 2/21
Final Answer: 5/42
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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 1/42 by 1, and multiply the numerator and denominator of 2/21 by 2 so both fractions share the common base 42.
Working: 1 × 1/42 × 1 = 1/42 and 2 × 2/21 × 2 = 4/42

Step 3: Add the Numerators
Now add the numerators (1 + 4 = 5) and keep the common denominator 42 unchanged.
Working: 1 + 4/42 = 5/42

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 5 and 42 is 1, confirming that 5/42 cannot be reduced further—it is already in its simplest irreducible form.
Working: 5/42

Step 5: Decimal & Percentage Representation
Dividing the numerator 5 by denominator 42 produces a repeating decimal (approximately 0.119048, or 11.9048%).
Working: 5 ÷ 42 = 0.119048 (11.9048%)

Key Values:
- Simplified Fraction: 5/42
- Mixed Number Form: 5/42
- Decimal Value: 0.119048
- Percentage: 11.9048%

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Solved with FractionsCalc:
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1/42 + 2/21 = 5/42

Simplified Fraction

5/42

Mixed Number

Proper (5/42)

Decimal Value

0.119048

Percentage

11.9048%

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Step-by-Step Solution: 1/42 + 2/21

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

1 × 1/42 × 1 = 1/42 and 2 × 2/21 × 2 = 4/42

Step 3

Add the Numerators

Now add the numerators (1 + 4 = 5) and keep the common denominator 42 unchanged.

1 + 4/42 = 5/42

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 5 and 42 is 1, confirming that 5/42 cannot be reduced further—it is already in its simplest irreducible form.

5/42

Step 5

Decimal & Percentage Representation

Dividing the numerator 5 by denominator 42 produces a repeating decimal (approximately 0.119048, or 11.9048%).

5 ÷ 42 = 0.119048 (11.9048%)

Visual Representation

The diagram below illustrates 1/42 plus 2/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`5/42`
Mixed Number Form	`5/42`
Decimal Form	`0.119048`
Percentage	`11.9048%`

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Frequently Asked Questions

What is 1/42 plus 2/21 as a fraction?

1/42 + 2/21 in simplest fraction form is 5/42.

What is 1/42 plus 2/21 as a decimal?

1/42 + 2/21 converted to a decimal is 0.119048.

What is 1/42 plus 2/21 as a percentage?

1/42 + 2/21 expressed as a percentage is 11.9048%.

Does 1/42 plus 2/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.119048...) because the denominator contains prime factors other than 2 and 5.