What is 3/42 plus 4/21? (Answer: 11/42)

Exact Answer

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Problem: What is 3/42 plus 4/21?
Formula / Expression: 3/42 + 4/21
Final Answer: 11/42
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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 3/42 by 1, and multiply the numerator and denominator of 4/21 by 2 so both fractions share the common base 42.
Working: 3 × 1/42 × 1 = 3/42 and 4 × 2/21 × 2 = 8/42

Step 3: Add the Numerators
Now add the numerators (3 + 8 = 11) and keep the common denominator 42 unchanged.
Working: 3 + 8/42 = 11/42

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 11 and 42 is 1, confirming that 11/42 cannot be reduced further—it is already in its simplest irreducible form.
Working: 11/42

Step 5: Decimal & Percentage Representation
Dividing the numerator 11 by denominator 42 produces a repeating decimal (approximately 0.261905, or 26.1905%).
Working: 11 ÷ 42 = 0.261905 (26.1905%)

Key Values:
- Simplified Fraction: 11/42
- Mixed Number Form: 11/42
- Decimal Value: 0.261905
- Percentage: 26.1905%

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Solved with FractionsCalc:
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3/42 + 4/21 = 11/42

Simplified Fraction

11/42

Mixed Number

Proper (11/42)

Decimal Value

0.261905

Percentage

26.1905%

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Step-by-Step Solution: 3/42 + 4/21

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 4/21 by 2 so both fractions share the common base 42.

3 × 1/42 × 1 = 3/42 and 4 × 2/21 × 2 = 8/42

Step 3

Add the Numerators

Now add the numerators (3 + 8 = 11) and keep the common denominator 42 unchanged.

3 + 8/42 = 11/42

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 11 and 42 is 1, confirming that 11/42 cannot be reduced further—it is already in its simplest irreducible form.

11/42

Step 5

Decimal & Percentage Representation

Dividing the numerator 11 by denominator 42 produces a repeating decimal (approximately 0.261905, or 26.1905%).

11 ÷ 42 = 0.261905 (26.1905%)

Visual Representation

The diagram below illustrates 3/42 plus 4/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`11/42`
Mixed Number Form	`11/42`
Decimal Form	`0.261905`
Percentage	`26.1905%`

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Frequently Asked Questions

What is 3/42 plus 4/21 as a fraction?

3/42 + 4/21 in simplest fraction form is 11/42.

What is 3/42 plus 4/21 as a decimal?

3/42 + 4/21 converted to a decimal is 0.261905.

What is 3/42 plus 4/21 as a percentage?

3/42 + 4/21 expressed as a percentage is 26.1905%.

Does 3/42 plus 4/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.261905...) because the denominator contains prime factors other than 2 and 5.