What is 3/42 plus 5/21? (Answer: 13/42)

Exact Answer

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Problem: What is 3/42 plus 5/21?
Formula / Expression: 3/42 + 5/21
Final Answer: 13/42
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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 5/21 by 2 so both fractions share the common base 42.
Working: 3 × 1/42 × 1 = 3/42 and 5 × 2/21 × 2 = 10/42

Step 3: Add the Numerators
Now add the numerators (3 + 10 = 13) and keep the common denominator 42 unchanged.
Working: 3 + 10/42 = 13/42

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 13 and 42 is 1, confirming that 13/42 cannot be reduced further—it is already in its simplest irreducible form.
Working: 13/42

Step 5: Decimal & Percentage Representation
Dividing the numerator 13 by denominator 42 produces a repeating decimal (approximately 0.309524, or 30.9524%).
Working: 13 ÷ 42 = 0.309524 (30.9524%)

Key Values:
- Simplified Fraction: 13/42
- Mixed Number Form: 13/42
- Decimal Value: 0.309524
- Percentage: 30.9524%

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Solved with FractionsCalc:
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3/42 + 5/21 = 13/42

Simplified Fraction

13/42

Mixed Number

Proper (13/42)

Decimal Value

0.309524

Percentage

30.9524%

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Step-by-Step Solution: 3/42 + 5/21

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 5/21 by 2 so both fractions share the common base 42.

3 × 1/42 × 1 = 3/42 and 5 × 2/21 × 2 = 10/42

Step 3

Add the Numerators

Now add the numerators (3 + 10 = 13) and keep the common denominator 42 unchanged.

3 + 10/42 = 13/42

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 13 and 42 is 1, confirming that 13/42 cannot be reduced further—it is already in its simplest irreducible form.

13/42

Step 5

Decimal & Percentage Representation

Dividing the numerator 13 by denominator 42 produces a repeating decimal (approximately 0.309524, or 30.9524%).

13 ÷ 42 = 0.309524 (30.9524%)

Visual Representation

The diagram below illustrates 3/42 plus 5/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`13/42`
Mixed Number Form	`13/42`
Decimal Form	`0.309524`
Percentage	`30.9524%`

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Frequently Asked Questions

What is 3/42 plus 5/21 as a fraction?

3/42 + 5/21 in simplest fraction form is 13/42.

What is 3/42 plus 5/21 as a decimal?

3/42 + 5/21 converted to a decimal is 0.309524.

What is 3/42 plus 5/21 as a percentage?

3/42 + 5/21 expressed as a percentage is 30.9524%.

Does 3/42 plus 5/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.309524...) because the denominator contains prime factors other than 2 and 5.