What is 3/14 plus 5/21? (Answer: 19/42)

Exact Answer

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Problem: What is 3/14 plus 5/21?
Formula / Expression: 3/14 + 5/21
Final Answer: 19/42
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 14 and 21 share a common factor (GCD = 7). Finding their Least Common Multiple gives an LCD of 42 (which is smaller than their product 14 × 21 = 294, keeping the calculation simpler).
Working: LCD(14, 21) = 42

Step 2: Convert to Equivalent Fractions with Common Denominator 42
Multiply the numerator and denominator of 3/14 by 3, and multiply the numerator and denominator of 5/21 by 2 so both fractions share the common base 42.
Working: 3 × 3/14 × 3 = 9/42 and 5 × 2/21 × 2 = 10/42

Step 3: Add the Numerators
Now add the numerators (9 + 10 = 19) and keep the common denominator 42 unchanged.
Working: 9 + 10/42 = 19/42

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 19 and 42 is 1, confirming that 19/42 cannot be reduced further—it is already in its simplest irreducible form.
Working: 19/42

Step 5: Decimal & Percentage Representation
Dividing the numerator 19 by denominator 42 produces a repeating decimal (approximately 0.452381, or 45.2381%).
Working: 19 ÷ 42 = 0.452381 (45.2381%)

Key Values:
- Simplified Fraction: 19/42
- Mixed Number Form: 19/42
- Decimal Value: 0.452381
- Percentage: 45.2381%

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Solved with FractionsCalc:
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3/14 + 5/21 = 19/42

Simplified Fraction

19/42

Mixed Number

Proper (19/42)

Decimal Value

0.452381

Percentage

45.2381%

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Step-by-Step Solution: 3/14 + 5/21

Step 1

Find the Least Common Denominator (LCD)

The denominators 14 and 21 share a common factor (GCD = 7). Finding their Least Common Multiple gives an LCD of 42 (which is smaller than their product 14 × 21 = 294, keeping the calculation simpler).

LCD(14, 21) = 42

Step 2

Convert to Equivalent Fractions with Common Denominator 42

Multiply the numerator and denominator of 3/14 by 3, and multiply the numerator and denominator of 5/21 by 2 so both fractions share the common base 42.

3 × 3/14 × 3 = 9/42 and 5 × 2/21 × 2 = 10/42

Step 3

Add the Numerators

Now add the numerators (9 + 10 = 19) and keep the common denominator 42 unchanged.

9 + 10/42 = 19/42

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 19 and 42 is 1, confirming that 19/42 cannot be reduced further—it is already in its simplest irreducible form.

19/42

Step 5

Decimal & Percentage Representation

Dividing the numerator 19 by denominator 42 produces a repeating decimal (approximately 0.452381, or 45.2381%).

19 ÷ 42 = 0.452381 (45.2381%)

Visual Representation

The diagram below illustrates 3/14 plus 5/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`19/42`
Mixed Number Form	`19/42`
Decimal Form	`0.452381`
Percentage	`45.2381%`

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Frequently Asked Questions

What is 3/14 plus 5/21 as a fraction?

3/14 + 5/21 in simplest fraction form is 19/42.

What is 3/14 plus 5/21 as a decimal?

3/14 + 5/21 converted to a decimal is 0.452381.

What is 3/14 plus 5/21 as a percentage?

3/14 + 5/21 expressed as a percentage is 45.2381%.

Does 3/14 plus 5/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.452381...) because the denominator contains prime factors other than 2 and 5.