What is 4/21 plus 3/14? (Answer: 17/42)

Exact Answer

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Problem: What is 4/21 plus 3/14?
Formula / Expression: 4/21 + 3/14
Final Answer: 17/42
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Step-by-Step Solution:

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

Step 2: Convert to Equivalent Fractions with Common Denominator 42
Multiply the numerator and denominator of 4/21 by 2, and multiply the numerator and denominator of 3/14 by 3 so both fractions share the common base 42.
Working: 4 × 2/21 × 2 = 8/42 and 3 × 3/14 × 3 = 9/42

Step 3: Add the Numerators
Now add the numerators (8 + 9 = 17) and keep the common denominator 42 unchanged.
Working: 8 + 9/42 = 17/42

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 17 and 42 is 1, confirming that 17/42 cannot be reduced further—it is already in its simplest irreducible form.
Working: 17/42

Step 5: Decimal & Percentage Representation
Dividing the numerator 17 by denominator 42 produces a repeating decimal (approximately 0.404762, or 40.4762%).
Working: 17 ÷ 42 = 0.404762 (40.4762%)

Key Values:
- Simplified Fraction: 17/42
- Mixed Number Form: 17/42
- Decimal Value: 0.404762
- Percentage: 40.4762%

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Solved with FractionsCalc:
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4/21 + 3/14 = 17/42

Simplified Fraction

17/42

Mixed Number

Proper (17/42)

Decimal Value

0.404762

Percentage

40.4762%

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Step-by-Step Solution: 4/21 + 3/14

Step 1

Find the Least Common Denominator (LCD)

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

LCD(21, 14) = 42

Step 2

Convert to Equivalent Fractions with Common Denominator 42

Multiply the numerator and denominator of 4/21 by 2, and multiply the numerator and denominator of 3/14 by 3 so both fractions share the common base 42.

4 × 2/21 × 2 = 8/42 and 3 × 3/14 × 3 = 9/42

Step 3

Add the Numerators

Now add the numerators (8 + 9 = 17) and keep the common denominator 42 unchanged.

8 + 9/42 = 17/42

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 17 and 42 is 1, confirming that 17/42 cannot be reduced further—it is already in its simplest irreducible form.

17/42

Step 5

Decimal & Percentage Representation

Dividing the numerator 17 by denominator 42 produces a repeating decimal (approximately 0.404762, or 40.4762%).

17 ÷ 42 = 0.404762 (40.4762%)

Visual Representation

The diagram below illustrates 4/21 plus 3/14 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`17/42`
Mixed Number Form	`17/42`
Decimal Form	`0.404762`
Percentage	`40.4762%`

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Frequently Asked Questions

What is 4/21 plus 3/14 as a fraction?

4/21 + 3/14 in simplest fraction form is 17/42.

What is 4/21 plus 3/14 as a decimal?

4/21 + 3/14 converted to a decimal is 0.404762.

What is 4/21 plus 3/14 as a percentage?

4/21 + 3/14 expressed as a percentage is 40.4762%.

Does 4/21 plus 3/14 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.404762...) because the denominator contains prime factors other than 2 and 5.