What is 3/42 plus 7/21? (Answer: 17/42)

Exact Answer

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Problem: What is 3/42 plus 7/21?
Formula / Expression: 3/42 + 7/21
Final Answer: 17/42
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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 7/21 by 2 so both fractions share the common base 42.
Working: 3 × 1/42 × 1 = 3/42 and 7 × 2/21 × 2 = 14/42

Step 3: Add the Numerators
Now add the numerators (3 + 14 = 17) and keep the common denominator 42 unchanged.
Working: 3 + 14/42 = 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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3/42 + 7/21 = 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: 3/42 + 7/21

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 7/21 by 2 so both fractions share the common base 42.

3 × 1/42 × 1 = 3/42 and 7 × 2/21 × 2 = 14/42

Step 3

Add the Numerators

Now add the numerators (3 + 14 = 17) and keep the common denominator 42 unchanged.

3 + 14/42 = 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 3/42 plus 7/21 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 3/42 plus 7/21 as a fraction?

3/42 + 7/21 in simplest fraction form is 17/42.

What is 3/42 plus 7/21 as a decimal?

3/42 + 7/21 converted to a decimal is 0.404762.

What is 3/42 plus 7/21 as a percentage?

3/42 + 7/21 expressed as a percentage is 40.4762%.

Does 3/42 plus 7/21 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.