What is 1/42 plus 3/21? (Answer: 1/6)

Exact Answer

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Problem: What is 1/42 plus 3/21?
Formula / Expression: 1/42 + 3/21
Final Answer: 1/6
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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 1/42 by 1, and multiply the numerator and denominator of 3/21 by 2 so both fractions share the common base 42.
Working: 1 × 1/42 × 1 = 1/42 and 3 × 2/21 × 2 = 6/42

Step 3: Add the Numerators
Now add the numerators (1 + 6 = 7) and keep the common denominator 42 unchanged.
Working: 1 + 6/42 = 7/42

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 7 and 42, which is 7. Divide both the numerator and denominator by 7.
Working: 7 ÷ 7/42 ÷ 7 = 1/6

Step 5: Decimal & Percentage Representation
Dividing the numerator 1 by denominator 6 produces a repeating decimal (approximately 0.166667, or 16.6667%).
Working: 1 ÷ 6 = 0.166667 (16.6667%)

Key Values:
- Simplified Fraction: 1/6
- Mixed Number Form: 1/6
- Decimal Value: 0.166667
- Percentage: 16.6667%

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Solved with FractionsCalc:
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1/42 + 3/21 = 1/6

Simplified Fraction

1/6

Mixed Number

Proper (1/6)

Decimal Value

0.166667

Percentage

16.6667%

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Step-by-Step Solution: 1/42 + 3/21

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 1/42 by 1, and multiply the numerator and denominator of 3/21 by 2 so both fractions share the common base 42.

1 × 1/42 × 1 = 1/42 and 3 × 2/21 × 2 = 6/42

Step 3

Add the Numerators

Now add the numerators (1 + 6 = 7) and keep the common denominator 42 unchanged.

1 + 6/42 = 7/42

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 7 and 42, which is 7. Divide both the numerator and denominator by 7.

7 ÷ 7/42 ÷ 7 = 1/6

Step 5

Decimal & Percentage Representation

Dividing the numerator 1 by denominator 6 produces a repeating decimal (approximately 0.166667, or 16.6667%).

1 ÷ 6 = 0.166667 (16.6667%)

Visual Representation

The diagram below illustrates 1/42 plus 3/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`1/6`
Mixed Number Form	`1/6`
Decimal Form	`0.166667`
Percentage	`16.6667%`

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Frequently Asked Questions

What is 1/42 plus 3/21 as a fraction?

1/42 + 3/21 in simplest fraction form is 1/6.

What is 1/42 plus 3/21 as a decimal?

1/42 + 3/21 converted to a decimal is 0.166667.

What is 1/42 plus 3/21 as a percentage?

1/42 + 3/21 expressed as a percentage is 16.6667%.

Does 1/42 plus 3/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.166667...) because the denominator contains prime factors other than 2 and 5.