What is 8/42 plus 12/21? (Answer: 16/21)

Exact Answer

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Problem: What is 8/42 plus 12/21?
Formula / Expression: 8/42 + 12/21
Final Answer: 16/21
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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 8/42 by 1, and multiply the numerator and denominator of 12/21 by 2 so both fractions share the common base 42.
Working: 8 × 1/42 × 1 = 8/42 and 12 × 2/21 × 2 = 24/42

Step 3: Add the Numerators
Now add the numerators (8 + 24 = 32) and keep the common denominator 42 unchanged.
Working: 8 + 24/42 = 32/42

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 32 and 42, which is 2. Divide both the numerator and denominator by 2.
Working: 32 ÷ 2/42 ÷ 2 = 16/21

Step 5: Decimal & Percentage Representation
Dividing the numerator 16 by denominator 21 produces a repeating decimal (approximately 0.761905, or 76.1905%).
Working: 16 ÷ 21 = 0.761905 (76.1905%)

Key Values:
- Simplified Fraction: 16/21
- Mixed Number Form: 16/21
- Decimal Value: 0.761905
- Percentage: 76.1905%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-8-42-plus-12-21/
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8/42 + 12/21 = 16/21

Simplified Fraction

16/21

Mixed Number

Proper (16/21)

Decimal Value

0.761905

Percentage

76.1905%

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Step-by-Step Solution: 8/42 + 12/21

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 8/42 by 1, and multiply the numerator and denominator of 12/21 by 2 so both fractions share the common base 42.

8 × 1/42 × 1 = 8/42 and 12 × 2/21 × 2 = 24/42

Step 3

Add the Numerators

Now add the numerators (8 + 24 = 32) and keep the common denominator 42 unchanged.

8 + 24/42 = 32/42

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 32 and 42, which is 2. Divide both the numerator and denominator by 2.

32 ÷ 2/42 ÷ 2 = 16/21

Step 5

Decimal & Percentage Representation

Dividing the numerator 16 by denominator 21 produces a repeating decimal (approximately 0.761905, or 76.1905%).

16 ÷ 21 = 0.761905 (76.1905%)

Visual Representation

The diagram below illustrates 8/42 plus 12/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`16/21`
Mixed Number Form	`16/21`
Decimal Form	`0.761905`
Percentage	`76.1905%`

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Frequently Asked Questions

What is 8/42 plus 12/21 as a fraction?

8/42 + 12/21 in simplest fraction form is 16/21.

What is 8/42 plus 12/21 as a decimal?

8/42 + 12/21 converted to a decimal is 0.761905.

What is 8/42 plus 12/21 as a percentage?

8/42 + 12/21 expressed as a percentage is 76.1905%.

Does 8/42 plus 12/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.761905...) because the denominator contains prime factors other than 2 and 5.