What is 8/42 plus 5/21? (Answer: 3/7)

Exact Answer

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Problem: What is 8/42 plus 5/21?
Formula / Expression: 8/42 + 5/21
Final Answer: 3/7
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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 5/21 by 2 so both fractions share the common base 42.
Working: 8 × 1/42 × 1 = 8/42 and 5 × 2/21 × 2 = 10/42

Step 3: Add the Numerators
Now add the numerators (8 + 10 = 18) and keep the common denominator 42 unchanged.
Working: 8 + 10/42 = 18/42

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 18 and 42, which is 6. Divide both the numerator and denominator by 6.
Working: 18 ÷ 6/42 ÷ 6 = 3/7

Step 5: Decimal & Percentage Representation
Dividing the numerator 3 by denominator 7 produces a repeating decimal (approximately 0.428571, or 42.8571%).
Working: 3 ÷ 7 = 0.428571 (42.8571%)

Key Values:
- Simplified Fraction: 3/7
- Mixed Number Form: 3/7
- Decimal Value: 0.428571
- Percentage: 42.8571%

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Solved with FractionsCalc:
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8/42 + 5/21 = 3/7

Simplified Fraction

3/7

Mixed Number

Proper (3/7)

Decimal Value

0.428571

Percentage

42.8571%

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Step-by-Step Solution: 8/42 + 5/21

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 5/21 by 2 so both fractions share the common base 42.

8 × 1/42 × 1 = 8/42 and 5 × 2/21 × 2 = 10/42

Step 3

Add the Numerators

Now add the numerators (8 + 10 = 18) and keep the common denominator 42 unchanged.

8 + 10/42 = 18/42

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 18 and 42, which is 6. Divide both the numerator and denominator by 6.

18 ÷ 6/42 ÷ 6 = 3/7

Step 5

Decimal & Percentage Representation

Dividing the numerator 3 by denominator 7 produces a repeating decimal (approximately 0.428571, or 42.8571%).

3 ÷ 7 = 0.428571 (42.8571%)

Visual Representation

The diagram below illustrates 8/42 plus 5/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`3/7`
Mixed Number Form	`3/7`
Decimal Form	`0.428571`
Percentage	`42.8571%`

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Frequently Asked Questions

What is 8/42 plus 5/21 as a fraction?

8/42 + 5/21 in simplest fraction form is 3/7.

What is 8/42 plus 5/21 as a decimal?

8/42 + 5/21 converted to a decimal is 0.428571.

What is 8/42 plus 5/21 as a percentage?

8/42 + 5/21 expressed as a percentage is 42.8571%.

Does 8/42 plus 5/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.428571...) because the denominator contains prime factors other than 2 and 5.