What is 3/8 plus 8/21? (Answer: 127/168)

Exact Answer

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Problem: What is 3/8 plus 8/21?
Formula / Expression: 3/8 + 8/21
Final Answer: 127/168
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 8 and 21 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 8 × 21 = 168.
Working: LCD(8, 21) = 168

Step 2: Convert to Equivalent Fractions with Common Denominator 168
Multiply the numerator and denominator of 3/8 by 21, and multiply the numerator and denominator of 8/21 by 8 so both fractions share the common base 168.
Working: 3 × 21/8 × 21 = 63/168 and 8 × 8/21 × 8 = 64/168

Step 3: Add the Numerators
Now add the numerators (63 + 64 = 127) and keep the common denominator 168 unchanged.
Working: 63 + 64/168 = 127/168

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 127 and 168 is 1, confirming that 127/168 cannot be reduced further—it is already in its simplest irreducible form.
Working: 127/168

Step 5: Decimal & Percentage Representation
Dividing the numerator 127 by denominator 168 produces a repeating decimal (approximately 0.755952, or 75.5952%).
Working: 127 ÷ 168 = 0.755952 (75.5952%)

Key Values:
- Simplified Fraction: 127/168
- Mixed Number Form: 127/168
- Decimal Value: 0.755952
- Percentage: 75.5952%

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Solved with FractionsCalc:
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3/8 + 8/21 = 127/168

Simplified Fraction

127/168

Mixed Number

Proper (127/168)

Decimal Value

0.755952

Percentage

75.5952%

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Step-by-Step Solution: 3/8 + 8/21

Step 1

Find the Least Common Denominator (LCD)

The denominators 8 and 21 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 8 × 21 = 168.

LCD(8, 21) = 168

Step 2

Convert to Equivalent Fractions with Common Denominator 168

Multiply the numerator and denominator of 3/8 by 21, and multiply the numerator and denominator of 8/21 by 8 so both fractions share the common base 168.

3 × 21/8 × 21 = 63/168 and 8 × 8/21 × 8 = 64/168

Step 3

Add the Numerators

Now add the numerators (63 + 64 = 127) and keep the common denominator 168 unchanged.

63 + 64/168 = 127/168

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 127 and 168 is 1, confirming that 127/168 cannot be reduced further—it is already in its simplest irreducible form.

127/168

Step 5

Decimal & Percentage Representation

Dividing the numerator 127 by denominator 168 produces a repeating decimal (approximately 0.755952, or 75.5952%).

127 ÷ 168 = 0.755952 (75.5952%)

Visual Representation

The diagram below illustrates 3/8 plus 8/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`127/168`
Mixed Number Form	`127/168`
Decimal Form	`0.755952`
Percentage	`75.5952%`

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Frequently Asked Questions

What is 3/8 plus 8/21 as a fraction?

3/8 + 8/21 in simplest fraction form is 127/168.

What is 3/8 plus 8/21 as a decimal?

3/8 + 8/21 converted to a decimal is 0.755952.

What is 3/8 plus 8/21 as a percentage?

3/8 + 8/21 expressed as a percentage is 75.5952%.

Does 3/8 plus 8/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.755952...) because the denominator contains prime factors other than 2 and 5.