What is 3/8 plus 10/21? (Answer: 143/168)

Exact Answer

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Problem: What is 3/8 plus 10/21?
Formula / Expression: 3/8 + 10/21
Final Answer: 143/168
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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 10/21 by 8 so both fractions share the common base 168.
Working: 3 × 21/8 × 21 = 63/168 and 10 × 8/21 × 8 = 80/168

Step 3: Add the Numerators
Now add the numerators (63 + 80 = 143) and keep the common denominator 168 unchanged.
Working: 63 + 80/168 = 143/168

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 143 and 168 is 1, confirming that 143/168 cannot be reduced further—it is already in its simplest irreducible form.
Working: 143/168

Step 5: Decimal & Percentage Representation
Dividing the numerator 143 by denominator 168 produces a repeating decimal (approximately 0.85119, or 85.119%).
Working: 143 ÷ 168 = 0.85119 (85.119%)

Key Values:
- Simplified Fraction: 143/168
- Mixed Number Form: 143/168
- Decimal Value: 0.85119
- Percentage: 85.119%

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Solved with FractionsCalc:
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3/8 + 10/21 = 143/168

Simplified Fraction

143/168

Mixed Number

Proper (143/168)

Decimal Value

0.85119

Percentage

85.119%

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Step-by-Step Solution: 3/8 + 10/21

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 10/21 by 8 so both fractions share the common base 168.

3 × 21/8 × 21 = 63/168 and 10 × 8/21 × 8 = 80/168

Step 3

Add the Numerators

Now add the numerators (63 + 80 = 143) and keep the common denominator 168 unchanged.

63 + 80/168 = 143/168

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 143 and 168 is 1, confirming that 143/168 cannot be reduced further—it is already in its simplest irreducible form.

143/168

Step 5

Decimal & Percentage Representation

Dividing the numerator 143 by denominator 168 produces a repeating decimal (approximately 0.85119, or 85.119%).

143 ÷ 168 = 0.85119 (85.119%)

Visual Representation

The diagram below illustrates 3/8 plus 10/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`143/168`
Mixed Number Form	`143/168`
Decimal Form	`0.85119`
Percentage	`85.119%`

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Frequently Asked Questions

What is 3/8 plus 10/21 as a fraction?

3/8 + 10/21 in simplest fraction form is 143/168.

What is 3/8 plus 10/21 as a decimal?

3/8 + 10/21 converted to a decimal is 0.85119.

What is 3/8 plus 10/21 as a percentage?

3/8 + 10/21 expressed as a percentage is 85.119%.

Does 3/8 plus 10/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.85119...) because the denominator contains prime factors other than 2 and 5.