What is 3/10 plus 8/21? (Answer: 143/210)

Exact Answer

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Problem: What is 3/10 plus 8/21?
Formula / Expression: 3/10 + 8/21
Final Answer: 143/210
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 10 and 21 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 10 × 21 = 210.
Working: LCD(10, 21) = 210

Step 2: Convert to Equivalent Fractions with Common Denominator 210
Multiply the numerator and denominator of 3/10 by 21, and multiply the numerator and denominator of 8/21 by 10 so both fractions share the common base 210.
Working: 3 × 21/10 × 21 = 63/210 and 8 × 10/21 × 10 = 80/210

Step 3: Add the Numerators
Now add the numerators (63 + 80 = 143) and keep the common denominator 210 unchanged.
Working: 63 + 80/210 = 143/210

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 143 and 210 is 1, confirming that 143/210 cannot be reduced further—it is already in its simplest irreducible form.
Working: 143/210

Step 5: Decimal & Percentage Representation
Dividing the numerator 143 by denominator 210 produces a repeating decimal (approximately 0.680952, or 68.0952%).
Working: 143 ÷ 210 = 0.680952 (68.0952%)

Key Values:
- Simplified Fraction: 143/210
- Mixed Number Form: 143/210
- Decimal Value: 0.680952
- Percentage: 68.0952%

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3/10 + 8/21 = 143/210

Simplified Fraction

143/210

Mixed Number

Proper (143/210)

Decimal Value

0.680952

Percentage

68.0952%

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

Step 1

Find the Least Common Denominator (LCD)

The denominators 10 and 21 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 10 × 21 = 210.

LCD(10, 21) = 210

Step 2

Convert to Equivalent Fractions with Common Denominator 210

Multiply the numerator and denominator of 3/10 by 21, and multiply the numerator and denominator of 8/21 by 10 so both fractions share the common base 210.

3 × 21/10 × 21 = 63/210 and 8 × 10/21 × 10 = 80/210

Step 3

Add the Numerators

Now add the numerators (63 + 80 = 143) and keep the common denominator 210 unchanged.

63 + 80/210 = 143/210

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 143 and 210 is 1, confirming that 143/210 cannot be reduced further—it is already in its simplest irreducible form.

143/210

Step 5

Decimal & Percentage Representation

Dividing the numerator 143 by denominator 210 produces a repeating decimal (approximately 0.680952, or 68.0952%).

143 ÷ 210 = 0.680952 (68.0952%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`143/210`
Mixed Number Form	`143/210`
Decimal Form	`0.680952`
Percentage	`68.0952%`

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Frequently Asked Questions

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

3/10 + 8/21 in simplest fraction form is 143/210.

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

3/10 + 8/21 converted to a decimal is 0.680952.

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

3/10 + 8/21 expressed as a percentage is 68.0952%.

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

It results in a repeating decimal (approximately 0.680952...) because the denominator contains prime factors other than 2 and 5.