What is 3/10 plus 10/21? (Answer: 163/210)

Exact Answer

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Problem: What is 3/10 plus 10/21?
Formula / Expression: 3/10 + 10/21
Final Answer: 163/210
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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 10/21 by 10 so both fractions share the common base 210.
Working: 3 × 21/10 × 21 = 63/210 and 10 × 10/21 × 10 = 100/210

Step 3: Add the Numerators
Now add the numerators (63 + 100 = 163) and keep the common denominator 210 unchanged.
Working: 63 + 100/210 = 163/210

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 163 and 210 is 1, confirming that 163/210 cannot be reduced further—it is already in its simplest irreducible form.
Working: 163/210

Step 5: Decimal & Percentage Representation
Dividing the numerator 163 by denominator 210 produces a repeating decimal (approximately 0.77619, or 77.619%).
Working: 163 ÷ 210 = 0.77619 (77.619%)

Key Values:
- Simplified Fraction: 163/210
- Mixed Number Form: 163/210
- Decimal Value: 0.77619
- Percentage: 77.619%

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3/10 + 10/21 = 163/210

Simplified Fraction

163/210

Mixed Number

Proper (163/210)

Decimal Value

0.77619

Percentage

77.619%

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

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 10/21 by 10 so both fractions share the common base 210.

3 × 21/10 × 21 = 63/210 and 10 × 10/21 × 10 = 100/210

Step 3

Add the Numerators

Now add the numerators (63 + 100 = 163) and keep the common denominator 210 unchanged.

63 + 100/210 = 163/210

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 163 and 210 is 1, confirming that 163/210 cannot be reduced further—it is already in its simplest irreducible form.

163/210

Step 5

Decimal & Percentage Representation

Dividing the numerator 163 by denominator 210 produces a repeating decimal (approximately 0.77619, or 77.619%).

163 ÷ 210 = 0.77619 (77.619%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`163/210`
Mixed Number Form	`163/210`
Decimal Form	`0.77619`
Percentage	`77.619%`

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Frequently Asked Questions

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

3/10 + 10/21 in simplest fraction form is 163/210.

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

3/10 + 10/21 converted to a decimal is 0.77619.

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

3/10 + 10/21 expressed as a percentage is 77.619%.

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

It results in a repeating decimal (approximately 0.77619...) because the denominator contains prime factors other than 2 and 5.