What is 3/30 plus 8/21? (Answer: 101/210)

Exact Answer

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Problem: What is 3/30 plus 8/21?
Formula / Expression: 3/30 + 8/21
Final Answer: 101/210
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 30 and 21 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 210 (which is smaller than their product 30 × 21 = 630, keeping the calculation simpler).
Working: LCD(30, 21) = 210

Step 2: Convert to Equivalent Fractions with Common Denominator 210
Multiply the numerator and denominator of 3/30 by 7, and multiply the numerator and denominator of 8/21 by 10 so both fractions share the common base 210.
Working: 3 × 7/30 × 7 = 21/210 and 8 × 10/21 × 10 = 80/210

Step 3: Add the Numerators
Now add the numerators (21 + 80 = 101) and keep the common denominator 210 unchanged.
Working: 21 + 80/210 = 101/210

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 101 and 210 is 1, confirming that 101/210 cannot be reduced further—it is already in its simplest irreducible form.
Working: 101/210

Step 5: Decimal & Percentage Representation
Dividing the numerator 101 by denominator 210 produces a repeating decimal (approximately 0.480952, or 48.0952%).
Working: 101 ÷ 210 = 0.480952 (48.0952%)

Key Values:
- Simplified Fraction: 101/210
- Mixed Number Form: 101/210
- Decimal Value: 0.480952
- Percentage: 48.0952%

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3/30 + 8/21 = 101/210

Simplified Fraction

101/210

Mixed Number

Proper (101/210)

Decimal Value

0.480952

Percentage

48.0952%

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Step-by-Step Solution: 3/30 + 8/21

Step 1

Find the Least Common Denominator (LCD)

The denominators 30 and 21 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 210 (which is smaller than their product 30 × 21 = 630, keeping the calculation simpler).

LCD(30, 21) = 210

Step 2

Convert to Equivalent Fractions with Common Denominator 210

Multiply the numerator and denominator of 3/30 by 7, and multiply the numerator and denominator of 8/21 by 10 so both fractions share the common base 210.

3 × 7/30 × 7 = 21/210 and 8 × 10/21 × 10 = 80/210

Step 3

Add the Numerators

Now add the numerators (21 + 80 = 101) and keep the common denominator 210 unchanged.

21 + 80/210 = 101/210

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 101 and 210 is 1, confirming that 101/210 cannot be reduced further—it is already in its simplest irreducible form.

101/210

Step 5

Decimal & Percentage Representation

Dividing the numerator 101 by denominator 210 produces a repeating decimal (approximately 0.480952, or 48.0952%).

101 ÷ 210 = 0.480952 (48.0952%)

Visual Representation

The diagram below illustrates 3/30 plus 8/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`101/210`
Mixed Number Form	`101/210`
Decimal Form	`0.480952`
Percentage	`48.0952%`

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Frequently Asked Questions

What is 3/30 plus 8/21 as a fraction?

3/30 + 8/21 in simplest fraction form is 101/210.

What is 3/30 plus 8/21 as a decimal?

3/30 + 8/21 converted to a decimal is 0.480952.

What is 3/30 plus 8/21 as a percentage?

3/30 + 8/21 expressed as a percentage is 48.0952%.

Does 3/30 plus 8/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.480952...) because the denominator contains prime factors other than 2 and 5.