What is 7/30 plus 12/21? (Answer: 169/210)

Exact Answer

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Problem: What is 7/30 plus 12/21?
Formula / Expression: 7/30 + 12/21
Final Answer: 169/210
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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 7/30 by 7, and multiply the numerator and denominator of 12/21 by 10 so both fractions share the common base 210.
Working: 7 × 7/30 × 7 = 49/210 and 12 × 10/21 × 10 = 120/210

Step 3: Add the Numerators
Now add the numerators (49 + 120 = 169) and keep the common denominator 210 unchanged.
Working: 49 + 120/210 = 169/210

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 169 and 210 is 1, confirming that 169/210 cannot be reduced further—it is already in its simplest irreducible form.
Working: 169/210

Step 5: Decimal & Percentage Representation
Dividing the numerator 169 by denominator 210 produces a repeating decimal (approximately 0.804762, or 80.4762%).
Working: 169 ÷ 210 = 0.804762 (80.4762%)

Key Values:
- Simplified Fraction: 169/210
- Mixed Number Form: 169/210
- Decimal Value: 0.804762
- Percentage: 80.4762%

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Solved with FractionsCalc:
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7/30 + 12/21 = 169/210

Simplified Fraction

169/210

Mixed Number

Proper (169/210)

Decimal Value

0.804762

Percentage

80.4762%

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Step-by-Step Solution: 7/30 + 12/21

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 7/30 by 7, and multiply the numerator and denominator of 12/21 by 10 so both fractions share the common base 210.

7 × 7/30 × 7 = 49/210 and 12 × 10/21 × 10 = 120/210

Step 3

Add the Numerators

Now add the numerators (49 + 120 = 169) and keep the common denominator 210 unchanged.

49 + 120/210 = 169/210

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 169 and 210 is 1, confirming that 169/210 cannot be reduced further—it is already in its simplest irreducible form.

169/210

Step 5

Decimal & Percentage Representation

Dividing the numerator 169 by denominator 210 produces a repeating decimal (approximately 0.804762, or 80.4762%).

169 ÷ 210 = 0.804762 (80.4762%)

Visual Representation

The diagram below illustrates 7/30 plus 12/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`169/210`
Mixed Number Form	`169/210`
Decimal Form	`0.804762`
Percentage	`80.4762%`

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Frequently Asked Questions

What is 7/30 plus 12/21 as a fraction?

7/30 + 12/21 in simplest fraction form is 169/210.

What is 7/30 plus 12/21 as a decimal?

7/30 + 12/21 converted to a decimal is 0.804762.

What is 7/30 plus 12/21 as a percentage?

7/30 + 12/21 expressed as a percentage is 80.4762%.

Does 7/30 plus 12/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.804762...) because the denominator contains prime factors other than 2 and 5.