What is 9/30 plus 12/21? (Answer: 61/70)

Exact Answer

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Problem: What is 9/30 plus 12/21?
Formula / Expression: 9/30 + 12/21
Final Answer: 61/70
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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 9/30 by 7, and multiply the numerator and denominator of 12/21 by 10 so both fractions share the common base 210.
Working: 9 × 7/30 × 7 = 63/210 and 12 × 10/21 × 10 = 120/210

Step 3: Add the Numerators
Now add the numerators (63 + 120 = 183) and keep the common denominator 210 unchanged.
Working: 63 + 120/210 = 183/210

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 183 and 210, which is 3. Divide both the numerator and denominator by 3.
Working: 183 ÷ 3/210 ÷ 3 = 61/70

Step 5: Decimal & Percentage Representation
Dividing the numerator 61 by denominator 70 produces a repeating decimal (approximately 0.871429, or 87.1429%).
Working: 61 ÷ 70 = 0.871429 (87.1429%)

Key Values:
- Simplified Fraction: 61/70
- Mixed Number Form: 61/70
- Decimal Value: 0.871429
- Percentage: 87.1429%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-9-30-plus-12-21/
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9/30 + 12/21 = 61/70

Simplified Fraction

61/70

Mixed Number

Proper (61/70)

Decimal Value

0.871429

Percentage

87.1429%

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Step-by-Step Solution: 9/30 + 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 9/30 by 7, and multiply the numerator and denominator of 12/21 by 10 so both fractions share the common base 210.

9 × 7/30 × 7 = 63/210 and 12 × 10/21 × 10 = 120/210

Step 3

Add the Numerators

Now add the numerators (63 + 120 = 183) and keep the common denominator 210 unchanged.

63 + 120/210 = 183/210

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 183 and 210, which is 3. Divide both the numerator and denominator by 3.

183 ÷ 3/210 ÷ 3 = 61/70

Step 5

Decimal & Percentage Representation

Dividing the numerator 61 by denominator 70 produces a repeating decimal (approximately 0.871429, or 87.1429%).

61 ÷ 70 = 0.871429 (87.1429%)

Visual Representation

The diagram below illustrates 9/30 plus 12/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`61/70`
Mixed Number Form	`61/70`
Decimal Form	`0.871429`
Percentage	`87.1429%`

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Frequently Asked Questions

What is 9/30 plus 12/21 as a fraction?

9/30 + 12/21 in simplest fraction form is 61/70.

What is 9/30 plus 12/21 as a decimal?

9/30 + 12/21 converted to a decimal is 0.871429.

What is 9/30 plus 12/21 as a percentage?

9/30 + 12/21 expressed as a percentage is 87.1429%.

Does 9/30 plus 12/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.871429...) because the denominator contains prime factors other than 2 and 5.