What is 9/18 plus 12/21? (Answer: 15/14)

Exact Answer

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Problem: What is 9/18 plus 12/21?
Formula / Expression: 9/18 + 12/21
Final Answer: 1 1/14 (15/14)
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 18 and 21 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 126 (which is smaller than their product 18 × 21 = 378, keeping the calculation simpler).
Working: LCD(18, 21) = 126

Step 2: Convert to Equivalent Fractions with Common Denominator 126
Multiply the numerator and denominator of 9/18 by 7, and multiply the numerator and denominator of 12/21 by 6 so both fractions share the common base 126.
Working: 9 × 7/18 × 7 = 63/126 and 12 × 6/21 × 6 = 72/126

Step 3: Add the Numerators
Now add the numerators (63 + 72 = 135) and keep the common denominator 126 unchanged.
Working: 63 + 72/126 = 135/126

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 135 and 126, which is 9. Divide both the numerator and denominator by 9.
Working: 135 ÷ 9/126 ÷ 9 = 15/14

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (15) is greater than the denominator (14), divide 15 by 14: it goes in 1 whole time(s) with a remainder of 1, giving the mixed number 1 1/14.
Working: 15/14 = 1 1/14

Step 6: Decimal & Percentage Representation
Dividing the numerator 15 by denominator 14 produces a repeating decimal (approximately 1.071429, or 107.1429%).
Working: 15 ÷ 14 = 1.071429 (107.1429%)

Key Values:
- Simplified Fraction: 15/14
- Mixed Number Form: 1 1/14
- Decimal Value: 1.071429
- Percentage: 107.1429%

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Solved with FractionsCalc:
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9/18 + 12/21 = 15/14

Simplified Fraction

15/14

Mixed Number

1 1/14

Decimal Value

1.071429

Percentage

107.1429%

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Step-by-Step Solution: 9/18 + 12/21

Step 1

Find the Least Common Denominator (LCD)

The denominators 18 and 21 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 126 (which is smaller than their product 18 × 21 = 378, keeping the calculation simpler).

LCD(18, 21) = 126

Step 2

Convert to Equivalent Fractions with Common Denominator 126

Multiply the numerator and denominator of 9/18 by 7, and multiply the numerator and denominator of 12/21 by 6 so both fractions share the common base 126.

9 × 7/18 × 7 = 63/126 and 12 × 6/21 × 6 = 72/126

Step 3

Add the Numerators

Now add the numerators (63 + 72 = 135) and keep the common denominator 126 unchanged.

63 + 72/126 = 135/126

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 135 and 126, which is 9. Divide both the numerator and denominator by 9.

135 ÷ 9/126 ÷ 9 = 15/14

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (15) is greater than the denominator (14), divide 15 by 14: it goes in 1 whole time(s) with a remainder of 1, giving the mixed number 1 1/14.

15/14 = 11/14

Step 6

Decimal & Percentage Representation

Dividing the numerator 15 by denominator 14 produces a repeating decimal (approximately 1.071429, or 107.1429%).

15 ÷ 14 = 1.071429 (107.1429%)

Visual Representation

The diagram below illustrates 9/18 plus 12/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`15/14`
Mixed Number Form	`1 1/14`
Decimal Form	`1.071429`
Percentage	`107.1429%`

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Frequently Asked Questions

What is 9/18 plus 12/21 as a fraction?

9/18 + 12/21 in simplest fraction form is 15/14 (or 1 1/14 as a mixed number).

What is 9/18 plus 12/21 as a decimal?

9/18 + 12/21 converted to a decimal is 1.071429.

What is 9/18 plus 12/21 as a percentage?

9/18 + 12/21 expressed as a percentage is 107.1429%.

How do you write 9/18 plus 12/21 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 15/14 can be written as the mixed number 1 1/14.

Does 9/18 plus 12/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.071429...) because the denominator contains prime factors other than 2 and 5.