What is 12/63 plus 9/21? (Answer: 13/21)

Exact Answer

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Problem: What is 12/63 plus 9/21?
Formula / Expression: 12/63 + 9/21
Final Answer: 13/21
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
Notice that 63 is an exact multiple of 21 (21 × 3 = 63). The Least Common Denominator (LCD) is simply 63, meaning we only need to scale one fraction.
Working: LCD(63, 21) = 63

Step 2: Convert to Equivalent Fractions with Common Denominator 63
Multiply the numerator and denominator of 12/63 by 1, and multiply the numerator and denominator of 9/21 by 3 so both fractions share the common base 63.
Working: 12 × 1/63 × 1 = 12/63 and 9 × 3/21 × 3 = 27/63

Step 3: Add the Numerators
Now add the numerators (12 + 27 = 39) and keep the common denominator 63 unchanged.
Working: 12 + 27/63 = 39/63

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 39 and 63, which is 3. Divide both the numerator and denominator by 3.
Working: 39 ÷ 3/63 ÷ 3 = 13/21

Step 5: Decimal & Percentage Representation
Dividing the numerator 13 by denominator 21 produces a repeating decimal (approximately 0.619048, or 61.9048%).
Working: 13 ÷ 21 = 0.619048 (61.9048%)

Key Values:
- Simplified Fraction: 13/21
- Mixed Number Form: 13/21
- Decimal Value: 0.619048
- Percentage: 61.9048%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-12-63-plus-9-21/
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12/63 + 9/21 = 13/21

Simplified Fraction

13/21

Mixed Number

Proper (13/21)

Decimal Value

0.619048

Percentage

61.9048%

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Step-by-Step Solution: 12/63 + 9/21

Step 1

Find the Least Common Denominator (LCD)

Notice that 63 is an exact multiple of 21 (21 × 3 = 63). The Least Common Denominator (LCD) is simply 63, meaning we only need to scale one fraction.

LCD(63, 21) = 63

Step 2

Convert to Equivalent Fractions with Common Denominator 63

Multiply the numerator and denominator of 12/63 by 1, and multiply the numerator and denominator of 9/21 by 3 so both fractions share the common base 63.

12 × 1/63 × 1 = 12/63 and 9 × 3/21 × 3 = 27/63

Step 3

Add the Numerators

Now add the numerators (12 + 27 = 39) and keep the common denominator 63 unchanged.

12 + 27/63 = 39/63

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 39 and 63, which is 3. Divide both the numerator and denominator by 3.

39 ÷ 3/63 ÷ 3 = 13/21

Step 5

Decimal & Percentage Representation

Dividing the numerator 13 by denominator 21 produces a repeating decimal (approximately 0.619048, or 61.9048%).

13 ÷ 21 = 0.619048 (61.9048%)

Visual Representation

The diagram below illustrates 12/63 plus 9/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`13/21`
Mixed Number Form	`13/21`
Decimal Form	`0.619048`
Percentage	`61.9048%`

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Frequently Asked Questions

What is 12/63 plus 9/21 as a fraction?

12/63 + 9/21 in simplest fraction form is 13/21.

What is 12/63 plus 9/21 as a decimal?

12/63 + 9/21 converted to a decimal is 0.619048.

What is 12/63 plus 9/21 as a percentage?

12/63 + 9/21 expressed as a percentage is 61.9048%.

Does 12/63 plus 9/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.619048...) because the denominator contains prime factors other than 2 and 5.