What is 9/45 plus 12/21? (Answer: 27/35)

Exact Answer

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Problem: What is 9/45 plus 12/21?
Formula / Expression: 9/45 + 12/21
Final Answer: 27/35
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 45 and 21 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 315 (which is smaller than their product 45 × 21 = 945, keeping the calculation simpler).
Working: LCD(45, 21) = 315

Step 2: Convert to Equivalent Fractions with Common Denominator 315
Multiply the numerator and denominator of 9/45 by 7, and multiply the numerator and denominator of 12/21 by 15 so both fractions share the common base 315.
Working: 9 × 7/45 × 7 = 63/315 and 12 × 15/21 × 15 = 180/315

Step 3: Add the Numerators
Now add the numerators (63 + 180 = 243) and keep the common denominator 315 unchanged.
Working: 63 + 180/315 = 243/315

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 243 and 315, which is 9. Divide both the numerator and denominator by 9.
Working: 243 ÷ 9/315 ÷ 9 = 27/35

Step 5: Decimal & Percentage Representation
Dividing the numerator 27 by denominator 35 produces a repeating decimal (approximately 0.771429, or 77.1429%).
Working: 27 ÷ 35 = 0.771429 (77.1429%)

Key Values:
- Simplified Fraction: 27/35
- Mixed Number Form: 27/35
- Decimal Value: 0.771429
- Percentage: 77.1429%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-9-45-plus-12-21/
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9/45 + 12/21 = 27/35

Simplified Fraction

27/35

Mixed Number

Proper (27/35)

Decimal Value

0.771429

Percentage

77.1429%

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Step-by-Step Solution: 9/45 + 12/21

Step 1

Find the Least Common Denominator (LCD)

The denominators 45 and 21 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 315 (which is smaller than their product 45 × 21 = 945, keeping the calculation simpler).

LCD(45, 21) = 315

Step 2

Convert to Equivalent Fractions with Common Denominator 315

Multiply the numerator and denominator of 9/45 by 7, and multiply the numerator and denominator of 12/21 by 15 so both fractions share the common base 315.

9 × 7/45 × 7 = 63/315 and 12 × 15/21 × 15 = 180/315

Step 3

Add the Numerators

Now add the numerators (63 + 180 = 243) and keep the common denominator 315 unchanged.

63 + 180/315 = 243/315

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 243 and 315, which is 9. Divide both the numerator and denominator by 9.

243 ÷ 9/315 ÷ 9 = 27/35

Step 5

Decimal & Percentage Representation

Dividing the numerator 27 by denominator 35 produces a repeating decimal (approximately 0.771429, or 77.1429%).

27 ÷ 35 = 0.771429 (77.1429%)

Visual Representation

The diagram below illustrates 9/45 plus 12/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`27/35`
Mixed Number Form	`27/35`
Decimal Form	`0.771429`
Percentage	`77.1429%`

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Frequently Asked Questions

What is 9/45 plus 12/21 as a fraction?

9/45 + 12/21 in simplest fraction form is 27/35.

What is 9/45 plus 12/21 as a decimal?

9/45 + 12/21 converted to a decimal is 0.771429.

What is 9/45 plus 12/21 as a percentage?

9/45 + 12/21 expressed as a percentage is 77.1429%.

Does 9/45 plus 12/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.771429...) because the denominator contains prime factors other than 2 and 5.