What is 22/45 plus 12/21? (Answer: 334/315)

Exact Answer

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Problem: What is 22/45 plus 12/21?
Formula / Expression: 22/45 + 12/21
Final Answer: 1 19/315 (334/315)
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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 22/45 by 7, and multiply the numerator and denominator of 12/21 by 15 so both fractions share the common base 315.
Working: 22 × 7/45 × 7 = 154/315 and 12 × 15/21 × 15 = 180/315

Step 3: Add the Numerators
Now add the numerators (154 + 180 = 334) and keep the common denominator 315 unchanged.
Working: 154 + 180/315 = 334/315

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 334 and 315 is 1, confirming that 334/315 cannot be reduced further—it is already in its simplest irreducible form.
Working: 334/315

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (334) is greater than the denominator (315), divide 334 by 315: it goes in 1 whole time(s) with a remainder of 19, giving the mixed number 1 19/315.
Working: 334/315 = 1 19/315

Step 6: Decimal & Percentage Representation
Dividing the numerator 334 by denominator 315 produces a repeating decimal (approximately 1.060317, or 106.0317%).
Working: 334 ÷ 315 = 1.060317 (106.0317%)

Key Values:
- Simplified Fraction: 334/315
- Mixed Number Form: 1 19/315
- Decimal Value: 1.060317
- Percentage: 106.0317%

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Solved with FractionsCalc:
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22/45 + 12/21 = 334/315

Simplified Fraction

334/315

Mixed Number

1 19/315

Decimal Value

1.060317

Percentage

106.0317%

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Step-by-Step Solution: 22/45 + 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 22/45 by 7, and multiply the numerator and denominator of 12/21 by 15 so both fractions share the common base 315.

22 × 7/45 × 7 = 154/315 and 12 × 15/21 × 15 = 180/315

Step 3

Add the Numerators

Now add the numerators (154 + 180 = 334) and keep the common denominator 315 unchanged.

154 + 180/315 = 334/315

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 334 and 315 is 1, confirming that 334/315 cannot be reduced further—it is already in its simplest irreducible form.

334/315

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (334) is greater than the denominator (315), divide 334 by 315: it goes in 1 whole time(s) with a remainder of 19, giving the mixed number 1 19/315.

334/315 = 119/315

Step 6

Decimal & Percentage Representation

Dividing the numerator 334 by denominator 315 produces a repeating decimal (approximately 1.060317, or 106.0317%).

334 ÷ 315 = 1.060317 (106.0317%)

Visual Representation

The diagram below illustrates 22/45 plus 12/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`334/315`
Mixed Number Form	`1 19/315`
Decimal Form	`1.060317`
Percentage	`106.0317%`

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Frequently Asked Questions

What is 22/45 plus 12/21 as a fraction?

22/45 + 12/21 in simplest fraction form is 334/315 (or 1 19/315 as a mixed number).

What is 22/45 plus 12/21 as a decimal?

22/45 + 12/21 converted to a decimal is 1.060317.

What is 22/45 plus 12/21 as a percentage?

22/45 + 12/21 expressed as a percentage is 106.0317%.

How do you write 22/45 plus 12/21 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 334/315 can be written as the mixed number 1 19/315.

Does 22/45 plus 12/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.060317...) because the denominator contains prime factors other than 2 and 5.