What is 7/45 plus 12/21? (Answer: 229/315)

Exact Answer

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Problem: What is 7/45 plus 12/21?
Formula / Expression: 7/45 + 12/21
Final Answer: 229/315
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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 7/45 by 7, and multiply the numerator and denominator of 12/21 by 15 so both fractions share the common base 315.
Working: 7 × 7/45 × 7 = 49/315 and 12 × 15/21 × 15 = 180/315

Step 3: Add the Numerators
Now add the numerators (49 + 180 = 229) and keep the common denominator 315 unchanged.
Working: 49 + 180/315 = 229/315

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 229 and 315 is 1, confirming that 229/315 cannot be reduced further—it is already in its simplest irreducible form.
Working: 229/315

Step 5: Decimal & Percentage Representation
Dividing the numerator 229 by denominator 315 produces a repeating decimal (approximately 0.726984, or 72.6984%).
Working: 229 ÷ 315 = 0.726984 (72.6984%)

Key Values:
- Simplified Fraction: 229/315
- Mixed Number Form: 229/315
- Decimal Value: 0.726984
- Percentage: 72.6984%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-7-45-plus-12-21/
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7/45 + 12/21 = 229/315

Simplified Fraction

229/315

Mixed Number

Proper (229/315)

Decimal Value

0.726984

Percentage

72.6984%

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

7 × 7/45 × 7 = 49/315 and 12 × 15/21 × 15 = 180/315

Step 3

Add the Numerators

Now add the numerators (49 + 180 = 229) and keep the common denominator 315 unchanged.

49 + 180/315 = 229/315

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 229 and 315 is 1, confirming that 229/315 cannot be reduced further—it is already in its simplest irreducible form.

229/315

Step 5

Decimal & Percentage Representation

Dividing the numerator 229 by denominator 315 produces a repeating decimal (approximately 0.726984, or 72.6984%).

229 ÷ 315 = 0.726984 (72.6984%)

Visual Representation

The diagram below illustrates 7/45 plus 12/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`229/315`
Mixed Number Form	`229/315`
Decimal Form	`0.726984`
Percentage	`72.6984%`

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Frequently Asked Questions

What is 7/45 plus 12/21 as a fraction?

7/45 + 12/21 in simplest fraction form is 229/315.

What is 7/45 plus 12/21 as a decimal?

7/45 + 12/21 converted to a decimal is 0.726984.

What is 7/45 plus 12/21 as a percentage?

7/45 + 12/21 expressed as a percentage is 72.6984%.

Does 7/45 plus 12/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.726984...) because the denominator contains prime factors other than 2 and 5.