What is 14/45 plus 9/21? (Answer: 233/315)

Exact Answer

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Problem: What is 14/45 plus 9/21?
Formula / Expression: 14/45 + 9/21
Final Answer: 233/315
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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 14/45 by 7, and multiply the numerator and denominator of 9/21 by 15 so both fractions share the common base 315.
Working: 14 × 7/45 × 7 = 98/315 and 9 × 15/21 × 15 = 135/315

Step 3: Add the Numerators
Now add the numerators (98 + 135 = 233) and keep the common denominator 315 unchanged.
Working: 98 + 135/315 = 233/315

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 233 and 315 is 1, confirming that 233/315 cannot be reduced further—it is already in its simplest irreducible form.
Working: 233/315

Step 5: Decimal & Percentage Representation
Dividing the numerator 233 by denominator 315 produces a repeating decimal (approximately 0.739683, or 73.9683%).
Working: 233 ÷ 315 = 0.739683 (73.9683%)

Key Values:
- Simplified Fraction: 233/315
- Mixed Number Form: 233/315
- Decimal Value: 0.739683
- Percentage: 73.9683%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-14-45-plus-9-21/
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14/45 + 9/21 = 233/315

Simplified Fraction

233/315

Mixed Number

Proper (233/315)

Decimal Value

0.739683

Percentage

73.9683%

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Step-by-Step Solution: 14/45 + 9/21

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 14/45 by 7, and multiply the numerator and denominator of 9/21 by 15 so both fractions share the common base 315.

14 × 7/45 × 7 = 98/315 and 9 × 15/21 × 15 = 135/315

Step 3

Add the Numerators

Now add the numerators (98 + 135 = 233) and keep the common denominator 315 unchanged.

98 + 135/315 = 233/315

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 233 and 315 is 1, confirming that 233/315 cannot be reduced further—it is already in its simplest irreducible form.

233/315

Step 5

Decimal & Percentage Representation

Dividing the numerator 233 by denominator 315 produces a repeating decimal (approximately 0.739683, or 73.9683%).

233 ÷ 315 = 0.739683 (73.9683%)

Visual Representation

The diagram below illustrates 14/45 plus 9/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`233/315`
Mixed Number Form	`233/315`
Decimal Form	`0.739683`
Percentage	`73.9683%`

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Frequently Asked Questions

What is 14/45 plus 9/21 as a fraction?

14/45 + 9/21 in simplest fraction form is 233/315.

What is 14/45 plus 9/21 as a decimal?

14/45 + 9/21 converted to a decimal is 0.739683.

What is 14/45 plus 9/21 as a percentage?

14/45 + 9/21 expressed as a percentage is 73.9683%.

Does 14/45 plus 9/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.739683...) because the denominator contains prime factors other than 2 and 5.