What is 4/45 plus 12/21? (Answer: 208/315)

Exact Answer

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Problem: What is 4/45 plus 12/21?
Formula / Expression: 4/45 + 12/21
Final Answer: 208/315
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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 4/45 by 7, and multiply the numerator and denominator of 12/21 by 15 so both fractions share the common base 315.
Working: 4 × 7/45 × 7 = 28/315 and 12 × 15/21 × 15 = 180/315

Step 3: Add the Numerators
Now add the numerators (28 + 180 = 208) and keep the common denominator 315 unchanged.
Working: 28 + 180/315 = 208/315

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 208 and 315 is 1, confirming that 208/315 cannot be reduced further—it is already in its simplest irreducible form.
Working: 208/315

Step 5: Decimal & Percentage Representation
Dividing the numerator 208 by denominator 315 produces a repeating decimal (approximately 0.660317, or 66.0317%).
Working: 208 ÷ 315 = 0.660317 (66.0317%)

Key Values:
- Simplified Fraction: 208/315
- Mixed Number Form: 208/315
- Decimal Value: 0.660317
- Percentage: 66.0317%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-4-45-plus-12-21/
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4/45 + 12/21 = 208/315

Simplified Fraction

208/315

Mixed Number

Proper (208/315)

Decimal Value

0.660317

Percentage

66.0317%

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Step-by-Step Solution: 4/45 + 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 4/45 by 7, and multiply the numerator and denominator of 12/21 by 15 so both fractions share the common base 315.

4 × 7/45 × 7 = 28/315 and 12 × 15/21 × 15 = 180/315

Step 3

Add the Numerators

Now add the numerators (28 + 180 = 208) and keep the common denominator 315 unchanged.

28 + 180/315 = 208/315

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 208 and 315 is 1, confirming that 208/315 cannot be reduced further—it is already in its simplest irreducible form.

208/315

Step 5

Decimal & Percentage Representation

Dividing the numerator 208 by denominator 315 produces a repeating decimal (approximately 0.660317, or 66.0317%).

208 ÷ 315 = 0.660317 (66.0317%)

Visual Representation

The diagram below illustrates 4/45 plus 12/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`208/315`
Mixed Number Form	`208/315`
Decimal Form	`0.660317`
Percentage	`66.0317%`

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Frequently Asked Questions

What is 4/45 plus 12/21 as a fraction?

4/45 + 12/21 in simplest fraction form is 208/315.

What is 4/45 plus 12/21 as a decimal?

4/45 + 12/21 converted to a decimal is 0.660317.

What is 4/45 plus 12/21 as a percentage?

4/45 + 12/21 expressed as a percentage is 66.0317%.

Does 4/45 plus 12/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.660317...) because the denominator contains prime factors other than 2 and 5.