What is 7/45 plus 11/21? (Answer: 214/315)

Exact Answer

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Problem: What is 7/45 plus 11/21?
Formula / Expression: 7/45 + 11/21
Final Answer: 214/315
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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 11/21 by 15 so both fractions share the common base 315.
Working: 7 × 7/45 × 7 = 49/315 and 11 × 15/21 × 15 = 165/315

Step 3: Add the Numerators
Now add the numerators (49 + 165 = 214) and keep the common denominator 315 unchanged.
Working: 49 + 165/315 = 214/315

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 214 and 315 is 1, confirming that 214/315 cannot be reduced further—it is already in its simplest irreducible form.
Working: 214/315

Step 5: Decimal & Percentage Representation
Dividing the numerator 214 by denominator 315 produces a repeating decimal (approximately 0.679365, or 67.9365%).
Working: 214 ÷ 315 = 0.679365 (67.9365%)

Key Values:
- Simplified Fraction: 214/315
- Mixed Number Form: 214/315
- Decimal Value: 0.679365
- Percentage: 67.9365%

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Solved with FractionsCalc:
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7/45 + 11/21 = 214/315

Simplified Fraction

214/315

Mixed Number

Proper (214/315)

Decimal Value

0.679365

Percentage

67.9365%

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Step-by-Step Solution: 7/45 + 11/21

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 11/21 by 15 so both fractions share the common base 315.

7 × 7/45 × 7 = 49/315 and 11 × 15/21 × 15 = 165/315

Step 3

Add the Numerators

Now add the numerators (49 + 165 = 214) and keep the common denominator 315 unchanged.

49 + 165/315 = 214/315

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 214 and 315 is 1, confirming that 214/315 cannot be reduced further—it is already in its simplest irreducible form.

214/315

Step 5

Decimal & Percentage Representation

Dividing the numerator 214 by denominator 315 produces a repeating decimal (approximately 0.679365, or 67.9365%).

214 ÷ 315 = 0.679365 (67.9365%)

Visual Representation

The diagram below illustrates 7/45 plus 11/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`214/315`
Mixed Number Form	`214/315`
Decimal Form	`0.679365`
Percentage	`67.9365%`

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Frequently Asked Questions

What is 7/45 plus 11/21 as a fraction?

7/45 + 11/21 in simplest fraction form is 214/315.

What is 7/45 plus 11/21 as a decimal?

7/45 + 11/21 converted to a decimal is 0.679365.

What is 7/45 plus 11/21 as a percentage?

7/45 + 11/21 expressed as a percentage is 67.9365%.

Does 7/45 plus 11/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.679365...) because the denominator contains prime factors other than 2 and 5.