What is 3/21 plus 7/45? (Answer: 94/315)

Exact Answer

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Problem: What is 3/21 plus 7/45?
Formula / Expression: 3/21 + 7/45
Final Answer: 94/315
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 21 and 45 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 315 (which is smaller than their product 21 × 45 = 945, keeping the calculation simpler).
Working: LCD(21, 45) = 315

Step 2: Convert to Equivalent Fractions with Common Denominator 315
Multiply the numerator and denominator of 3/21 by 15, and multiply the numerator and denominator of 7/45 by 7 so both fractions share the common base 315.
Working: 3 × 15/21 × 15 = 45/315 and 7 × 7/45 × 7 = 49/315

Step 3: Add the Numerators
Now add the numerators (45 + 49 = 94) and keep the common denominator 315 unchanged.
Working: 45 + 49/315 = 94/315

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 94 and 315 is 1, confirming that 94/315 cannot be reduced further—it is already in its simplest irreducible form.
Working: 94/315

Step 5: Decimal & Percentage Representation
Dividing the numerator 94 by denominator 315 produces a repeating decimal (approximately 0.298413, or 29.8413%).
Working: 94 ÷ 315 = 0.298413 (29.8413%)

Key Values:
- Simplified Fraction: 94/315
- Mixed Number Form: 94/315
- Decimal Value: 0.298413
- Percentage: 29.8413%

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Solved with FractionsCalc:
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3/21 + 7/45 = 94/315

Simplified Fraction

94/315

Mixed Number

Proper (94/315)

Decimal Value

0.298413

Percentage

29.8413%

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Step-by-Step Solution: 3/21 + 7/45

Step 1

Find the Least Common Denominator (LCD)

The denominators 21 and 45 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 315 (which is smaller than their product 21 × 45 = 945, keeping the calculation simpler).

LCD(21, 45) = 315

Step 2

Convert to Equivalent Fractions with Common Denominator 315

Multiply the numerator and denominator of 3/21 by 15, and multiply the numerator and denominator of 7/45 by 7 so both fractions share the common base 315.

3 × 15/21 × 15 = 45/315 and 7 × 7/45 × 7 = 49/315

Step 3

Add the Numerators

Now add the numerators (45 + 49 = 94) and keep the common denominator 315 unchanged.

45 + 49/315 = 94/315

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 94 and 315 is 1, confirming that 94/315 cannot be reduced further—it is already in its simplest irreducible form.

94/315

Step 5

Decimal & Percentage Representation

Dividing the numerator 94 by denominator 315 produces a repeating decimal (approximately 0.298413, or 29.8413%).

94 ÷ 315 = 0.298413 (29.8413%)

Visual Representation

The diagram below illustrates 3/21 plus 7/45 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`94/315`
Mixed Number Form	`94/315`
Decimal Form	`0.298413`
Percentage	`29.8413%`

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Frequently Asked Questions

What is 3/21 plus 7/45 as a fraction?

3/21 + 7/45 in simplest fraction form is 94/315.

What is 3/21 plus 7/45 as a decimal?

3/21 + 7/45 converted to a decimal is 0.298413.

What is 3/21 plus 7/45 as a percentage?

3/21 + 7/45 expressed as a percentage is 29.8413%.

Does 3/21 plus 7/45 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.298413...) because the denominator contains prime factors other than 2 and 5.