What is 8/45 plus 6/21? (Answer: 146/315)

Exact Answer

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Problem: What is 8/45 plus 6/21?
Formula / Expression: 8/45 + 6/21
Final Answer: 146/315
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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 8/45 by 7, and multiply the numerator and denominator of 6/21 by 15 so both fractions share the common base 315.
Working: 8 × 7/45 × 7 = 56/315 and 6 × 15/21 × 15 = 90/315

Step 3: Add the Numerators
Now add the numerators (56 + 90 = 146) and keep the common denominator 315 unchanged.
Working: 56 + 90/315 = 146/315

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 146 and 315 is 1, confirming that 146/315 cannot be reduced further—it is already in its simplest irreducible form.
Working: 146/315

Step 5: Decimal & Percentage Representation
Dividing the numerator 146 by denominator 315 produces a repeating decimal (approximately 0.463492, or 46.3492%).
Working: 146 ÷ 315 = 0.463492 (46.3492%)

Key Values:
- Simplified Fraction: 146/315
- Mixed Number Form: 146/315
- Decimal Value: 0.463492
- Percentage: 46.3492%

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Solved with FractionsCalc:
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8/45 + 6/21 = 146/315

Simplified Fraction

146/315

Mixed Number

Proper (146/315)

Decimal Value

0.463492

Percentage

46.3492%

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Step-by-Step Solution: 8/45 + 6/21

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 8/45 by 7, and multiply the numerator and denominator of 6/21 by 15 so both fractions share the common base 315.

8 × 7/45 × 7 = 56/315 and 6 × 15/21 × 15 = 90/315

Step 3

Add the Numerators

Now add the numerators (56 + 90 = 146) and keep the common denominator 315 unchanged.

56 + 90/315 = 146/315

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 146 and 315 is 1, confirming that 146/315 cannot be reduced further—it is already in its simplest irreducible form.

146/315

Step 5

Decimal & Percentage Representation

Dividing the numerator 146 by denominator 315 produces a repeating decimal (approximately 0.463492, or 46.3492%).

146 ÷ 315 = 0.463492 (46.3492%)

Visual Representation

The diagram below illustrates 8/45 plus 6/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`146/315`
Mixed Number Form	`146/315`
Decimal Form	`0.463492`
Percentage	`46.3492%`

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Frequently Asked Questions

What is 8/45 plus 6/21 as a fraction?

8/45 + 6/21 in simplest fraction form is 146/315.

What is 8/45 plus 6/21 as a decimal?

8/45 + 6/21 converted to a decimal is 0.463492.

What is 8/45 plus 6/21 as a percentage?

8/45 + 6/21 expressed as a percentage is 46.3492%.

Does 8/45 plus 6/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.463492...) because the denominator contains prime factors other than 2 and 5.