What is 2/45 plus 4/21? (Answer: 74/315)

Exact Answer

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Problem: What is 2/45 plus 4/21?
Formula / Expression: 2/45 + 4/21
Final Answer: 74/315
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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 2/45 by 7, and multiply the numerator and denominator of 4/21 by 15 so both fractions share the common base 315.
Working: 2 × 7/45 × 7 = 14/315 and 4 × 15/21 × 15 = 60/315

Step 3: Add the Numerators
Now add the numerators (14 + 60 = 74) and keep the common denominator 315 unchanged.
Working: 14 + 60/315 = 74/315

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 74 and 315 is 1, confirming that 74/315 cannot be reduced further—it is already in its simplest irreducible form.
Working: 74/315

Step 5: Decimal & Percentage Representation
Dividing the numerator 74 by denominator 315 produces a repeating decimal (approximately 0.234921, or 23.4921%).
Working: 74 ÷ 315 = 0.234921 (23.4921%)

Key Values:
- Simplified Fraction: 74/315
- Mixed Number Form: 74/315
- Decimal Value: 0.234921
- Percentage: 23.4921%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-45-plus-4-21/
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2/45 + 4/21 = 74/315

Simplified Fraction

74/315

Mixed Number

Proper (74/315)

Decimal Value

0.234921

Percentage

23.4921%

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Step-by-Step Solution: 2/45 + 4/21

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 2/45 by 7, and multiply the numerator and denominator of 4/21 by 15 so both fractions share the common base 315.

2 × 7/45 × 7 = 14/315 and 4 × 15/21 × 15 = 60/315

Step 3

Add the Numerators

Now add the numerators (14 + 60 = 74) and keep the common denominator 315 unchanged.

14 + 60/315 = 74/315

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 74 and 315 is 1, confirming that 74/315 cannot be reduced further—it is already in its simplest irreducible form.

74/315

Step 5

Decimal & Percentage Representation

Dividing the numerator 74 by denominator 315 produces a repeating decimal (approximately 0.234921, or 23.4921%).

74 ÷ 315 = 0.234921 (23.4921%)

Visual Representation

The diagram below illustrates 2/45 plus 4/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`74/315`
Mixed Number Form	`74/315`
Decimal Form	`0.234921`
Percentage	`23.4921%`

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Frequently Asked Questions

What is 2/45 plus 4/21 as a fraction?

2/45 + 4/21 in simplest fraction form is 74/315.

What is 2/45 plus 4/21 as a decimal?

2/45 + 4/21 converted to a decimal is 0.234921.

What is 2/45 plus 4/21 as a percentage?

2/45 + 4/21 expressed as a percentage is 23.4921%.

Does 2/45 plus 4/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.234921...) because the denominator contains prime factors other than 2 and 5.