What is 5/21 plus 11/45? (Answer: 152/315)

Exact Answer

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Problem: What is 5/21 plus 11/45?
Formula / Expression: 5/21 + 11/45
Final Answer: 152/315
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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 5/21 by 15, and multiply the numerator and denominator of 11/45 by 7 so both fractions share the common base 315.
Working: 5 × 15/21 × 15 = 75/315 and 11 × 7/45 × 7 = 77/315

Step 3: Add the Numerators
Now add the numerators (75 + 77 = 152) and keep the common denominator 315 unchanged.
Working: 75 + 77/315 = 152/315

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 152 and 315 is 1, confirming that 152/315 cannot be reduced further—it is already in its simplest irreducible form.
Working: 152/315

Step 5: Decimal & Percentage Representation
Dividing the numerator 152 by denominator 315 produces a repeating decimal (approximately 0.48254, or 48.254%).
Working: 152 ÷ 315 = 0.48254 (48.254%)

Key Values:
- Simplified Fraction: 152/315
- Mixed Number Form: 152/315
- Decimal Value: 0.48254
- Percentage: 48.254%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-5-21-plus-11-45/
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5/21 + 11/45 = 152/315

Simplified Fraction

152/315

Mixed Number

Proper (152/315)

Decimal Value

0.48254

Percentage

48.254%

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Step-by-Step Solution: 5/21 + 11/45

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 5/21 by 15, and multiply the numerator and denominator of 11/45 by 7 so both fractions share the common base 315.

5 × 15/21 × 15 = 75/315 and 11 × 7/45 × 7 = 77/315

Step 3

Add the Numerators

Now add the numerators (75 + 77 = 152) and keep the common denominator 315 unchanged.

75 + 77/315 = 152/315

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 152 and 315 is 1, confirming that 152/315 cannot be reduced further—it is already in its simplest irreducible form.

152/315

Step 5

Decimal & Percentage Representation

Dividing the numerator 152 by denominator 315 produces a repeating decimal (approximately 0.48254, or 48.254%).

152 ÷ 315 = 0.48254 (48.254%)

Visual Representation

The diagram below illustrates 5/21 plus 11/45 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`152/315`
Mixed Number Form	`152/315`
Decimal Form	`0.48254`
Percentage	`48.254%`

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Frequently Asked Questions

What is 5/21 plus 11/45 as a fraction?

5/21 + 11/45 in simplest fraction form is 152/315.

What is 5/21 plus 11/45 as a decimal?

5/21 + 11/45 converted to a decimal is 0.48254.

What is 5/21 plus 11/45 as a percentage?

5/21 + 11/45 expressed as a percentage is 48.254%.

Does 5/21 plus 11/45 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.48254...) because the denominator contains prime factors other than 2 and 5.