What is 5/36 plus 9/21? (Answer: 143/252)

Exact Answer

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Problem: What is 5/36 plus 9/21?
Formula / Expression: 5/36 + 9/21
Final Answer: 143/252
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 36 and 21 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 252 (which is smaller than their product 36 × 21 = 756, keeping the calculation simpler).
Working: LCD(36, 21) = 252

Step 2: Convert to Equivalent Fractions with Common Denominator 252
Multiply the numerator and denominator of 5/36 by 7, and multiply the numerator and denominator of 9/21 by 12 so both fractions share the common base 252.
Working: 5 × 7/36 × 7 = 35/252 and 9 × 12/21 × 12 = 108/252

Step 3: Add the Numerators
Now add the numerators (35 + 108 = 143) and keep the common denominator 252 unchanged.
Working: 35 + 108/252 = 143/252

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 143 and 252 is 1, confirming that 143/252 cannot be reduced further—it is already in its simplest irreducible form.
Working: 143/252

Step 5: Decimal & Percentage Representation
Dividing the numerator 143 by denominator 252 produces a repeating decimal (approximately 0.56746, or 56.746%).
Working: 143 ÷ 252 = 0.56746 (56.746%)

Key Values:
- Simplified Fraction: 143/252
- Mixed Number Form: 143/252
- Decimal Value: 0.56746
- Percentage: 56.746%

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Solved with FractionsCalc:
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5/36 + 9/21 = 143/252

Simplified Fraction

143/252

Mixed Number

Proper (143/252)

Decimal Value

0.56746

Percentage

56.746%

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Step-by-Step Solution: 5/36 + 9/21

Step 1

Find the Least Common Denominator (LCD)

The denominators 36 and 21 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 252 (which is smaller than their product 36 × 21 = 756, keeping the calculation simpler).

LCD(36, 21) = 252

Step 2

Convert to Equivalent Fractions with Common Denominator 252

Multiply the numerator and denominator of 5/36 by 7, and multiply the numerator and denominator of 9/21 by 12 so both fractions share the common base 252.

5 × 7/36 × 7 = 35/252 and 9 × 12/21 × 12 = 108/252

Step 3

Add the Numerators

Now add the numerators (35 + 108 = 143) and keep the common denominator 252 unchanged.

35 + 108/252 = 143/252

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 143 and 252 is 1, confirming that 143/252 cannot be reduced further—it is already in its simplest irreducible form.

143/252

Step 5

Decimal & Percentage Representation

Dividing the numerator 143 by denominator 252 produces a repeating decimal (approximately 0.56746, or 56.746%).

143 ÷ 252 = 0.56746 (56.746%)

Visual Representation

The diagram below illustrates 5/36 plus 9/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`143/252`
Mixed Number Form	`143/252`
Decimal Form	`0.56746`
Percentage	`56.746%`

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Frequently Asked Questions

What is 5/36 plus 9/21 as a fraction?

5/36 + 9/21 in simplest fraction form is 143/252.

What is 5/36 plus 9/21 as a decimal?

5/36 + 9/21 converted to a decimal is 0.56746.

What is 5/36 plus 9/21 as a percentage?

5/36 + 9/21 expressed as a percentage is 56.746%.

Does 5/36 plus 9/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.56746...) because the denominator contains prime factors other than 2 and 5.