What is 21/36 plus 9/13? (Answer: 199/156)

Exact Answer

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Problem: What is 21/36 plus 9/13?
Formula / Expression: 21/36 + 9/13
Final Answer: 1 43/156 (199/156)
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 36 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 36 × 13 = 468.
Working: LCD(36, 13) = 468

Step 2: Convert to Equivalent Fractions with Common Denominator 468
Multiply the numerator and denominator of 21/36 by 13, and multiply the numerator and denominator of 9/13 by 36 so both fractions share the common base 468.
Working: 21 × 13/36 × 13 = 273/468 and 9 × 36/13 × 36 = 324/468

Step 3: Add the Numerators
Now add the numerators (273 + 324 = 597) and keep the common denominator 468 unchanged.
Working: 273 + 324/468 = 597/468

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 597 and 468, which is 3. Divide both the numerator and denominator by 3.
Working: 597 ÷ 3/468 ÷ 3 = 199/156

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (199) is greater than the denominator (156), divide 199 by 156: it goes in 1 whole time(s) with a remainder of 43, giving the mixed number 1 43/156.
Working: 199/156 = 1 43/156

Step 6: Decimal & Percentage Representation
Dividing the numerator 199 by denominator 156 produces a repeating decimal (approximately 1.275641, or 127.5641%).
Working: 199 ÷ 156 = 1.275641 (127.5641%)

Key Values:
- Simplified Fraction: 199/156
- Mixed Number Form: 1 43/156
- Decimal Value: 1.275641
- Percentage: 127.5641%

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21/36 + 9/13 = 199/156

Simplified Fraction

199/156

Mixed Number

1 43/156

Decimal Value

1.275641

Percentage

127.5641%

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Step-by-Step Solution: 21/36 + 9/13

Step 1

Find the Least Common Denominator (LCD)

The denominators 36 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 36 × 13 = 468.

LCD(36, 13) = 468

Step 2

Convert to Equivalent Fractions with Common Denominator 468

Multiply the numerator and denominator of 21/36 by 13, and multiply the numerator and denominator of 9/13 by 36 so both fractions share the common base 468.

21 × 13/36 × 13 = 273/468 and 9 × 36/13 × 36 = 324/468

Step 3

Add the Numerators

Now add the numerators (273 + 324 = 597) and keep the common denominator 468 unchanged.

273 + 324/468 = 597/468

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 597 and 468, which is 3. Divide both the numerator and denominator by 3.

597 ÷ 3/468 ÷ 3 = 199/156

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (199) is greater than the denominator (156), divide 199 by 156: it goes in 1 whole time(s) with a remainder of 43, giving the mixed number 1 43/156.

199/156 = 143/156

Step 6

Decimal & Percentage Representation

Dividing the numerator 199 by denominator 156 produces a repeating decimal (approximately 1.275641, or 127.5641%).

199 ÷ 156 = 1.275641 (127.5641%)

Visual Representation

The diagram below illustrates 21/36 plus 9/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`199/156`
Mixed Number Form	`1 43/156`
Decimal Form	`1.275641`
Percentage	`127.5641%`

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Frequently Asked Questions

What is 21/36 plus 9/13 as a fraction?

21/36 + 9/13 in simplest fraction form is 199/156 (or 1 43/156 as a mixed number).

What is 21/36 plus 9/13 as a decimal?

21/36 + 9/13 converted to a decimal is 1.275641.

What is 21/36 plus 9/13 as a percentage?

21/36 + 9/13 expressed as a percentage is 127.5641%.

How do you write 21/36 plus 9/13 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 199/156 can be written as the mixed number 1 43/156.

Does 21/36 plus 9/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.275641...) because the denominator contains prime factors other than 2 and 5.