What is 9/36 plus 11/21? (Answer: 65/84)

Exact Answer

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Problem: What is 9/36 plus 11/21?
Formula / Expression: 9/36 + 11/21
Final Answer: 65/84
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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 9/36 by 7, and multiply the numerator and denominator of 11/21 by 12 so both fractions share the common base 252.
Working: 9 × 7/36 × 7 = 63/252 and 11 × 12/21 × 12 = 132/252

Step 3: Add the Numerators
Now add the numerators (63 + 132 = 195) and keep the common denominator 252 unchanged.
Working: 63 + 132/252 = 195/252

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 195 and 252, which is 3. Divide both the numerator and denominator by 3.
Working: 195 ÷ 3/252 ÷ 3 = 65/84

Step 5: Decimal & Percentage Representation
Dividing the numerator 65 by denominator 84 produces a repeating decimal (approximately 0.77381, or 77.381%).
Working: 65 ÷ 84 = 0.77381 (77.381%)

Key Values:
- Simplified Fraction: 65/84
- Mixed Number Form: 65/84
- Decimal Value: 0.77381
- Percentage: 77.381%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-9-36-plus-11-21/
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9/36 + 11/21 = 65/84

Simplified Fraction

65/84

Mixed Number

Proper (65/84)

Decimal Value

0.77381

Percentage

77.381%

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Step-by-Step Solution: 9/36 + 11/21

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 9/36 by 7, and multiply the numerator and denominator of 11/21 by 12 so both fractions share the common base 252.

9 × 7/36 × 7 = 63/252 and 11 × 12/21 × 12 = 132/252

Step 3

Add the Numerators

Now add the numerators (63 + 132 = 195) and keep the common denominator 252 unchanged.

63 + 132/252 = 195/252

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 195 and 252, which is 3. Divide both the numerator and denominator by 3.

195 ÷ 3/252 ÷ 3 = 65/84

Step 5

Decimal & Percentage Representation

Dividing the numerator 65 by denominator 84 produces a repeating decimal (approximately 0.77381, or 77.381%).

65 ÷ 84 = 0.77381 (77.381%)

Visual Representation

The diagram below illustrates 9/36 plus 11/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`65/84`
Mixed Number Form	`65/84`
Decimal Form	`0.77381`
Percentage	`77.381%`

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Frequently Asked Questions

What is 9/36 plus 11/21 as a fraction?

9/36 + 11/21 in simplest fraction form is 65/84.

What is 9/36 plus 11/21 as a decimal?

9/36 + 11/21 converted to a decimal is 0.77381.

What is 9/36 plus 11/21 as a percentage?

9/36 + 11/21 expressed as a percentage is 77.381%.

Does 9/36 plus 11/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.77381...) because the denominator contains prime factors other than 2 and 5.