What is 11/36 plus 7/21? (Answer: 23/36)

Exact Answer

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Problem: What is 11/36 plus 7/21?
Formula / Expression: 11/36 + 7/21
Final Answer: 23/36
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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 11/36 by 7, and multiply the numerator and denominator of 7/21 by 12 so both fractions share the common base 252.
Working: 11 × 7/36 × 7 = 77/252 and 7 × 12/21 × 12 = 84/252

Step 3: Add the Numerators
Now add the numerators (77 + 84 = 161) and keep the common denominator 252 unchanged.
Working: 77 + 84/252 = 161/252

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 161 and 252, which is 7. Divide both the numerator and denominator by 7.
Working: 161 ÷ 7/252 ÷ 7 = 23/36

Step 5: Decimal & Percentage Representation
Dividing the numerator 23 by denominator 36 produces a repeating decimal (approximately 0.638889, or 63.8889%).
Working: 23 ÷ 36 = 0.638889 (63.8889%)

Key Values:
- Simplified Fraction: 23/36
- Mixed Number Form: 23/36
- Decimal Value: 0.638889
- Percentage: 63.8889%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-11-36-plus-7-21/
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11/36 + 7/21 = 23/36

Simplified Fraction

23/36

Mixed Number

Proper (23/36)

Decimal Value

0.638889

Percentage

63.8889%

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Step-by-Step Solution: 11/36 + 7/21

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

11 × 7/36 × 7 = 77/252 and 7 × 12/21 × 12 = 84/252

Step 3

Add the Numerators

Now add the numerators (77 + 84 = 161) and keep the common denominator 252 unchanged.

77 + 84/252 = 161/252

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 161 and 252, which is 7. Divide both the numerator and denominator by 7.

161 ÷ 7/252 ÷ 7 = 23/36

Step 5

Decimal & Percentage Representation

Dividing the numerator 23 by denominator 36 produces a repeating decimal (approximately 0.638889, or 63.8889%).

23 ÷ 36 = 0.638889 (63.8889%)

Visual Representation

The diagram below illustrates 11/36 plus 7/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`23/36`
Mixed Number Form	`23/36`
Decimal Form	`0.638889`
Percentage	`63.8889%`

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Frequently Asked Questions

What is 11/36 plus 7/21 as a fraction?

11/36 + 7/21 in simplest fraction form is 23/36.

What is 11/36 plus 7/21 as a decimal?

11/36 + 7/21 converted to a decimal is 0.638889.

What is 11/36 plus 7/21 as a percentage?

11/36 + 7/21 expressed as a percentage is 63.8889%.

Does 11/36 plus 7/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.638889...) because the denominator contains prime factors other than 2 and 5.