What is 3/36 plus 11/21? (Answer: 17/28)

Exact Answer

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Problem: What is 3/36 plus 11/21?
Formula / Expression: 3/36 + 11/21
Final Answer: 17/28
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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 3/36 by 7, and multiply the numerator and denominator of 11/21 by 12 so both fractions share the common base 252.
Working: 3 × 7/36 × 7 = 21/252 and 11 × 12/21 × 12 = 132/252

Step 3: Add the Numerators
Now add the numerators (21 + 132 = 153) and keep the common denominator 252 unchanged.
Working: 21 + 132/252 = 153/252

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 153 and 252, which is 9. Divide both the numerator and denominator by 9.
Working: 153 ÷ 9/252 ÷ 9 = 17/28

Step 5: Decimal & Percentage Representation
Dividing the numerator 17 by denominator 28 produces a repeating decimal (approximately 0.607143, or 60.7143%).
Working: 17 ÷ 28 = 0.607143 (60.7143%)

Key Values:
- Simplified Fraction: 17/28
- Mixed Number Form: 17/28
- Decimal Value: 0.607143
- Percentage: 60.7143%

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Solved with FractionsCalc:
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3/36 + 11/21 = 17/28

Simplified Fraction

17/28

Mixed Number

Proper (17/28)

Decimal Value

0.607143

Percentage

60.7143%

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Step-by-Step Solution: 3/36 + 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 3/36 by 7, and multiply the numerator and denominator of 11/21 by 12 so both fractions share the common base 252.

3 × 7/36 × 7 = 21/252 and 11 × 12/21 × 12 = 132/252

Step 3

Add the Numerators

Now add the numerators (21 + 132 = 153) and keep the common denominator 252 unchanged.

21 + 132/252 = 153/252

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 153 and 252, which is 9. Divide both the numerator and denominator by 9.

153 ÷ 9/252 ÷ 9 = 17/28

Step 5

Decimal & Percentage Representation

Dividing the numerator 17 by denominator 28 produces a repeating decimal (approximately 0.607143, or 60.7143%).

17 ÷ 28 = 0.607143 (60.7143%)

Visual Representation

The diagram below illustrates 3/36 plus 11/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`17/28`
Mixed Number Form	`17/28`
Decimal Form	`0.607143`
Percentage	`60.7143%`

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Frequently Asked Questions

What is 3/36 plus 11/21 as a fraction?

3/36 + 11/21 in simplest fraction form is 17/28.

What is 3/36 plus 11/21 as a decimal?

3/36 + 11/21 converted to a decimal is 0.607143.

What is 3/36 plus 11/21 as a percentage?

3/36 + 11/21 expressed as a percentage is 60.7143%.

Does 3/36 plus 11/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.607143...) because the denominator contains prime factors other than 2 and 5.