What is 3/36 plus 3/21? (Answer: 19/84)

Exact Answer

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Problem: What is 3/36 plus 3/21?
Formula / Expression: 3/36 + 3/21
Final Answer: 19/84
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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 3/36 by 7, and multiply the numerator and denominator of 3/21 by 12 so both fractions share the common base 252.
Working: 3 × 7/36 × 7 = 21/252 and 3 × 12/21 × 12 = 36/252

Step 3: Add the Numerators
Now add the numerators (21 + 36 = 57) and keep the common denominator 252 unchanged.
Working: 21 + 36/252 = 57/252

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 57 and 252, which is 3. Divide both the numerator and denominator by 3.
Working: 57 ÷ 3/252 ÷ 3 = 19/84

Step 5: Decimal & Percentage Representation
Dividing the numerator 19 by denominator 84 produces a repeating decimal (approximately 0.22619, or 22.619%).
Working: 19 ÷ 84 = 0.22619 (22.619%)

Key Values:
- Simplified Fraction: 19/84
- Mixed Number Form: 19/84
- Decimal Value: 0.22619
- Percentage: 22.619%

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Solved with FractionsCalc:
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3/36 + 3/21 = 19/84

Simplified Fraction

19/84

Mixed Number

Proper (19/84)

Decimal Value

0.22619

Percentage

22.619%

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Step-by-Step Solution: 3/36 + 3/21

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 3/21 by 12 so both fractions share the common base 252.

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

Step 3

Add the Numerators

Now add the numerators (21 + 36 = 57) and keep the common denominator 252 unchanged.

21 + 36/252 = 57/252

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 57 and 252, which is 3. Divide both the numerator and denominator by 3.

57 ÷ 3/252 ÷ 3 = 19/84

Step 5

Decimal & Percentage Representation

Dividing the numerator 19 by denominator 84 produces a repeating decimal (approximately 0.22619, or 22.619%).

19 ÷ 84 = 0.22619 (22.619%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`19/84`
Mixed Number Form	`19/84`
Decimal Form	`0.22619`
Percentage	`22.619%`

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Frequently Asked Questions

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

3/36 + 3/21 in simplest fraction form is 19/84.

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

3/36 + 3/21 converted to a decimal is 0.22619.

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

3/36 + 3/21 expressed as a percentage is 22.619%.

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

It results in a repeating decimal (approximately 0.22619...) because the denominator contains prime factors other than 2 and 5.