What is 20/36 plus 12/21? (Answer: 71/63)

Exact Answer

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Problem: What is 20/36 plus 12/21?
Formula / Expression: 20/36 + 12/21
Final Answer: 1 8/63 (71/63)
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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 20/36 by 7, and multiply the numerator and denominator of 12/21 by 12 so both fractions share the common base 252.
Working: 20 × 7/36 × 7 = 140/252 and 12 × 12/21 × 12 = 144/252

Step 3: Add the Numerators
Now add the numerators (140 + 144 = 284) and keep the common denominator 252 unchanged.
Working: 140 + 144/252 = 284/252

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 284 and 252, which is 4. Divide both the numerator and denominator by 4.
Working: 284 ÷ 4/252 ÷ 4 = 71/63

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (71) is greater than the denominator (63), divide 71 by 63: it goes in 1 whole time(s) with a remainder of 8, giving the mixed number 1 8/63.
Working: 71/63 = 1 8/63

Step 6: Decimal & Percentage Representation
Dividing the numerator 71 by denominator 63 produces a repeating decimal (approximately 1.126984, or 112.6984%).
Working: 71 ÷ 63 = 1.126984 (112.6984%)

Key Values:
- Simplified Fraction: 71/63
- Mixed Number Form: 1 8/63
- Decimal Value: 1.126984
- Percentage: 112.6984%

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Solved with FractionsCalc:
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20/36 + 12/21 = 71/63

Simplified Fraction

71/63

Mixed Number

1 8/63

Decimal Value

1.126984

Percentage

112.6984%

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Step-by-Step Solution: 20/36 + 12/21

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 20/36 by 7, and multiply the numerator and denominator of 12/21 by 12 so both fractions share the common base 252.

20 × 7/36 × 7 = 140/252 and 12 × 12/21 × 12 = 144/252

Step 3

Add the Numerators

Now add the numerators (140 + 144 = 284) and keep the common denominator 252 unchanged.

140 + 144/252 = 284/252

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 284 and 252, which is 4. Divide both the numerator and denominator by 4.

284 ÷ 4/252 ÷ 4 = 71/63

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (71) is greater than the denominator (63), divide 71 by 63: it goes in 1 whole time(s) with a remainder of 8, giving the mixed number 1 8/63.

71/63 = 18/63

Step 6

Decimal & Percentage Representation

Dividing the numerator 71 by denominator 63 produces a repeating decimal (approximately 1.126984, or 112.6984%).

71 ÷ 63 = 1.126984 (112.6984%)

Visual Representation

The diagram below illustrates 20/36 plus 12/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`71/63`
Mixed Number Form	`1 8/63`
Decimal Form	`1.126984`
Percentage	`112.6984%`

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Frequently Asked Questions

What is 20/36 plus 12/21 as a fraction?

20/36 + 12/21 in simplest fraction form is 71/63 (or 1 8/63 as a mixed number).

What is 20/36 plus 12/21 as a decimal?

20/36 + 12/21 converted to a decimal is 1.126984.

What is 20/36 plus 12/21 as a percentage?

20/36 + 12/21 expressed as a percentage is 112.6984%.

How do you write 20/36 plus 12/21 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 71/63 can be written as the mixed number 1 8/63.

Does 20/36 plus 12/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.126984...) because the denominator contains prime factors other than 2 and 5.