What is 15/36 plus 12/21? (Answer: 83/84)

Exact Answer

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Problem: What is 15/36 plus 12/21?
Formula / Expression: 15/36 + 12/21
Final Answer: 83/84
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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 15/36 by 7, and multiply the numerator and denominator of 12/21 by 12 so both fractions share the common base 252.
Working: 15 × 7/36 × 7 = 105/252 and 12 × 12/21 × 12 = 144/252

Step 3: Add the Numerators
Now add the numerators (105 + 144 = 249) and keep the common denominator 252 unchanged.
Working: 105 + 144/252 = 249/252

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 249 and 252, which is 3. Divide both the numerator and denominator by 3.
Working: 249 ÷ 3/252 ÷ 3 = 83/84

Step 5: Decimal & Percentage Representation
Dividing the numerator 83 by denominator 84 produces a repeating decimal (approximately 0.988095, or 98.8095%).
Working: 83 ÷ 84 = 0.988095 (98.8095%)

Key Values:
- Simplified Fraction: 83/84
- Mixed Number Form: 83/84
- Decimal Value: 0.988095
- Percentage: 98.8095%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-15-36-plus-12-21/
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15/36 + 12/21 = 83/84

Simplified Fraction

83/84

Mixed Number

Proper (83/84)

Decimal Value

0.988095

Percentage

98.8095%

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Step-by-Step Solution: 15/36 + 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 15/36 by 7, and multiply the numerator and denominator of 12/21 by 12 so both fractions share the common base 252.

15 × 7/36 × 7 = 105/252 and 12 × 12/21 × 12 = 144/252

Step 3

Add the Numerators

Now add the numerators (105 + 144 = 249) and keep the common denominator 252 unchanged.

105 + 144/252 = 249/252

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 249 and 252, which is 3. Divide both the numerator and denominator by 3.

249 ÷ 3/252 ÷ 3 = 83/84

Step 5

Decimal & Percentage Representation

Dividing the numerator 83 by denominator 84 produces a repeating decimal (approximately 0.988095, or 98.8095%).

83 ÷ 84 = 0.988095 (98.8095%)

Visual Representation

The diagram below illustrates 15/36 plus 12/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`83/84`
Mixed Number Form	`83/84`
Decimal Form	`0.988095`
Percentage	`98.8095%`

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Frequently Asked Questions

What is 15/36 plus 12/21 as a fraction?

15/36 + 12/21 in simplest fraction form is 83/84.

What is 15/36 plus 12/21 as a decimal?

15/36 + 12/21 converted to a decimal is 0.988095.

What is 15/36 plus 12/21 as a percentage?

15/36 + 12/21 expressed as a percentage is 98.8095%.

Does 15/36 plus 12/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.988095...) because the denominator contains prime factors other than 2 and 5.