What is 15/36 plus 9/21? (Answer: 71/84)

Exact Answer

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Problem: What is 15/36 plus 9/21?
Formula / Expression: 15/36 + 9/21
Final Answer: 71/84
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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 9/21 by 12 so both fractions share the common base 252.
Working: 15 × 7/36 × 7 = 105/252 and 9 × 12/21 × 12 = 108/252

Step 3: Add the Numerators
Now add the numerators (105 + 108 = 213) and keep the common denominator 252 unchanged.
Working: 105 + 108/252 = 213/252

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 213 and 252, which is 3. Divide both the numerator and denominator by 3.
Working: 213 ÷ 3/252 ÷ 3 = 71/84

Step 5: Decimal & Percentage Representation
Dividing the numerator 71 by denominator 84 produces a repeating decimal (approximately 0.845238, or 84.5238%).
Working: 71 ÷ 84 = 0.845238 (84.5238%)

Key Values:
- Simplified Fraction: 71/84
- Mixed Number Form: 71/84
- Decimal Value: 0.845238
- Percentage: 84.5238%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-15-36-plus-9-21/
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15/36 + 9/21 = 71/84

Simplified Fraction

71/84

Mixed Number

Proper (71/84)

Decimal Value

0.845238

Percentage

84.5238%

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Step-by-Step Solution: 15/36 + 9/21

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 9/21 by 12 so both fractions share the common base 252.

15 × 7/36 × 7 = 105/252 and 9 × 12/21 × 12 = 108/252

Step 3

Add the Numerators

Now add the numerators (105 + 108 = 213) and keep the common denominator 252 unchanged.

105 + 108/252 = 213/252

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 213 and 252, which is 3. Divide both the numerator and denominator by 3.

213 ÷ 3/252 ÷ 3 = 71/84

Step 5

Decimal & Percentage Representation

Dividing the numerator 71 by denominator 84 produces a repeating decimal (approximately 0.845238, or 84.5238%).

71 ÷ 84 = 0.845238 (84.5238%)

Visual Representation

The diagram below illustrates 15/36 plus 9/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`71/84`
Mixed Number Form	`71/84`
Decimal Form	`0.845238`
Percentage	`84.5238%`

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Frequently Asked Questions

What is 15/36 plus 9/21 as a fraction?

15/36 + 9/21 in simplest fraction form is 71/84.

What is 15/36 plus 9/21 as a decimal?

15/36 + 9/21 converted to a decimal is 0.845238.

What is 15/36 plus 9/21 as a percentage?

15/36 + 9/21 expressed as a percentage is 84.5238%.

Does 15/36 plus 9/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.845238...) because the denominator contains prime factors other than 2 and 5.