What is 9/36 plus 8/21? (Answer: 53/84)

Exact Answer

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Problem: What is 9/36 plus 8/21?
Formula / Expression: 9/36 + 8/21
Final Answer: 53/84
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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 9/36 by 7, and multiply the numerator and denominator of 8/21 by 12 so both fractions share the common base 252.
Working: 9 × 7/36 × 7 = 63/252 and 8 × 12/21 × 12 = 96/252

Step 3: Add the Numerators
Now add the numerators (63 + 96 = 159) and keep the common denominator 252 unchanged.
Working: 63 + 96/252 = 159/252

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 159 and 252, which is 3. Divide both the numerator and denominator by 3.
Working: 159 ÷ 3/252 ÷ 3 = 53/84

Step 5: Decimal & Percentage Representation
Dividing the numerator 53 by denominator 84 produces a repeating decimal (approximately 0.630952, or 63.0952%).
Working: 53 ÷ 84 = 0.630952 (63.0952%)

Key Values:
- Simplified Fraction: 53/84
- Mixed Number Form: 53/84
- Decimal Value: 0.630952
- Percentage: 63.0952%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-9-36-plus-8-21/
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9/36 + 8/21 = 53/84

Simplified Fraction

53/84

Mixed Number

Proper (53/84)

Decimal Value

0.630952

Percentage

63.0952%

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Step-by-Step Solution: 9/36 + 8/21

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 9/36 by 7, and multiply the numerator and denominator of 8/21 by 12 so both fractions share the common base 252.

9 × 7/36 × 7 = 63/252 and 8 × 12/21 × 12 = 96/252

Step 3

Add the Numerators

Now add the numerators (63 + 96 = 159) and keep the common denominator 252 unchanged.

63 + 96/252 = 159/252

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 159 and 252, which is 3. Divide both the numerator and denominator by 3.

159 ÷ 3/252 ÷ 3 = 53/84

Step 5

Decimal & Percentage Representation

Dividing the numerator 53 by denominator 84 produces a repeating decimal (approximately 0.630952, or 63.0952%).

53 ÷ 84 = 0.630952 (63.0952%)

Visual Representation

The diagram below illustrates 9/36 plus 8/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`53/84`
Mixed Number Form	`53/84`
Decimal Form	`0.630952`
Percentage	`63.0952%`

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Frequently Asked Questions

What is 9/36 plus 8/21 as a fraction?

9/36 + 8/21 in simplest fraction form is 53/84.

What is 9/36 plus 8/21 as a decimal?

9/36 + 8/21 converted to a decimal is 0.630952.

What is 9/36 plus 8/21 as a percentage?

9/36 + 8/21 expressed as a percentage is 63.0952%.

Does 9/36 plus 8/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.630952...) because the denominator contains prime factors other than 2 and 5.