What is 5/21 plus 9/36? (Answer: 41/84)

Exact Answer

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Problem: What is 5/21 plus 9/36?
Formula / Expression: 5/21 + 9/36
Final Answer: 41/84
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 21 and 36 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 252 (which is smaller than their product 21 × 36 = 756, keeping the calculation simpler).
Working: LCD(21, 36) = 252

Step 2: Convert to Equivalent Fractions with Common Denominator 252
Multiply the numerator and denominator of 5/21 by 12, and multiply the numerator and denominator of 9/36 by 7 so both fractions share the common base 252.
Working: 5 × 12/21 × 12 = 60/252 and 9 × 7/36 × 7 = 63/252

Step 3: Add the Numerators
Now add the numerators (60 + 63 = 123) and keep the common denominator 252 unchanged.
Working: 60 + 63/252 = 123/252

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 123 and 252, which is 3. Divide both the numerator and denominator by 3.
Working: 123 ÷ 3/252 ÷ 3 = 41/84

Step 5: Decimal & Percentage Representation
Dividing the numerator 41 by denominator 84 produces a repeating decimal (approximately 0.488095, or 48.8095%).
Working: 41 ÷ 84 = 0.488095 (48.8095%)

Key Values:
- Simplified Fraction: 41/84
- Mixed Number Form: 41/84
- Decimal Value: 0.488095
- Percentage: 48.8095%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-5-21-plus-9-36/
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5/21 + 9/36 = 41/84

Simplified Fraction

41/84

Mixed Number

Proper (41/84)

Decimal Value

0.488095

Percentage

48.8095%

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Step-by-Step Solution: 5/21 + 9/36

Step 1

Find the Least Common Denominator (LCD)

The denominators 21 and 36 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 252 (which is smaller than their product 21 × 36 = 756, keeping the calculation simpler).

LCD(21, 36) = 252

Step 2

Convert to Equivalent Fractions with Common Denominator 252

Multiply the numerator and denominator of 5/21 by 12, and multiply the numerator and denominator of 9/36 by 7 so both fractions share the common base 252.

5 × 12/21 × 12 = 60/252 and 9 × 7/36 × 7 = 63/252

Step 3

Add the Numerators

Now add the numerators (60 + 63 = 123) and keep the common denominator 252 unchanged.

60 + 63/252 = 123/252

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 123 and 252, which is 3. Divide both the numerator and denominator by 3.

123 ÷ 3/252 ÷ 3 = 41/84

Step 5

Decimal & Percentage Representation

Dividing the numerator 41 by denominator 84 produces a repeating decimal (approximately 0.488095, or 48.8095%).

41 ÷ 84 = 0.488095 (48.8095%)

Visual Representation

The diagram below illustrates 5/21 plus 9/36 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`41/84`
Mixed Number Form	`41/84`
Decimal Form	`0.488095`
Percentage	`48.8095%`

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Frequently Asked Questions

What is 5/21 plus 9/36 as a fraction?

5/21 + 9/36 in simplest fraction form is 41/84.

What is 5/21 plus 9/36 as a decimal?

5/21 + 9/36 converted to a decimal is 0.488095.

What is 5/21 plus 9/36 as a percentage?

5/21 + 9/36 expressed as a percentage is 48.8095%.

Does 5/21 plus 9/36 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.488095...) because the denominator contains prime factors other than 2 and 5.