What is 9/36 plus 10/21? (Answer: 61/84)

Exact Answer

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Problem: What is 9/36 plus 10/21?
Formula / Expression: 9/36 + 10/21
Final Answer: 61/84
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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 10/21 by 12 so both fractions share the common base 252.
Working: 9 × 7/36 × 7 = 63/252 and 10 × 12/21 × 12 = 120/252

Step 3: Add the Numerators
Now add the numerators (63 + 120 = 183) and keep the common denominator 252 unchanged.
Working: 63 + 120/252 = 183/252

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 183 and 252, which is 3. Divide both the numerator and denominator by 3.
Working: 183 ÷ 3/252 ÷ 3 = 61/84

Step 5: Decimal & Percentage Representation
Dividing the numerator 61 by denominator 84 produces a repeating decimal (approximately 0.72619, or 72.619%).
Working: 61 ÷ 84 = 0.72619 (72.619%)

Key Values:
- Simplified Fraction: 61/84
- Mixed Number Form: 61/84
- Decimal Value: 0.72619
- Percentage: 72.619%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-9-36-plus-10-21/
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9/36 + 10/21 = 61/84

Simplified Fraction

61/84

Mixed Number

Proper (61/84)

Decimal Value

0.72619

Percentage

72.619%

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Step-by-Step Solution: 9/36 + 10/21

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 10/21 by 12 so both fractions share the common base 252.

9 × 7/36 × 7 = 63/252 and 10 × 12/21 × 12 = 120/252

Step 3

Add the Numerators

Now add the numerators (63 + 120 = 183) and keep the common denominator 252 unchanged.

63 + 120/252 = 183/252

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 183 and 252, which is 3. Divide both the numerator and denominator by 3.

183 ÷ 3/252 ÷ 3 = 61/84

Step 5

Decimal & Percentage Representation

Dividing the numerator 61 by denominator 84 produces a repeating decimal (approximately 0.72619, or 72.619%).

61 ÷ 84 = 0.72619 (72.619%)

Visual Representation

The diagram below illustrates 9/36 plus 10/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`61/84`
Mixed Number Form	`61/84`
Decimal Form	`0.72619`
Percentage	`72.619%`

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Frequently Asked Questions

What is 9/36 plus 10/21 as a fraction?

9/36 + 10/21 in simplest fraction form is 61/84.

What is 9/36 plus 10/21 as a decimal?

9/36 + 10/21 converted to a decimal is 0.72619.

What is 9/36 plus 10/21 as a percentage?

9/36 + 10/21 expressed as a percentage is 72.619%.

Does 9/36 plus 10/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.72619...) because the denominator contains prime factors other than 2 and 5.