What is 10/36 plus 8/21? (Answer: 83/126)

Exact Answer

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Problem: What is 10/36 plus 8/21?
Formula / Expression: 10/36 + 8/21
Final Answer: 83/126
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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 10/36 by 7, and multiply the numerator and denominator of 8/21 by 12 so both fractions share the common base 252.
Working: 10 × 7/36 × 7 = 70/252 and 8 × 12/21 × 12 = 96/252

Step 3: Add the Numerators
Now add the numerators (70 + 96 = 166) and keep the common denominator 252 unchanged.
Working: 70 + 96/252 = 166/252

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 166 and 252, which is 2. Divide both the numerator and denominator by 2.
Working: 166 ÷ 2/252 ÷ 2 = 83/126

Step 5: Decimal & Percentage Representation
Dividing the numerator 83 by denominator 126 produces a repeating decimal (approximately 0.65873, or 65.873%).
Working: 83 ÷ 126 = 0.65873 (65.873%)

Key Values:
- Simplified Fraction: 83/126
- Mixed Number Form: 83/126
- Decimal Value: 0.65873
- Percentage: 65.873%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-10-36-plus-8-21/
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10/36 + 8/21 = 83/126

Simplified Fraction

83/126

Mixed Number

Proper (83/126)

Decimal Value

0.65873

Percentage

65.873%

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Step-by-Step Solution: 10/36 + 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 10/36 by 7, and multiply the numerator and denominator of 8/21 by 12 so both fractions share the common base 252.

10 × 7/36 × 7 = 70/252 and 8 × 12/21 × 12 = 96/252

Step 3

Add the Numerators

Now add the numerators (70 + 96 = 166) and keep the common denominator 252 unchanged.

70 + 96/252 = 166/252

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 166 and 252, which is 2. Divide both the numerator and denominator by 2.

166 ÷ 2/252 ÷ 2 = 83/126

Step 5

Decimal & Percentage Representation

Dividing the numerator 83 by denominator 126 produces a repeating decimal (approximately 0.65873, or 65.873%).

83 ÷ 126 = 0.65873 (65.873%)

Visual Representation

The diagram below illustrates 10/36 plus 8/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`83/126`
Mixed Number Form	`83/126`
Decimal Form	`0.65873`
Percentage	`65.873%`

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Frequently Asked Questions

What is 10/36 plus 8/21 as a fraction?

10/36 + 8/21 in simplest fraction form is 83/126.

What is 10/36 plus 8/21 as a decimal?

10/36 + 8/21 converted to a decimal is 0.65873.

What is 10/36 plus 8/21 as a percentage?

10/36 + 8/21 expressed as a percentage is 65.873%.

Does 10/36 plus 8/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.65873...) because the denominator contains prime factors other than 2 and 5.