What is 10/36 plus 9/21? (Answer: 89/126)

Exact Answer

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Problem: What is 10/36 plus 9/21?
Formula / Expression: 10/36 + 9/21
Final Answer: 89/126
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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 9/21 by 12 so both fractions share the common base 252.
Working: 10 × 7/36 × 7 = 70/252 and 9 × 12/21 × 12 = 108/252

Step 3: Add the Numerators
Now add the numerators (70 + 108 = 178) and keep the common denominator 252 unchanged.
Working: 70 + 108/252 = 178/252

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 178 and 252, which is 2. Divide both the numerator and denominator by 2.
Working: 178 ÷ 2/252 ÷ 2 = 89/126

Step 5: Decimal & Percentage Representation
Dividing the numerator 89 by denominator 126 produces a repeating decimal (approximately 0.706349, or 70.6349%).
Working: 89 ÷ 126 = 0.706349 (70.6349%)

Key Values:
- Simplified Fraction: 89/126
- Mixed Number Form: 89/126
- Decimal Value: 0.706349
- Percentage: 70.6349%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-10-36-plus-9-21/
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10/36 + 9/21 = 89/126

Simplified Fraction

89/126

Mixed Number

Proper (89/126)

Decimal Value

0.706349

Percentage

70.6349%

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Step-by-Step Solution: 10/36 + 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 10/36 by 7, and multiply the numerator and denominator of 9/21 by 12 so both fractions share the common base 252.

10 × 7/36 × 7 = 70/252 and 9 × 12/21 × 12 = 108/252

Step 3

Add the Numerators

Now add the numerators (70 + 108 = 178) and keep the common denominator 252 unchanged.

70 + 108/252 = 178/252

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 178 and 252, which is 2. Divide both the numerator and denominator by 2.

178 ÷ 2/252 ÷ 2 = 89/126

Step 5

Decimal & Percentage Representation

Dividing the numerator 89 by denominator 126 produces a repeating decimal (approximately 0.706349, or 70.6349%).

89 ÷ 126 = 0.706349 (70.6349%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`89/126`
Mixed Number Form	`89/126`
Decimal Form	`0.706349`
Percentage	`70.6349%`

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Frequently Asked Questions

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

10/36 + 9/21 in simplest fraction form is 89/126.

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

10/36 + 9/21 converted to a decimal is 0.706349.

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

10/36 + 9/21 expressed as a percentage is 70.6349%.

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

It results in a repeating decimal (approximately 0.706349...) because the denominator contains prime factors other than 2 and 5.