What is 10/36 plus 7/21? (Answer: 11/18)

Exact Answer

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Problem: What is 10/36 plus 7/21?
Formula / Expression: 10/36 + 7/21
Final Answer: 11/18
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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 7/21 by 12 so both fractions share the common base 252.
Working: 10 × 7/36 × 7 = 70/252 and 7 × 12/21 × 12 = 84/252

Step 3: Add the Numerators
Now add the numerators (70 + 84 = 154) and keep the common denominator 252 unchanged.
Working: 70 + 84/252 = 154/252

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 154 and 252, which is 14. Divide both the numerator and denominator by 14.
Working: 154 ÷ 14/252 ÷ 14 = 11/18

Step 5: Decimal & Percentage Representation
Dividing the numerator 11 by denominator 18 produces a repeating decimal (approximately 0.611111, or 61.1111%).
Working: 11 ÷ 18 = 0.611111 (61.1111%)

Key Values:
- Simplified Fraction: 11/18
- Mixed Number Form: 11/18
- Decimal Value: 0.611111
- Percentage: 61.1111%

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Solved with FractionsCalc:
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10/36 + 7/21 = 11/18

Simplified Fraction

11/18

Mixed Number

Proper (11/18)

Decimal Value

0.611111

Percentage

61.1111%

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Step-by-Step Solution: 10/36 + 7/21

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 7/21 by 12 so both fractions share the common base 252.

10 × 7/36 × 7 = 70/252 and 7 × 12/21 × 12 = 84/252

Step 3

Add the Numerators

Now add the numerators (70 + 84 = 154) and keep the common denominator 252 unchanged.

70 + 84/252 = 154/252

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 154 and 252, which is 14. Divide both the numerator and denominator by 14.

154 ÷ 14/252 ÷ 14 = 11/18

Step 5

Decimal & Percentage Representation

Dividing the numerator 11 by denominator 18 produces a repeating decimal (approximately 0.611111, or 61.1111%).

11 ÷ 18 = 0.611111 (61.1111%)

Visual Representation

The diagram below illustrates 10/36 plus 7/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`11/18`
Mixed Number Form	`11/18`
Decimal Form	`0.611111`
Percentage	`61.1111%`

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Frequently Asked Questions

What is 10/36 plus 7/21 as a fraction?

10/36 + 7/21 in simplest fraction form is 11/18.

What is 10/36 plus 7/21 as a decimal?

10/36 + 7/21 converted to a decimal is 0.611111.

What is 10/36 plus 7/21 as a percentage?

10/36 + 7/21 expressed as a percentage is 61.1111%.

Does 10/36 plus 7/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.611111...) because the denominator contains prime factors other than 2 and 5.