What is 8/18 plus 11/21? (Answer: 61/63)

Exact Answer

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Problem: What is 8/18 plus 11/21?
Formula / Expression: 8/18 + 11/21
Final Answer: 61/63
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 18 and 21 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 126 (which is smaller than their product 18 × 21 = 378, keeping the calculation simpler).
Working: LCD(18, 21) = 126

Step 2: Convert to Equivalent Fractions with Common Denominator 126
Multiply the numerator and denominator of 8/18 by 7, and multiply the numerator and denominator of 11/21 by 6 so both fractions share the common base 126.
Working: 8 × 7/18 × 7 = 56/126 and 11 × 6/21 × 6 = 66/126

Step 3: Add the Numerators
Now add the numerators (56 + 66 = 122) and keep the common denominator 126 unchanged.
Working: 56 + 66/126 = 122/126

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 122 and 126, which is 2. Divide both the numerator and denominator by 2.
Working: 122 ÷ 2/126 ÷ 2 = 61/63

Step 5: Decimal & Percentage Representation
Dividing the numerator 61 by denominator 63 produces a repeating decimal (approximately 0.968254, or 96.8254%).
Working: 61 ÷ 63 = 0.968254 (96.8254%)

Key Values:
- Simplified Fraction: 61/63
- Mixed Number Form: 61/63
- Decimal Value: 0.968254
- Percentage: 96.8254%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-8-18-plus-11-21/
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8/18 + 11/21 = 61/63

Simplified Fraction

61/63

Mixed Number

Proper (61/63)

Decimal Value

0.968254

Percentage

96.8254%

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Step-by-Step Solution: 8/18 + 11/21

Step 1

Find the Least Common Denominator (LCD)

The denominators 18 and 21 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 126 (which is smaller than their product 18 × 21 = 378, keeping the calculation simpler).

LCD(18, 21) = 126

Step 2

Convert to Equivalent Fractions with Common Denominator 126

Multiply the numerator and denominator of 8/18 by 7, and multiply the numerator and denominator of 11/21 by 6 so both fractions share the common base 126.

8 × 7/18 × 7 = 56/126 and 11 × 6/21 × 6 = 66/126

Step 3

Add the Numerators

Now add the numerators (56 + 66 = 122) and keep the common denominator 126 unchanged.

56 + 66/126 = 122/126

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 122 and 126, which is 2. Divide both the numerator and denominator by 2.

122 ÷ 2/126 ÷ 2 = 61/63

Step 5

Decimal & Percentage Representation

Dividing the numerator 61 by denominator 63 produces a repeating decimal (approximately 0.968254, or 96.8254%).

61 ÷ 63 = 0.968254 (96.8254%)

Visual Representation

The diagram below illustrates 8/18 plus 11/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`61/63`
Mixed Number Form	`61/63`
Decimal Form	`0.968254`
Percentage	`96.8254%`

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Frequently Asked Questions

What is 8/18 plus 11/21 as a fraction?

8/18 + 11/21 in simplest fraction form is 61/63.

What is 8/18 plus 11/21 as a decimal?

8/18 + 11/21 converted to a decimal is 0.968254.

What is 8/18 plus 11/21 as a percentage?

8/18 + 11/21 expressed as a percentage is 96.8254%.

Does 8/18 plus 11/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.968254...) because the denominator contains prime factors other than 2 and 5.