What is 9/18 plus 11/21? (Answer: 43/42)

Exact Answer

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Problem: What is 9/18 plus 11/21?
Formula / Expression: 9/18 + 11/21
Final Answer: 1 1/42 (43/42)
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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 9/18 by 7, and multiply the numerator and denominator of 11/21 by 6 so both fractions share the common base 126.
Working: 9 × 7/18 × 7 = 63/126 and 11 × 6/21 × 6 = 66/126

Step 3: Add the Numerators
Now add the numerators (63 + 66 = 129) and keep the common denominator 126 unchanged.
Working: 63 + 66/126 = 129/126

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 129 and 126, which is 3. Divide both the numerator and denominator by 3.
Working: 129 ÷ 3/126 ÷ 3 = 43/42

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (43) is greater than the denominator (42), divide 43 by 42: it goes in 1 whole time(s) with a remainder of 1, giving the mixed number 1 1/42.
Working: 43/42 = 1 1/42

Step 6: Decimal & Percentage Representation
Dividing the numerator 43 by denominator 42 produces a repeating decimal (approximately 1.02381, or 102.381%).
Working: 43 ÷ 42 = 1.02381 (102.381%)

Key Values:
- Simplified Fraction: 43/42
- Mixed Number Form: 1 1/42
- Decimal Value: 1.02381
- Percentage: 102.381%

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9/18 + 11/21 = 43/42

Simplified Fraction

43/42

Mixed Number

1 1/42

Decimal Value

1.02381

Percentage

102.381%

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Step-by-Step Solution: 9/18 + 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 9/18 by 7, and multiply the numerator and denominator of 11/21 by 6 so both fractions share the common base 126.

9 × 7/18 × 7 = 63/126 and 11 × 6/21 × 6 = 66/126

Step 3

Add the Numerators

Now add the numerators (63 + 66 = 129) and keep the common denominator 126 unchanged.

63 + 66/126 = 129/126

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 129 and 126, which is 3. Divide both the numerator and denominator by 3.

129 ÷ 3/126 ÷ 3 = 43/42

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (43) is greater than the denominator (42), divide 43 by 42: it goes in 1 whole time(s) with a remainder of 1, giving the mixed number 1 1/42.

43/42 = 11/42

Step 6

Decimal & Percentage Representation

Dividing the numerator 43 by denominator 42 produces a repeating decimal (approximately 1.02381, or 102.381%).

43 ÷ 42 = 1.02381 (102.381%)

Visual Representation

The diagram below illustrates 9/18 plus 11/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`43/42`
Mixed Number Form	`1 1/42`
Decimal Form	`1.02381`
Percentage	`102.381%`

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Frequently Asked Questions

What is 9/18 plus 11/21 as a fraction?

9/18 + 11/21 in simplest fraction form is 43/42 (or 1 1/42 as a mixed number).

What is 9/18 plus 11/21 as a decimal?

9/18 + 11/21 converted to a decimal is 1.02381.

What is 9/18 plus 11/21 as a percentage?

9/18 + 11/21 expressed as a percentage is 102.381%.

How do you write 9/18 plus 11/21 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 43/42 can be written as the mixed number 1 1/42.

Does 9/18 plus 11/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.02381...) because the denominator contains prime factors other than 2 and 5.