What is 4/18 plus 9/21? (Answer: 41/63)

Exact Answer

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Problem: What is 4/18 plus 9/21?
Formula / Expression: 4/18 + 9/21
Final Answer: 41/63
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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 4/18 by 7, and multiply the numerator and denominator of 9/21 by 6 so both fractions share the common base 126.
Working: 4 × 7/18 × 7 = 28/126 and 9 × 6/21 × 6 = 54/126

Step 3: Add the Numerators
Now add the numerators (28 + 54 = 82) and keep the common denominator 126 unchanged.
Working: 28 + 54/126 = 82/126

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 82 and 126, which is 2. Divide both the numerator and denominator by 2.
Working: 82 ÷ 2/126 ÷ 2 = 41/63

Step 5: Decimal & Percentage Representation
Dividing the numerator 41 by denominator 63 produces a repeating decimal (approximately 0.650794, or 65.0794%).
Working: 41 ÷ 63 = 0.650794 (65.0794%)

Key Values:
- Simplified Fraction: 41/63
- Mixed Number Form: 41/63
- Decimal Value: 0.650794
- Percentage: 65.0794%

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Solved with FractionsCalc:
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4/18 + 9/21 = 41/63

Simplified Fraction

41/63

Mixed Number

Proper (41/63)

Decimal Value

0.650794

Percentage

65.0794%

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Step-by-Step Solution: 4/18 + 9/21

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 4/18 by 7, and multiply the numerator and denominator of 9/21 by 6 so both fractions share the common base 126.

4 × 7/18 × 7 = 28/126 and 9 × 6/21 × 6 = 54/126

Step 3

Add the Numerators

Now add the numerators (28 + 54 = 82) and keep the common denominator 126 unchanged.

28 + 54/126 = 82/126

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 82 and 126, which is 2. Divide both the numerator and denominator by 2.

82 ÷ 2/126 ÷ 2 = 41/63

Step 5

Decimal & Percentage Representation

Dividing the numerator 41 by denominator 63 produces a repeating decimal (approximately 0.650794, or 65.0794%).

41 ÷ 63 = 0.650794 (65.0794%)

Visual Representation

The diagram below illustrates 4/18 plus 9/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`41/63`
Mixed Number Form	`41/63`
Decimal Form	`0.650794`
Percentage	`65.0794%`

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Frequently Asked Questions

What is 4/18 plus 9/21 as a fraction?

4/18 + 9/21 in simplest fraction form is 41/63.

What is 4/18 plus 9/21 as a decimal?

4/18 + 9/21 converted to a decimal is 0.650794.

What is 4/18 plus 9/21 as a percentage?

4/18 + 9/21 expressed as a percentage is 65.0794%.

Does 4/18 plus 9/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.650794...) because the denominator contains prime factors other than 2 and 5.