What is 3/18 plus 4/21? (Answer: 5/14)

Exact Answer

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Problem: What is 3/18 plus 4/21?
Formula / Expression: 3/18 + 4/21
Final Answer: 5/14
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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 3/18 by 7, and multiply the numerator and denominator of 4/21 by 6 so both fractions share the common base 126.
Working: 3 × 7/18 × 7 = 21/126 and 4 × 6/21 × 6 = 24/126

Step 3: Add the Numerators
Now add the numerators (21 + 24 = 45) and keep the common denominator 126 unchanged.
Working: 21 + 24/126 = 45/126

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 45 and 126, which is 9. Divide both the numerator and denominator by 9.
Working: 45 ÷ 9/126 ÷ 9 = 5/14

Step 5: Decimal & Percentage Representation
Dividing the numerator 5 by denominator 14 produces a repeating decimal (approximately 0.357143, or 35.7143%).
Working: 5 ÷ 14 = 0.357143 (35.7143%)

Key Values:
- Simplified Fraction: 5/14
- Mixed Number Form: 5/14
- Decimal Value: 0.357143
- Percentage: 35.7143%

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Solved with FractionsCalc:
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3/18 + 4/21 = 5/14

Simplified Fraction

5/14

Mixed Number

Proper (5/14)

Decimal Value

0.357143

Percentage

35.7143%

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Step-by-Step Solution: 3/18 + 4/21

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 3/18 by 7, and multiply the numerator and denominator of 4/21 by 6 so both fractions share the common base 126.

3 × 7/18 × 7 = 21/126 and 4 × 6/21 × 6 = 24/126

Step 3

Add the Numerators

Now add the numerators (21 + 24 = 45) and keep the common denominator 126 unchanged.

21 + 24/126 = 45/126

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 45 and 126, which is 9. Divide both the numerator and denominator by 9.

45 ÷ 9/126 ÷ 9 = 5/14

Step 5

Decimal & Percentage Representation

Dividing the numerator 5 by denominator 14 produces a repeating decimal (approximately 0.357143, or 35.7143%).

5 ÷ 14 = 0.357143 (35.7143%)

Visual Representation

The diagram below illustrates 3/18 plus 4/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`5/14`
Mixed Number Form	`5/14`
Decimal Form	`0.357143`
Percentage	`35.7143%`

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Frequently Asked Questions

What is 3/18 plus 4/21 as a fraction?

3/18 + 4/21 in simplest fraction form is 5/14.

What is 3/18 plus 4/21 as a decimal?

3/18 + 4/21 converted to a decimal is 0.357143.

What is 3/18 plus 4/21 as a percentage?

3/18 + 4/21 expressed as a percentage is 35.7143%.

Does 3/18 plus 4/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.357143...) because the denominator contains prime factors other than 2 and 5.