What is 3/18 plus 5/21? (Answer: 17/42)

Exact Answer

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Problem: What is 3/18 plus 5/21?
Formula / Expression: 3/18 + 5/21
Final Answer: 17/42
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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 3/18 by 7, and multiply the numerator and denominator of 5/21 by 6 so both fractions share the common base 126.
Working: 3 × 7/18 × 7 = 21/126 and 5 × 6/21 × 6 = 30/126

Step 3: Add the Numerators
Now add the numerators (21 + 30 = 51) and keep the common denominator 126 unchanged.
Working: 21 + 30/126 = 51/126

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 51 and 126, which is 3. Divide both the numerator and denominator by 3.
Working: 51 ÷ 3/126 ÷ 3 = 17/42

Step 5: Decimal & Percentage Representation
Dividing the numerator 17 by denominator 42 produces a repeating decimal (approximately 0.404762, or 40.4762%).
Working: 17 ÷ 42 = 0.404762 (40.4762%)

Key Values:
- Simplified Fraction: 17/42
- Mixed Number Form: 17/42
- Decimal Value: 0.404762
- Percentage: 40.4762%

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Solved with FractionsCalc:
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3/18 + 5/21 = 17/42

Simplified Fraction

17/42

Mixed Number

Proper (17/42)

Decimal Value

0.404762

Percentage

40.4762%

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Step-by-Step Solution: 3/18 + 5/21

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 5/21 by 6 so both fractions share the common base 126.

3 × 7/18 × 7 = 21/126 and 5 × 6/21 × 6 = 30/126

Step 3

Add the Numerators

Now add the numerators (21 + 30 = 51) and keep the common denominator 126 unchanged.

21 + 30/126 = 51/126

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 51 and 126, which is 3. Divide both the numerator and denominator by 3.

51 ÷ 3/126 ÷ 3 = 17/42

Step 5

Decimal & Percentage Representation

Dividing the numerator 17 by denominator 42 produces a repeating decimal (approximately 0.404762, or 40.4762%).

17 ÷ 42 = 0.404762 (40.4762%)

Visual Representation

The diagram below illustrates 3/18 plus 5/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`17/42`
Mixed Number Form	`17/42`
Decimal Form	`0.404762`
Percentage	`40.4762%`

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Frequently Asked Questions

What is 3/18 plus 5/21 as a fraction?

3/18 + 5/21 in simplest fraction form is 17/42.

What is 3/18 plus 5/21 as a decimal?

3/18 + 5/21 converted to a decimal is 0.404762.

What is 3/18 plus 5/21 as a percentage?

3/18 + 5/21 expressed as a percentage is 40.4762%.

Does 3/18 plus 5/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.404762...) because the denominator contains prime factors other than 2 and 5.