What is 3/18 plus 7/21? (Answer: 1/2)

Exact Answer

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Problem: What is 3/18 plus 7/21?
Formula / Expression: 3/18 + 7/21
Final Answer: 1/2
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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 7/21 by 6 so both fractions share the common base 126.
Working: 3 × 7/18 × 7 = 21/126 and 7 × 6/21 × 6 = 42/126

Step 3: Add the Numerators
Now add the numerators (21 + 42 = 63) and keep the common denominator 126 unchanged.
Working: 21 + 42/126 = 63/126

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 63 and 126, which is 63. Divide both the numerator and denominator by 63.
Working: 63 ÷ 63/126 ÷ 63 = 1/2

Step 5: Decimal & Percentage Representation
Dividing the numerator 1 by denominator 2 yields an exact terminating decimal of 0.5 (or 50%).
Working: 1 ÷ 2 = 0.5 (50%)

Key Values:
- Simplified Fraction: 1/2
- Mixed Number Form: 1/2
- Decimal Value: 0.5
- Percentage: 50%

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Solved with FractionsCalc:
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3/18 + 7/21 = 1/2

Simplified Fraction

1/2

Mixed Number

Proper (1/2)

Decimal Value

0.5

Percentage

50%

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Step-by-Step Solution: 3/18 + 7/21

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 7/21 by 6 so both fractions share the common base 126.

3 × 7/18 × 7 = 21/126 and 7 × 6/21 × 6 = 42/126

Step 3

Add the Numerators

Now add the numerators (21 + 42 = 63) and keep the common denominator 126 unchanged.

21 + 42/126 = 63/126

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 63 and 126, which is 63. Divide both the numerator and denominator by 63.

63 ÷ 63/126 ÷ 63 = 1/2

Step 5

Decimal & Percentage Representation

Dividing the numerator 1 by denominator 2 yields an exact terminating decimal of 0.5 (or 50%).

1 ÷ 2 = 0.5 (50%)

Visual Representation

The diagram below illustrates 3/18 plus 7/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`1/2`
Mixed Number Form	`1/2`
Decimal Form	`0.5`
Percentage	`50%`

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Frequently Asked Questions

What is 3/18 plus 7/21 as a fraction?

3/18 + 7/21 in simplest fraction form is 1/2.

What is 3/18 plus 7/21 as a decimal?

3/18 + 7/21 converted to a decimal is 0.5.

What is 3/18 plus 7/21 as a percentage?

3/18 + 7/21 expressed as a percentage is 50%.

Does 3/18 plus 7/21 result in a terminating or repeating decimal?

It results in an exact terminating decimal (0.5) because the denominator in simplest terms contains only prime factors 2 and/or 5.