What is 1/14 plus 9/21? (Answer: 1/2)

Exact Answer

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Problem: What is 1/14 plus 9/21?
Formula / Expression: 1/14 + 9/21
Final Answer: 1/2
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 14 and 21 share a common factor (GCD = 7). Finding their Least Common Multiple gives an LCD of 42 (which is smaller than their product 14 × 21 = 294, keeping the calculation simpler).
Working: LCD(14, 21) = 42

Step 2: Convert to Equivalent Fractions with Common Denominator 42
Multiply the numerator and denominator of 1/14 by 3, and multiply the numerator and denominator of 9/21 by 2 so both fractions share the common base 42.
Working: 1 × 3/14 × 3 = 3/42 and 9 × 2/21 × 2 = 18/42

Step 3: Add the Numerators
Now add the numerators (3 + 18 = 21) and keep the common denominator 42 unchanged.
Working: 3 + 18/42 = 21/42

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 21 and 42, which is 21. Divide both the numerator and denominator by 21.
Working: 21 ÷ 21/42 ÷ 21 = 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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1/14 + 9/21 = 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: 1/14 + 9/21

Step 1

Find the Least Common Denominator (LCD)

The denominators 14 and 21 share a common factor (GCD = 7). Finding their Least Common Multiple gives an LCD of 42 (which is smaller than their product 14 × 21 = 294, keeping the calculation simpler).

LCD(14, 21) = 42

Step 2

Convert to Equivalent Fractions with Common Denominator 42

Multiply the numerator and denominator of 1/14 by 3, and multiply the numerator and denominator of 9/21 by 2 so both fractions share the common base 42.

1 × 3/14 × 3 = 3/42 and 9 × 2/21 × 2 = 18/42

Step 3

Add the Numerators

Now add the numerators (3 + 18 = 21) and keep the common denominator 42 unchanged.

3 + 18/42 = 21/42

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 21 and 42, which is 21. Divide both the numerator and denominator by 21.

21 ÷ 21/42 ÷ 21 = 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 1/14 plus 9/21 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 1/14 plus 9/21 as a fraction?

1/14 + 9/21 in simplest fraction form is 1/2.

What is 1/14 plus 9/21 as a decimal?

1/14 + 9/21 converted to a decimal is 0.5.

What is 1/14 plus 9/21 as a percentage?

1/14 + 9/21 expressed as a percentage is 50%.

Does 1/14 plus 9/21 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.