What is 6/14 plus 12/21? (Answer: 1)

Exact Answer

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Problem: What is 6/14 plus 12/21?
Formula / Expression: 6/14 + 12/21
Final Answer: 1
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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 6/14 by 3, and multiply the numerator and denominator of 12/21 by 2 so both fractions share the common base 42.
Working: 6 × 3/14 × 3 = 18/42 and 12 × 2/21 × 2 = 24/42

Step 3: Add the Numerators
Now add the numerators (18 + 24 = 42) and keep the common denominator 42 unchanged.
Working: 18 + 24/42 = 42/42

Step 4: Simplify to an Exact Whole Number
Notice that the numerator (42) is completely divisible by the denominator (42). Dividing 42 by 42 yields the whole number 1 with zero remainder.
Working: 42/42 = 1

Step 5: Decimal & Percentage Representation
Dividing the numerator 1 by denominator 1 yields an exact terminating decimal of 1 (or 100%).
Working: 1 ÷ 1 = 1 (100%)

Key Values:
- Simplified Fraction: 1
- Mixed Number Form: 1
- Decimal Value: 1
- Percentage: 100%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-6-14-plus-12-21/
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6/14 + 12/21 = 1

Simplified Fraction

Mixed Number

Decimal Value

Percentage

100%

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Step-by-Step Solution: 6/14 + 12/21

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 6/14 by 3, and multiply the numerator and denominator of 12/21 by 2 so both fractions share the common base 42.

6 × 3/14 × 3 = 18/42 and 12 × 2/21 × 2 = 24/42

Step 3

Add the Numerators

Now add the numerators (18 + 24 = 42) and keep the common denominator 42 unchanged.

18 + 24/42 = 42/42

Step 4

Simplify to an Exact Whole Number

Notice that the numerator (42) is completely divisible by the denominator (42). Dividing 42 by 42 yields the whole number 1 with zero remainder.

42/42 = 1

Step 5

Decimal & Percentage Representation

Dividing the numerator 1 by denominator 1 yields an exact terminating decimal of 1 (or 100%).

1 ÷ 1 = 1 (100%)

Visual Representation

The diagram below illustrates 6/14 plus 12/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`1`
Mixed Number Form	`1`
Decimal Form	`1`
Percentage	`100%`

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Frequently Asked Questions

What is 6/14 plus 12/21 as a fraction?

6/14 + 12/21 in simplest fraction form is 1.

What is 6/14 plus 12/21 as a decimal?

6/14 + 12/21 converted to a decimal is 1.

What is 6/14 plus 12/21 as a percentage?

6/14 + 12/21 expressed as a percentage is 100%.

Is the answer to 6/14 plus 12/21 a whole number?

Yes, 6/14 + 12/21 simplifies completely to the whole number 1 with no remaining fractional part.