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

Exact Answer

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Problem: What is 7/21 plus 2/3?
Formula / Expression: 7/21 + 2/3
Final Answer: 1
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
Notice that 21 is an exact multiple of 3 (3 × 7 = 21). The Least Common Denominator (LCD) is simply 21, meaning we only need to scale one fraction.
Working: LCD(21, 3) = 21

Step 2: Convert to Equivalent Fractions with Common Denominator 21
Multiply the numerator and denominator of 7/21 by 1, and multiply the numerator and denominator of 2/3 by 7 so both fractions share the common base 21.
Working: 7 × 1/21 × 1 = 7/21 and 2 × 7/3 × 7 = 14/21

Step 3: Add the Numerators
Now add the numerators (7 + 14 = 21) and keep the common denominator 21 unchanged.
Working: 7 + 14/21 = 21/21

Step 4: Simplify to an Exact Whole Number
Notice that the numerator (21) is completely divisible by the denominator (21). Dividing 21 by 21 yields the whole number 1 with zero remainder.
Working: 21/21 = 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:
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7/21 + 2/3 = 1

Simplified Fraction

Mixed Number

Decimal Value

Percentage

100%

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Step-by-Step Solution: 7/21 + 2/3

Step 1

Find the Least Common Denominator (LCD)

Notice that 21 is an exact multiple of 3 (3 × 7 = 21). The Least Common Denominator (LCD) is simply 21, meaning we only need to scale one fraction.

LCD(21, 3) = 21

Step 2

Convert to Equivalent Fractions with Common Denominator 21

Multiply the numerator and denominator of 7/21 by 1, and multiply the numerator and denominator of 2/3 by 7 so both fractions share the common base 21.

7 × 1/21 × 1 = 7/21 and 2 × 7/3 × 7 = 14/21

Step 3

Add the Numerators

Now add the numerators (7 + 14 = 21) and keep the common denominator 21 unchanged.

7 + 14/21 = 21/21

Step 4

Simplify to an Exact Whole Number

Notice that the numerator (21) is completely divisible by the denominator (21). Dividing 21 by 21 yields the whole number 1 with zero remainder.

21/21 = 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 7/21 plus 2/3 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 7/21 plus 2/3 as a fraction?

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

What is 7/21 plus 2/3 as a decimal?

7/21 + 2/3 converted to a decimal is 1.

What is 7/21 plus 2/3 as a percentage?

7/21 + 2/3 expressed as a percentage is 100%.

Is the answer to 7/21 plus 2/3 a whole number?

Yes, 7/21 + 2/3 simplifies completely to the whole number 1 with no remaining fractional part.