What is 7/21 plus 4/8? (Answer: 5/6)

Exact Answer

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Problem: What is 7/21 plus 4/8?
Formula / Expression: 7/21 + 4/8
Final Answer: 5/6
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 21 and 8 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 21 × 8 = 168.
Working: LCD(21, 8) = 168

Step 2: Convert to Equivalent Fractions with Common Denominator 168
Multiply the numerator and denominator of 7/21 by 8, and multiply the numerator and denominator of 4/8 by 21 so both fractions share the common base 168.
Working: 7 × 8/21 × 8 = 56/168 and 4 × 21/8 × 21 = 84/168

Step 3: Add the Numerators
Now add the numerators (56 + 84 = 140) and keep the common denominator 168 unchanged.
Working: 56 + 84/168 = 140/168

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 140 and 168, which is 28. Divide both the numerator and denominator by 28.
Working: 140 ÷ 28/168 ÷ 28 = 5/6

Step 5: Decimal & Percentage Representation
Dividing the numerator 5 by denominator 6 produces a repeating decimal (approximately 0.833333, or 83.3333%).
Working: 5 ÷ 6 = 0.833333 (83.3333%)

Key Values:
- Simplified Fraction: 5/6
- Mixed Number Form: 5/6
- Decimal Value: 0.833333
- Percentage: 83.3333%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-7-21-plus-4-8/
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7/21 + 4/8 = 5/6

Simplified Fraction

5/6

Mixed Number

Proper (5/6)

Decimal Value

0.833333

Percentage

83.3333%

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Step-by-Step Solution: 7/21 + 4/8

Step 1

Find the Least Common Denominator (LCD)

The denominators 21 and 8 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 21 × 8 = 168.

LCD(21, 8) = 168

Step 2

Convert to Equivalent Fractions with Common Denominator 168

Multiply the numerator and denominator of 7/21 by 8, and multiply the numerator and denominator of 4/8 by 21 so both fractions share the common base 168.

7 × 8/21 × 8 = 56/168 and 4 × 21/8 × 21 = 84/168

Step 3

Add the Numerators

Now add the numerators (56 + 84 = 140) and keep the common denominator 168 unchanged.

56 + 84/168 = 140/168

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 140 and 168, which is 28. Divide both the numerator and denominator by 28.

140 ÷ 28/168 ÷ 28 = 5/6

Step 5

Decimal & Percentage Representation

Dividing the numerator 5 by denominator 6 produces a repeating decimal (approximately 0.833333, or 83.3333%).

5 ÷ 6 = 0.833333 (83.3333%)

Visual Representation

The diagram below illustrates 7/21 plus 4/8 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`5/6`
Mixed Number Form	`5/6`
Decimal Form	`0.833333`
Percentage	`83.3333%`

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Frequently Asked Questions

What is 7/21 plus 4/8 as a fraction?

7/21 + 4/8 in simplest fraction form is 5/6.

What is 7/21 plus 4/8 as a decimal?

7/21 + 4/8 converted to a decimal is 0.833333.

What is 7/21 plus 4/8 as a percentage?

7/21 + 4/8 expressed as a percentage is 83.3333%.

Does 7/21 plus 4/8 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.833333...) because the denominator contains prime factors other than 2 and 5.