What is 8/21 plus 4/10? (Answer: 82/105)

Exact Answer

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Problem: What is 8/21 plus 4/10?
Formula / Expression: 8/21 + 4/10
Final Answer: 82/105
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 21 and 10 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 21 × 10 = 210.
Working: LCD(21, 10) = 210

Step 2: Convert to Equivalent Fractions with Common Denominator 210
Multiply the numerator and denominator of 8/21 by 10, and multiply the numerator and denominator of 4/10 by 21 so both fractions share the common base 210.
Working: 8 × 10/21 × 10 = 80/210 and 4 × 21/10 × 21 = 84/210

Step 3: Add the Numerators
Now add the numerators (80 + 84 = 164) and keep the common denominator 210 unchanged.
Working: 80 + 84/210 = 164/210

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 164 and 210, which is 2. Divide both the numerator and denominator by 2.
Working: 164 ÷ 2/210 ÷ 2 = 82/105

Step 5: Decimal & Percentage Representation
Dividing the numerator 82 by denominator 105 produces a repeating decimal (approximately 0.780952, or 78.0952%).
Working: 82 ÷ 105 = 0.780952 (78.0952%)

Key Values:
- Simplified Fraction: 82/105
- Mixed Number Form: 82/105
- Decimal Value: 0.780952
- Percentage: 78.0952%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-8-21-plus-4-10/
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8/21 + 4/10 = 82/105

Simplified Fraction

82/105

Mixed Number

Proper (82/105)

Decimal Value

0.780952

Percentage

78.0952%

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Step-by-Step Solution: 8/21 + 4/10

Step 1

Find the Least Common Denominator (LCD)

The denominators 21 and 10 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 21 × 10 = 210.

LCD(21, 10) = 210

Step 2

Convert to Equivalent Fractions with Common Denominator 210

Multiply the numerator and denominator of 8/21 by 10, and multiply the numerator and denominator of 4/10 by 21 so both fractions share the common base 210.

8 × 10/21 × 10 = 80/210 and 4 × 21/10 × 21 = 84/210

Step 3

Add the Numerators

Now add the numerators (80 + 84 = 164) and keep the common denominator 210 unchanged.

80 + 84/210 = 164/210

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 164 and 210, which is 2. Divide both the numerator and denominator by 2.

164 ÷ 2/210 ÷ 2 = 82/105

Step 5

Decimal & Percentage Representation

Dividing the numerator 82 by denominator 105 produces a repeating decimal (approximately 0.780952, or 78.0952%).

82 ÷ 105 = 0.780952 (78.0952%)

Visual Representation

The diagram below illustrates 8/21 plus 4/10 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`82/105`
Mixed Number Form	`82/105`
Decimal Form	`0.780952`
Percentage	`78.0952%`

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Frequently Asked Questions

What is 8/21 plus 4/10 as a fraction?

8/21 + 4/10 in simplest fraction form is 82/105.

What is 8/21 plus 4/10 as a decimal?

8/21 + 4/10 converted to a decimal is 0.780952.

What is 8/21 plus 4/10 as a percentage?

8/21 + 4/10 expressed as a percentage is 78.0952%.

Does 8/21 plus 4/10 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.780952...) because the denominator contains prime factors other than 2 and 5.