What is 10/21 plus 4/8? (Answer: 41/42)

Exact Answer

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Problem: What is 10/21 plus 4/8?
Formula / Expression: 10/21 + 4/8
Final Answer: 41/42
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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 10/21 by 8, and multiply the numerator and denominator of 4/8 by 21 so both fractions share the common base 168.
Working: 10 × 8/21 × 8 = 80/168 and 4 × 21/8 × 21 = 84/168

Step 3: Add the Numerators
Now add the numerators (80 + 84 = 164) and keep the common denominator 168 unchanged.
Working: 80 + 84/168 = 164/168

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 164 and 168, which is 4. Divide both the numerator and denominator by 4.
Working: 164 ÷ 4/168 ÷ 4 = 41/42

Step 5: Decimal & Percentage Representation
Dividing the numerator 41 by denominator 42 produces a repeating decimal (approximately 0.97619, or 97.619%).
Working: 41 ÷ 42 = 0.97619 (97.619%)

Key Values:
- Simplified Fraction: 41/42
- Mixed Number Form: 41/42
- Decimal Value: 0.97619
- Percentage: 97.619%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-10-21-plus-4-8/
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10/21 + 4/8 = 41/42

Simplified Fraction

41/42

Mixed Number

Proper (41/42)

Decimal Value

0.97619

Percentage

97.619%

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Step-by-Step Solution: 10/21 + 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 10/21 by 8, and multiply the numerator and denominator of 4/8 by 21 so both fractions share the common base 168.

10 × 8/21 × 8 = 80/168 and 4 × 21/8 × 21 = 84/168

Step 3

Add the Numerators

Now add the numerators (80 + 84 = 164) and keep the common denominator 168 unchanged.

80 + 84/168 = 164/168

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 164 and 168, which is 4. Divide both the numerator and denominator by 4.

164 ÷ 4/168 ÷ 4 = 41/42

Step 5

Decimal & Percentage Representation

Dividing the numerator 41 by denominator 42 produces a repeating decimal (approximately 0.97619, or 97.619%).

41 ÷ 42 = 0.97619 (97.619%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`41/42`
Mixed Number Form	`41/42`
Decimal Form	`0.97619`
Percentage	`97.619%`

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Frequently Asked Questions

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

10/21 + 4/8 in simplest fraction form is 41/42.

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

10/21 + 4/8 converted to a decimal is 0.97619.

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

10/21 + 4/8 expressed as a percentage is 97.619%.

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

It results in a repeating decimal (approximately 0.97619...) because the denominator contains prime factors other than 2 and 5.