What is 10/21 plus 5/10? (Answer: 41/42)

Exact Answer

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Problem: What is 10/21 plus 5/10?
Formula / Expression: 10/21 + 5/10
Final Answer: 41/42
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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 10/21 by 10, and multiply the numerator and denominator of 5/10 by 21 so both fractions share the common base 210.
Working: 10 × 10/21 × 10 = 100/210 and 5 × 21/10 × 21 = 105/210

Step 3: Add the Numerators
Now add the numerators (100 + 105 = 205) and keep the common denominator 210 unchanged.
Working: 100 + 105/210 = 205/210

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 205 and 210, which is 5. Divide both the numerator and denominator by 5.
Working: 205 ÷ 5/210 ÷ 5 = 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-5-10/
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10/21 + 5/10 = 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 + 5/10

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 10/21 by 10, and multiply the numerator and denominator of 5/10 by 21 so both fractions share the common base 210.

10 × 10/21 × 10 = 100/210 and 5 × 21/10 × 21 = 105/210

Step 3

Add the Numerators

Now add the numerators (100 + 105 = 205) and keep the common denominator 210 unchanged.

100 + 105/210 = 205/210

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 205 and 210, which is 5. Divide both the numerator and denominator by 5.

205 ÷ 5/210 ÷ 5 = 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 5/10 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 5/10 as a fraction?

10/21 + 5/10 in simplest fraction form is 41/42.

What is 10/21 plus 5/10 as a decimal?

10/21 + 5/10 converted to a decimal is 0.97619.

What is 10/21 plus 5/10 as a percentage?

10/21 + 5/10 expressed as a percentage is 97.619%.

Does 10/21 plus 5/10 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.