What is 10/21 plus 17/35? (Answer: 101/105)

Exact Answer

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Problem: What is 10/21 plus 17/35?
Formula / Expression: 10/21 + 17/35
Final Answer: 101/105
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 21 and 35 share a common factor (GCD = 7). Finding their Least Common Multiple gives an LCD of 105 (which is smaller than their product 21 × 35 = 735, keeping the calculation simpler).
Working: LCD(21, 35) = 105

Step 2: Convert to Equivalent Fractions with Common Denominator 105
Multiply the numerator and denominator of 10/21 by 5, and multiply the numerator and denominator of 17/35 by 3 so both fractions share the common base 105.
Working: 10 × 5/21 × 5 = 50/105 and 17 × 3/35 × 3 = 51/105

Step 3: Add the Numerators
Now add the numerators (50 + 51 = 101) and keep the common denominator 105 unchanged.
Working: 50 + 51/105 = 101/105

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 101 and 105 is 1, confirming that 101/105 cannot be reduced further—it is already in its simplest irreducible form.
Working: 101/105

Step 5: Decimal & Percentage Representation
Dividing the numerator 101 by denominator 105 produces a repeating decimal (approximately 0.961905, or 96.1905%).
Working: 101 ÷ 105 = 0.961905 (96.1905%)

Key Values:
- Simplified Fraction: 101/105
- Mixed Number Form: 101/105
- Decimal Value: 0.961905
- Percentage: 96.1905%

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Solved with FractionsCalc:
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10/21 + 17/35 = 101/105

Simplified Fraction

101/105

Mixed Number

Proper (101/105)

Decimal Value

0.961905

Percentage

96.1905%

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Step-by-Step Solution: 10/21 + 17/35

Step 1

Find the Least Common Denominator (LCD)

The denominators 21 and 35 share a common factor (GCD = 7). Finding their Least Common Multiple gives an LCD of 105 (which is smaller than their product 21 × 35 = 735, keeping the calculation simpler).

LCD(21, 35) = 105

Step 2

Convert to Equivalent Fractions with Common Denominator 105

Multiply the numerator and denominator of 10/21 by 5, and multiply the numerator and denominator of 17/35 by 3 so both fractions share the common base 105.

10 × 5/21 × 5 = 50/105 and 17 × 3/35 × 3 = 51/105

Step 3

Add the Numerators

Now add the numerators (50 + 51 = 101) and keep the common denominator 105 unchanged.

50 + 51/105 = 101/105

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 101 and 105 is 1, confirming that 101/105 cannot be reduced further—it is already in its simplest irreducible form.

101/105

Step 5

Decimal & Percentage Representation

Dividing the numerator 101 by denominator 105 produces a repeating decimal (approximately 0.961905, or 96.1905%).

101 ÷ 105 = 0.961905 (96.1905%)

Visual Representation

The diagram below illustrates 10/21 plus 17/35 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`101/105`
Mixed Number Form	`101/105`
Decimal Form	`0.961905`
Percentage	`96.1905%`

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Frequently Asked Questions

What is 10/21 plus 17/35 as a fraction?

10/21 + 17/35 in simplest fraction form is 101/105.

What is 10/21 plus 17/35 as a decimal?

10/21 + 17/35 converted to a decimal is 0.961905.

What is 10/21 plus 17/35 as a percentage?

10/21 + 17/35 expressed as a percentage is 96.1905%.

Does 10/21 plus 17/35 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.961905...) because the denominator contains prime factors other than 2 and 5.