What is 5/35 plus 2/3? (Answer: 17/21)

Exact Answer

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Problem: What is 5/35 plus 2/3?
Formula / Expression: 5/35 + 2/3
Final Answer: 17/21
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 35 and 3 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 35 × 3 = 105.
Working: LCD(35, 3) = 105

Step 2: Convert to Equivalent Fractions with Common Denominator 105
Multiply the numerator and denominator of 5/35 by 3, and multiply the numerator and denominator of 2/3 by 35 so both fractions share the common base 105.
Working: 5 × 3/35 × 3 = 15/105 and 2 × 35/3 × 35 = 70/105

Step 3: Add the Numerators
Now add the numerators (15 + 70 = 85) and keep the common denominator 105 unchanged.
Working: 15 + 70/105 = 85/105

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 85 and 105, which is 5. Divide both the numerator and denominator by 5.
Working: 85 ÷ 5/105 ÷ 5 = 17/21

Step 5: Decimal & Percentage Representation
Dividing the numerator 17 by denominator 21 produces a repeating decimal (approximately 0.809524, or 80.9524%).
Working: 17 ÷ 21 = 0.809524 (80.9524%)

Key Values:
- Simplified Fraction: 17/21
- Mixed Number Form: 17/21
- Decimal Value: 0.809524
- Percentage: 80.9524%

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Solved with FractionsCalc:
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5/35 + 2/3 = 17/21

Simplified Fraction

17/21

Mixed Number

Proper (17/21)

Decimal Value

0.809524

Percentage

80.9524%

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Step-by-Step Solution: 5/35 + 2/3

Step 1

Find the Least Common Denominator (LCD)

The denominators 35 and 3 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 35 × 3 = 105.

LCD(35, 3) = 105

Step 2

Convert to Equivalent Fractions with Common Denominator 105

Multiply the numerator and denominator of 5/35 by 3, and multiply the numerator and denominator of 2/3 by 35 so both fractions share the common base 105.

5 × 3/35 × 3 = 15/105 and 2 × 35/3 × 35 = 70/105

Step 3

Add the Numerators

Now add the numerators (15 + 70 = 85) and keep the common denominator 105 unchanged.

15 + 70/105 = 85/105

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 85 and 105, which is 5. Divide both the numerator and denominator by 5.

85 ÷ 5/105 ÷ 5 = 17/21

Step 5

Decimal & Percentage Representation

Dividing the numerator 17 by denominator 21 produces a repeating decimal (approximately 0.809524, or 80.9524%).

17 ÷ 21 = 0.809524 (80.9524%)

Visual Representation

The diagram below illustrates 5/35 plus 2/3 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`17/21`
Mixed Number Form	`17/21`
Decimal Form	`0.809524`
Percentage	`80.9524%`

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Frequently Asked Questions

What is 5/35 plus 2/3 as a fraction?

5/35 + 2/3 in simplest fraction form is 17/21.

What is 5/35 plus 2/3 as a decimal?

5/35 + 2/3 converted to a decimal is 0.809524.

What is 5/35 plus 2/3 as a percentage?

5/35 + 2/3 expressed as a percentage is 80.9524%.

Does 5/35 plus 2/3 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.809524...) because the denominator contains prime factors other than 2 and 5.