What is 5/35 plus 8/21? (Answer: 11/21)

Exact Answer

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Problem: What is 5/35 plus 8/21?
Formula / Expression: 5/35 + 8/21
Final Answer: 11/21
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 35 and 21 share a common factor (GCD = 7). Finding their Least Common Multiple gives an LCD of 105 (which is smaller than their product 35 × 21 = 735, keeping the calculation simpler).
Working: LCD(35, 21) = 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 8/21 by 5 so both fractions share the common base 105.
Working: 5 × 3/35 × 3 = 15/105 and 8 × 5/21 × 5 = 40/105

Step 3: Add the Numerators
Now add the numerators (15 + 40 = 55) and keep the common denominator 105 unchanged.
Working: 15 + 40/105 = 55/105

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 55 and 105, which is 5. Divide both the numerator and denominator by 5.
Working: 55 ÷ 5/105 ÷ 5 = 11/21

Step 5: Decimal & Percentage Representation
Dividing the numerator 11 by denominator 21 produces a repeating decimal (approximately 0.52381, or 52.381%).
Working: 11 ÷ 21 = 0.52381 (52.381%)

Key Values:
- Simplified Fraction: 11/21
- Mixed Number Form: 11/21
- Decimal Value: 0.52381
- Percentage: 52.381%

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Solved with FractionsCalc:
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5/35 + 8/21 = 11/21

Simplified Fraction

11/21

Mixed Number

Proper (11/21)

Decimal Value

0.52381

Percentage

52.381%

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Step-by-Step Solution: 5/35 + 8/21

Step 1

Find the Least Common Denominator (LCD)

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

LCD(35, 21) = 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 8/21 by 5 so both fractions share the common base 105.

5 × 3/35 × 3 = 15/105 and 8 × 5/21 × 5 = 40/105

Step 3

Add the Numerators

Now add the numerators (15 + 40 = 55) and keep the common denominator 105 unchanged.

15 + 40/105 = 55/105

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 55 and 105, which is 5. Divide both the numerator and denominator by 5.

55 ÷ 5/105 ÷ 5 = 11/21

Step 5

Decimal & Percentage Representation

Dividing the numerator 11 by denominator 21 produces a repeating decimal (approximately 0.52381, or 52.381%).

11 ÷ 21 = 0.52381 (52.381%)

Visual Representation

The diagram below illustrates 5/35 plus 8/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`11/21`
Mixed Number Form	`11/21`
Decimal Form	`0.52381`
Percentage	`52.381%`

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Frequently Asked Questions

What is 5/35 plus 8/21 as a fraction?

5/35 + 8/21 in simplest fraction form is 11/21.

What is 5/35 plus 8/21 as a decimal?

5/35 + 8/21 converted to a decimal is 0.52381.

What is 5/35 plus 8/21 as a percentage?

5/35 + 8/21 expressed as a percentage is 52.381%.

Does 5/35 plus 8/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.52381...) because the denominator contains prime factors other than 2 and 5.