What is 5/35 plus 6/21? (Answer: 3/7)

Exact Answer

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Problem: What is 5/35 plus 6/21?
Formula / Expression: 5/35 + 6/21
Final Answer: 3/7
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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 6/21 by 5 so both fractions share the common base 105.
Working: 5 × 3/35 × 3 = 15/105 and 6 × 5/21 × 5 = 30/105

Step 3: Add the Numerators
Now add the numerators (15 + 30 = 45) and keep the common denominator 105 unchanged.
Working: 15 + 30/105 = 45/105

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 45 and 105, which is 15. Divide both the numerator and denominator by 15.
Working: 45 ÷ 15/105 ÷ 15 = 3/7

Step 5: Decimal & Percentage Representation
Dividing the numerator 3 by denominator 7 produces a repeating decimal (approximately 0.428571, or 42.8571%).
Working: 3 ÷ 7 = 0.428571 (42.8571%)

Key Values:
- Simplified Fraction: 3/7
- Mixed Number Form: 3/7
- Decimal Value: 0.428571
- Percentage: 42.8571%

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Solved with FractionsCalc:
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5/35 + 6/21 = 3/7

Simplified Fraction

3/7

Mixed Number

Proper (3/7)

Decimal Value

0.428571

Percentage

42.8571%

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Step-by-Step Solution: 5/35 + 6/21

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 6/21 by 5 so both fractions share the common base 105.

5 × 3/35 × 3 = 15/105 and 6 × 5/21 × 5 = 30/105

Step 3

Add the Numerators

Now add the numerators (15 + 30 = 45) and keep the common denominator 105 unchanged.

15 + 30/105 = 45/105

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 45 and 105, which is 15. Divide both the numerator and denominator by 15.

45 ÷ 15/105 ÷ 15 = 3/7

Step 5

Decimal & Percentage Representation

Dividing the numerator 3 by denominator 7 produces a repeating decimal (approximately 0.428571, or 42.8571%).

3 ÷ 7 = 0.428571 (42.8571%)

Visual Representation

The diagram below illustrates 5/35 plus 6/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`3/7`
Mixed Number Form	`3/7`
Decimal Form	`0.428571`
Percentage	`42.8571%`

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Frequently Asked Questions

What is 5/35 plus 6/21 as a fraction?

5/35 + 6/21 in simplest fraction form is 3/7.

What is 5/35 plus 6/21 as a decimal?

5/35 + 6/21 converted to a decimal is 0.428571.

What is 5/35 plus 6/21 as a percentage?

5/35 + 6/21 expressed as a percentage is 42.8571%.

Does 5/35 plus 6/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.428571...) because the denominator contains prime factors other than 2 and 5.