What is 1/35 plus 4/21? (Answer: 23/105)

Exact Answer

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Problem: What is 1/35 plus 4/21?
Formula / Expression: 1/35 + 4/21
Final Answer: 23/105
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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 1/35 by 3, and multiply the numerator and denominator of 4/21 by 5 so both fractions share the common base 105.
Working: 1 × 3/35 × 3 = 3/105 and 4 × 5/21 × 5 = 20/105

Step 3: Add the Numerators
Now add the numerators (3 + 20 = 23) and keep the common denominator 105 unchanged.
Working: 3 + 20/105 = 23/105

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 23 and 105 is 1, confirming that 23/105 cannot be reduced further—it is already in its simplest irreducible form.
Working: 23/105

Step 5: Decimal & Percentage Representation
Dividing the numerator 23 by denominator 105 produces a repeating decimal (approximately 0.219048, or 21.9048%).
Working: 23 ÷ 105 = 0.219048 (21.9048%)

Key Values:
- Simplified Fraction: 23/105
- Mixed Number Form: 23/105
- Decimal Value: 0.219048
- Percentage: 21.9048%

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Solved with FractionsCalc:
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1/35 + 4/21 = 23/105

Simplified Fraction

23/105

Mixed Number

Proper (23/105)

Decimal Value

0.219048

Percentage

21.9048%

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Step-by-Step Solution: 1/35 + 4/21

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 1/35 by 3, and multiply the numerator and denominator of 4/21 by 5 so both fractions share the common base 105.

1 × 3/35 × 3 = 3/105 and 4 × 5/21 × 5 = 20/105

Step 3

Add the Numerators

Now add the numerators (3 + 20 = 23) and keep the common denominator 105 unchanged.

3 + 20/105 = 23/105

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 23 and 105 is 1, confirming that 23/105 cannot be reduced further—it is already in its simplest irreducible form.

23/105

Step 5

Decimal & Percentage Representation

Dividing the numerator 23 by denominator 105 produces a repeating decimal (approximately 0.219048, or 21.9048%).

23 ÷ 105 = 0.219048 (21.9048%)

Visual Representation

The diagram below illustrates 1/35 plus 4/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`23/105`
Mixed Number Form	`23/105`
Decimal Form	`0.219048`
Percentage	`21.9048%`

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Frequently Asked Questions

What is 1/35 plus 4/21 as a fraction?

1/35 + 4/21 in simplest fraction form is 23/105.

What is 1/35 plus 4/21 as a decimal?

1/35 + 4/21 converted to a decimal is 0.219048.

What is 1/35 plus 4/21 as a percentage?

1/35 + 4/21 expressed as a percentage is 21.9048%.

Does 1/35 plus 4/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.219048...) because the denominator contains prime factors other than 2 and 5.