What is 4/21 plus 7/35? (Answer: 41/105)

Exact Answer

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Problem: What is 4/21 plus 7/35?
Formula / Expression: 4/21 + 7/35
Final Answer: 41/105
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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 4/21 by 5, and multiply the numerator and denominator of 7/35 by 3 so both fractions share the common base 105.
Working: 4 × 5/21 × 5 = 20/105 and 7 × 3/35 × 3 = 21/105

Step 3: Add the Numerators
Now add the numerators (20 + 21 = 41) and keep the common denominator 105 unchanged.
Working: 20 + 21/105 = 41/105

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 41 and 105 is 1, confirming that 41/105 cannot be reduced further—it is already in its simplest irreducible form.
Working: 41/105

Step 5: Decimal & Percentage Representation
Dividing the numerator 41 by denominator 105 produces a repeating decimal (approximately 0.390476, or 39.0476%).
Working: 41 ÷ 105 = 0.390476 (39.0476%)

Key Values:
- Simplified Fraction: 41/105
- Mixed Number Form: 41/105
- Decimal Value: 0.390476
- Percentage: 39.0476%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-4-21-plus-7-35/
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4/21 + 7/35 = 41/105

Simplified Fraction

41/105

Mixed Number

Proper (41/105)

Decimal Value

0.390476

Percentage

39.0476%

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Step-by-Step Solution: 4/21 + 7/35

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 4/21 by 5, and multiply the numerator and denominator of 7/35 by 3 so both fractions share the common base 105.

4 × 5/21 × 5 = 20/105 and 7 × 3/35 × 3 = 21/105

Step 3

Add the Numerators

Now add the numerators (20 + 21 = 41) and keep the common denominator 105 unchanged.

20 + 21/105 = 41/105

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 41 and 105 is 1, confirming that 41/105 cannot be reduced further—it is already in its simplest irreducible form.

41/105

Step 5

Decimal & Percentage Representation

Dividing the numerator 41 by denominator 105 produces a repeating decimal (approximately 0.390476, or 39.0476%).

41 ÷ 105 = 0.390476 (39.0476%)

Visual Representation

The diagram below illustrates 4/21 plus 7/35 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`41/105`
Mixed Number Form	`41/105`
Decimal Form	`0.390476`
Percentage	`39.0476%`

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Frequently Asked Questions

What is 4/21 plus 7/35 as a fraction?

4/21 + 7/35 in simplest fraction form is 41/105.

What is 4/21 plus 7/35 as a decimal?

4/21 + 7/35 converted to a decimal is 0.390476.

What is 4/21 plus 7/35 as a percentage?

4/21 + 7/35 expressed as a percentage is 39.0476%.

Does 4/21 plus 7/35 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.390476...) because the denominator contains prime factors other than 2 and 5.