What is 4/7 plus 3/5? (Answer: 41/35)

Exact Answer

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Problem: What is 4/7 plus 3/5?
Formula / Expression: 4/7 + 3/5
Final Answer: 1 6/35 (41/35)
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 7 and 5 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 7 × 5 = 35.
Working: LCD(7, 5) = 35

Step 2: Convert to Equivalent Fractions with Common Denominator 35
Multiply the numerator and denominator of 4/7 by 5, and multiply the numerator and denominator of 3/5 by 7 so both fractions share the common base 35.
Working: 4 × 5/7 × 5 = 20/35 and 3 × 7/5 × 7 = 21/35

Step 3: Add the Numerators
Now add the numerators (20 + 21 = 41) and keep the common denominator 35 unchanged.
Working: 20 + 21/35 = 41/35

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 41 and 35 is 1, confirming that 41/35 cannot be reduced further—it is already in its simplest irreducible form.
Working: 41/35

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (41) is greater than the denominator (35), divide 41 by 35: it goes in 1 whole time(s) with a remainder of 6, giving the mixed number 1 6/35.
Working: 41/35 = 1 6/35

Step 6: Decimal & Percentage Representation
Dividing the numerator 41 by denominator 35 produces a repeating decimal (approximately 1.171429, or 117.1429%).
Working: 41 ÷ 35 = 1.171429 (117.1429%)

Key Values:
- Simplified Fraction: 41/35
- Mixed Number Form: 1 6/35
- Decimal Value: 1.171429
- Percentage: 117.1429%

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4/7 + 3/5 = 41/35

Simplified Fraction

41/35

Mixed Number

1 6/35

Decimal Value

1.171429

Percentage

117.1429%

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Step-by-Step Solution: 4/7 + 3/5

Step 1

Find the Least Common Denominator (LCD)

The denominators 7 and 5 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 7 × 5 = 35.

LCD(7, 5) = 35

Step 2

Convert to Equivalent Fractions with Common Denominator 35

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

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

Step 3

Add the Numerators

Now add the numerators (20 + 21 = 41) and keep the common denominator 35 unchanged.

20 + 21/35 = 41/35

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 41 and 35 is 1, confirming that 41/35 cannot be reduced further—it is already in its simplest irreducible form.

41/35

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (41) is greater than the denominator (35), divide 41 by 35: it goes in 1 whole time(s) with a remainder of 6, giving the mixed number 1 6/35.

41/35 = 16/35

Step 6

Decimal & Percentage Representation

Dividing the numerator 41 by denominator 35 produces a repeating decimal (approximately 1.171429, or 117.1429%).

41 ÷ 35 = 1.171429 (117.1429%)

Visual Representation

The diagram below illustrates 4/7 plus 3/5 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`41/35`
Mixed Number Form	`1 6/35`
Decimal Form	`1.171429`
Percentage	`117.1429%`

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Frequently Asked Questions

What is 4/7 plus 3/5 as a fraction?

4/7 + 3/5 in simplest fraction form is 41/35 (or 1 6/35 as a mixed number).

What is 4/7 plus 3/5 as a decimal?

4/7 + 3/5 converted to a decimal is 1.171429.

What is 4/7 plus 3/5 as a percentage?

4/7 + 3/5 expressed as a percentage is 117.1429%.

How do you write 4/7 plus 3/5 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 41/35 can be written as the mixed number 1 6/35.

Does 4/7 plus 3/5 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.171429...) because the denominator contains prime factors other than 2 and 5.