What is 4/10 plus 3/7? (Answer: 29/35)

Exact Answer

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Problem: What is 4/10 plus 3/7?
Formula / Expression: 4/10 + 3/7
Final Answer: 29/35
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 10 and 7 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 10 × 7 = 70.
Working: LCD(10, 7) = 70

Step 2: Convert to Equivalent Fractions with Common Denominator 70
Multiply the numerator and denominator of 4/10 by 7, and multiply the numerator and denominator of 3/7 by 10 so both fractions share the common base 70.
Working: 4 × 7/10 × 7 = 28/70 and 3 × 10/7 × 10 = 30/70

Step 3: Add the Numerators
Now add the numerators (28 + 30 = 58) and keep the common denominator 70 unchanged.
Working: 28 + 30/70 = 58/70

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 58 and 70, which is 2. Divide both the numerator and denominator by 2.
Working: 58 ÷ 2/70 ÷ 2 = 29/35

Step 5: Decimal & Percentage Representation
Dividing the numerator 29 by denominator 35 produces a repeating decimal (approximately 0.828571, or 82.8571%).
Working: 29 ÷ 35 = 0.828571 (82.8571%)

Key Values:
- Simplified Fraction: 29/35
- Mixed Number Form: 29/35
- Decimal Value: 0.828571
- Percentage: 82.8571%

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Solved with FractionsCalc:
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4/10 + 3/7 = 29/35

Simplified Fraction

29/35

Mixed Number

Proper (29/35)

Decimal Value

0.828571

Percentage

82.8571%

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Step-by-Step Solution: 4/10 + 3/7

Step 1

Find the Least Common Denominator (LCD)

The denominators 10 and 7 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 10 × 7 = 70.

LCD(10, 7) = 70

Step 2

Convert to Equivalent Fractions with Common Denominator 70

Multiply the numerator and denominator of 4/10 by 7, and multiply the numerator and denominator of 3/7 by 10 so both fractions share the common base 70.

4 × 7/10 × 7 = 28/70 and 3 × 10/7 × 10 = 30/70

Step 3

Add the Numerators

Now add the numerators (28 + 30 = 58) and keep the common denominator 70 unchanged.

28 + 30/70 = 58/70

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 58 and 70, which is 2. Divide both the numerator and denominator by 2.

58 ÷ 2/70 ÷ 2 = 29/35

Step 5

Decimal & Percentage Representation

Dividing the numerator 29 by denominator 35 produces a repeating decimal (approximately 0.828571, or 82.8571%).

29 ÷ 35 = 0.828571 (82.8571%)

Visual Representation

The diagram below illustrates 4/10 plus 3/7 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`29/35`
Mixed Number Form	`29/35`
Decimal Form	`0.828571`
Percentage	`82.8571%`

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Frequently Asked Questions

What is 4/10 plus 3/7 as a fraction?

4/10 + 3/7 in simplest fraction form is 29/35.

What is 4/10 plus 3/7 as a decimal?

4/10 + 3/7 converted to a decimal is 0.828571.

What is 4/10 plus 3/7 as a percentage?

4/10 + 3/7 expressed as a percentage is 82.8571%.

Does 4/10 plus 3/7 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.828571...) because the denominator contains prime factors other than 2 and 5.