What is 2/7 plus 4/10? (Answer: 24/35)

Exact Answer

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Problem: What is 2/7 plus 4/10?
Formula / Expression: 2/7 + 4/10
Final Answer: 24/35
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Step-by-Step Solution:

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

Step 2: Convert to Equivalent Fractions with Common Denominator 70
Multiply the numerator and denominator of 2/7 by 10, and multiply the numerator and denominator of 4/10 by 7 so both fractions share the common base 70.
Working: 2 × 10/7 × 10 = 20/70 and 4 × 7/10 × 7 = 28/70

Step 3: Add the Numerators
Now add the numerators (20 + 28 = 48) and keep the common denominator 70 unchanged.
Working: 20 + 28/70 = 48/70

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 48 and 70, which is 2. Divide both the numerator and denominator by 2.
Working: 48 ÷ 2/70 ÷ 2 = 24/35

Step 5: Decimal & Percentage Representation
Dividing the numerator 24 by denominator 35 produces a repeating decimal (approximately 0.685714, or 68.5714%).
Working: 24 ÷ 35 = 0.685714 (68.5714%)

Key Values:
- Simplified Fraction: 24/35
- Mixed Number Form: 24/35
- Decimal Value: 0.685714
- Percentage: 68.5714%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-7-plus-4-10/
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2/7 + 4/10 = 24/35

Simplified Fraction

24/35

Mixed Number

Proper (24/35)

Decimal Value

0.685714

Percentage

68.5714%

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Step-by-Step Solution: 2/7 + 4/10

Step 1

Find the Least Common Denominator (LCD)

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

LCD(7, 10) = 70

Step 2

Convert to Equivalent Fractions with Common Denominator 70

Multiply the numerator and denominator of 2/7 by 10, and multiply the numerator and denominator of 4/10 by 7 so both fractions share the common base 70.

2 × 10/7 × 10 = 20/70 and 4 × 7/10 × 7 = 28/70

Step 3

Add the Numerators

Now add the numerators (20 + 28 = 48) and keep the common denominator 70 unchanged.

20 + 28/70 = 48/70

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 48 and 70, which is 2. Divide both the numerator and denominator by 2.

48 ÷ 2/70 ÷ 2 = 24/35

Step 5

Decimal & Percentage Representation

Dividing the numerator 24 by denominator 35 produces a repeating decimal (approximately 0.685714, or 68.5714%).

24 ÷ 35 = 0.685714 (68.5714%)

Visual Representation

The diagram below illustrates 2/7 plus 4/10 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`24/35`
Mixed Number Form	`24/35`
Decimal Form	`0.685714`
Percentage	`68.5714%`

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Frequently Asked Questions

What is 2/7 plus 4/10 as a fraction?

2/7 + 4/10 in simplest fraction form is 24/35.

What is 2/7 plus 4/10 as a decimal?

2/7 + 4/10 converted to a decimal is 0.685714.

What is 2/7 plus 4/10 as a percentage?

2/7 + 4/10 expressed as a percentage is 68.5714%.

Does 2/7 plus 4/10 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.685714...) because the denominator contains prime factors other than 2 and 5.