What is 4/35 plus 2/7? (Answer: 2/5)

Exact Answer

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Problem: What is 4/35 plus 2/7?
Formula / Expression: 4/35 + 2/7
Final Answer: 2/5
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
Notice that 35 is an exact multiple of 7 (7 × 5 = 35). The Least Common Denominator (LCD) is simply 35, meaning we only need to scale one fraction.
Working: LCD(35, 7) = 35

Step 2: Convert to Equivalent Fractions with Common Denominator 35
Multiply the numerator and denominator of 4/35 by 1, and multiply the numerator and denominator of 2/7 by 5 so both fractions share the common base 35.
Working: 4 × 1/35 × 1 = 4/35 and 2 × 5/7 × 5 = 10/35

Step 3: Add the Numerators
Now add the numerators (4 + 10 = 14) and keep the common denominator 35 unchanged.
Working: 4 + 10/35 = 14/35

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 14 and 35, which is 7. Divide both the numerator and denominator by 7.
Working: 14 ÷ 7/35 ÷ 7 = 2/5

Step 5: Decimal & Percentage Representation
Dividing the numerator 2 by denominator 5 yields an exact terminating decimal of 0.4 (or 40%).
Working: 2 ÷ 5 = 0.4 (40%)

Key Values:
- Simplified Fraction: 2/5
- Mixed Number Form: 2/5
- Decimal Value: 0.4
- Percentage: 40%

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Solved with FractionsCalc:
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4/35 + 2/7 = 2/5

Simplified Fraction

2/5

Mixed Number

Proper (2/5)

Decimal Value

0.4

Percentage

40%

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Step-by-Step Solution: 4/35 + 2/7

Step 1

Find the Least Common Denominator (LCD)

Notice that 35 is an exact multiple of 7 (7 × 5 = 35). The Least Common Denominator (LCD) is simply 35, meaning we only need to scale one fraction.

LCD(35, 7) = 35

Step 2

Convert to Equivalent Fractions with Common Denominator 35

Multiply the numerator and denominator of 4/35 by 1, and multiply the numerator and denominator of 2/7 by 5 so both fractions share the common base 35.

4 × 1/35 × 1 = 4/35 and 2 × 5/7 × 5 = 10/35

Step 3

Add the Numerators

Now add the numerators (4 + 10 = 14) and keep the common denominator 35 unchanged.

4 + 10/35 = 14/35

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 14 and 35, which is 7. Divide both the numerator and denominator by 7.

14 ÷ 7/35 ÷ 7 = 2/5

Step 5

Decimal & Percentage Representation

Dividing the numerator 2 by denominator 5 yields an exact terminating decimal of 0.4 (or 40%).

2 ÷ 5 = 0.4 (40%)

Visual Representation

The diagram below illustrates 4/35 plus 2/7 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`2/5`
Mixed Number Form	`2/5`
Decimal Form	`0.4`
Percentage	`40%`

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Frequently Asked Questions

What is 4/35 plus 2/7 as a fraction?

4/35 + 2/7 in simplest fraction form is 2/5.

What is 4/35 plus 2/7 as a decimal?

4/35 + 2/7 converted to a decimal is 0.4.

What is 4/35 plus 2/7 as a percentage?

4/35 + 2/7 expressed as a percentage is 40%.

Does 4/35 plus 2/7 result in a terminating or repeating decimal?

It results in an exact terminating decimal (0.4) because the denominator in simplest terms contains only prime factors 2 and/or 5.