What is 7/35 plus 2/8? (Answer: 9/20)

Exact Answer

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Problem: What is 7/35 plus 2/8?
Formula / Expression: 7/35 + 2/8
Final Answer: 9/20
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 35 and 8 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 35 × 8 = 280.
Working: LCD(35, 8) = 280

Step 2: Convert to Equivalent Fractions with Common Denominator 280
Multiply the numerator and denominator of 7/35 by 8, and multiply the numerator and denominator of 2/8 by 35 so both fractions share the common base 280.
Working: 7 × 8/35 × 8 = 56/280 and 2 × 35/8 × 35 = 70/280

Step 3: Add the Numerators
Now add the numerators (56 + 70 = 126) and keep the common denominator 280 unchanged.
Working: 56 + 70/280 = 126/280

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 126 and 280, which is 14. Divide both the numerator and denominator by 14.
Working: 126 ÷ 14/280 ÷ 14 = 9/20

Step 5: Decimal & Percentage Representation
Dividing the numerator 9 by denominator 20 yields an exact terminating decimal of 0.45 (or 45%).
Working: 9 ÷ 20 = 0.45 (45%)

Key Values:
- Simplified Fraction: 9/20
- Mixed Number Form: 9/20
- Decimal Value: 0.45
- Percentage: 45%

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7/35 + 2/8 = 9/20

Simplified Fraction

9/20

Mixed Number

Proper (9/20)

Decimal Value

0.45

Percentage

45%

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Step-by-Step Solution: 7/35 + 2/8

Step 1

Find the Least Common Denominator (LCD)

The denominators 35 and 8 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 35 × 8 = 280.

LCD(35, 8) = 280

Step 2

Convert to Equivalent Fractions with Common Denominator 280

Multiply the numerator and denominator of 7/35 by 8, and multiply the numerator and denominator of 2/8 by 35 so both fractions share the common base 280.

7 × 8/35 × 8 = 56/280 and 2 × 35/8 × 35 = 70/280

Step 3

Add the Numerators

Now add the numerators (56 + 70 = 126) and keep the common denominator 280 unchanged.

56 + 70/280 = 126/280

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 126 and 280, which is 14. Divide both the numerator and denominator by 14.

126 ÷ 14/280 ÷ 14 = 9/20

Step 5

Decimal & Percentage Representation

Dividing the numerator 9 by denominator 20 yields an exact terminating decimal of 0.45 (or 45%).

9 ÷ 20 = 0.45 (45%)

Visual Representation

The diagram below illustrates 7/35 plus 2/8 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`9/20`
Mixed Number Form	`9/20`
Decimal Form	`0.45`
Percentage	`45%`

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Frequently Asked Questions

What is 7/35 plus 2/8 as a fraction?

7/35 + 2/8 in simplest fraction form is 9/20.

What is 7/35 plus 2/8 as a decimal?

7/35 + 2/8 converted to a decimal is 0.45.

What is 7/35 plus 2/8 as a percentage?

7/35 + 2/8 expressed as a percentage is 45%.

Does 7/35 plus 2/8 result in a terminating or repeating decimal?

It results in an exact terminating decimal (0.45) because the denominator in simplest terms contains only prime factors 2 and/or 5.