What is 9/32 plus 2/5? (Answer: 109/160)

Exact Answer

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Problem: What is 9/32 plus 2/5?
Formula / Expression: 9/32 + 2/5
Final Answer: 109/160
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 32 and 5 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 32 × 5 = 160.
Working: LCD(32, 5) = 160

Step 2: Convert to Equivalent Fractions with Common Denominator 160
Multiply the numerator and denominator of 9/32 by 5, and multiply the numerator and denominator of 2/5 by 32 so both fractions share the common base 160.
Working: 9 × 5/32 × 5 = 45/160 and 2 × 32/5 × 32 = 64/160

Step 3: Add the Numerators
Now add the numerators (45 + 64 = 109) and keep the common denominator 160 unchanged.
Working: 45 + 64/160 = 109/160

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 109 and 160 is 1, confirming that 109/160 cannot be reduced further—it is already in its simplest irreducible form.
Working: 109/160

Step 5: Decimal & Percentage Representation
Dividing the numerator 109 by denominator 160 yields an exact terminating decimal of 0.68125 (or 68.125%).
Working: 109 ÷ 160 = 0.68125 (68.125%)

Key Values:
- Simplified Fraction: 109/160
- Mixed Number Form: 109/160
- Decimal Value: 0.68125
- Percentage: 68.125%

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9/32 + 2/5 = 109/160

Simplified Fraction

109/160

Mixed Number

Proper (109/160)

Decimal Value

0.68125

Percentage

68.125%

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Step-by-Step Solution: 9/32 + 2/5

Step 1

Find the Least Common Denominator (LCD)

The denominators 32 and 5 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 32 × 5 = 160.

LCD(32, 5) = 160

Step 2

Convert to Equivalent Fractions with Common Denominator 160

Multiply the numerator and denominator of 9/32 by 5, and multiply the numerator and denominator of 2/5 by 32 so both fractions share the common base 160.

9 × 5/32 × 5 = 45/160 and 2 × 32/5 × 32 = 64/160

Step 3

Add the Numerators

Now add the numerators (45 + 64 = 109) and keep the common denominator 160 unchanged.

45 + 64/160 = 109/160

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 109 and 160 is 1, confirming that 109/160 cannot be reduced further—it is already in its simplest irreducible form.

109/160

Step 5

Decimal & Percentage Representation

Dividing the numerator 109 by denominator 160 yields an exact terminating decimal of 0.68125 (or 68.125%).

109 ÷ 160 = 0.68125 (68.125%)

Visual Representation

The diagram below illustrates 9/32 plus 2/5 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`109/160`
Mixed Number Form	`109/160`
Decimal Form	`0.68125`
Percentage	`68.125%`

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Frequently Asked Questions

What is 9/32 plus 2/5 as a fraction?

9/32 + 2/5 in simplest fraction form is 109/160.

What is 9/32 plus 2/5 as a decimal?

9/32 + 2/5 converted to a decimal is 0.68125.

What is 9/32 plus 2/5 as a percentage?

9/32 + 2/5 expressed as a percentage is 68.125%.

Does 9/32 plus 2/5 result in a terminating or repeating decimal?

It results in an exact terminating decimal (0.68125) because the denominator in simplest terms contains only prime factors 2 and/or 5.