What is 2/40 plus 9/22? (Answer: 101/220)

Exact Answer

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Problem: What is 2/40 plus 9/22?
Formula / Expression: 2/40 + 9/22
Final Answer: 101/220
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 40 and 22 share a common factor (GCD = 2). Finding their Least Common Multiple gives an LCD of 440 (which is smaller than their product 40 × 22 = 880, keeping the calculation simpler).
Working: LCD(40, 22) = 440

Step 2: Convert to Equivalent Fractions with Common Denominator 440
Multiply the numerator and denominator of 2/40 by 11, and multiply the numerator and denominator of 9/22 by 20 so both fractions share the common base 440.
Working: 2 × 11/40 × 11 = 22/440 and 9 × 20/22 × 20 = 180/440

Step 3: Add the Numerators
Now add the numerators (22 + 180 = 202) and keep the common denominator 440 unchanged.
Working: 22 + 180/440 = 202/440

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 202 and 440, which is 2. Divide both the numerator and denominator by 2.
Working: 202 ÷ 2/440 ÷ 2 = 101/220

Step 5: Decimal & Percentage Representation
Dividing the numerator 101 by denominator 220 produces a repeating decimal (approximately 0.459091, or 45.9091%).
Working: 101 ÷ 220 = 0.459091 (45.9091%)

Key Values:
- Simplified Fraction: 101/220
- Mixed Number Form: 101/220
- Decimal Value: 0.459091
- Percentage: 45.9091%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-40-plus-9-22/
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2/40 + 9/22 = 101/220

Simplified Fraction

101/220

Mixed Number

Proper (101/220)

Decimal Value

0.459091

Percentage

45.9091%

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Step-by-Step Solution: 2/40 + 9/22

Step 1

Find the Least Common Denominator (LCD)

The denominators 40 and 22 share a common factor (GCD = 2). Finding their Least Common Multiple gives an LCD of 440 (which is smaller than their product 40 × 22 = 880, keeping the calculation simpler).

LCD(40, 22) = 440

Step 2

Convert to Equivalent Fractions with Common Denominator 440

Multiply the numerator and denominator of 2/40 by 11, and multiply the numerator and denominator of 9/22 by 20 so both fractions share the common base 440.

2 × 11/40 × 11 = 22/440 and 9 × 20/22 × 20 = 180/440

Step 3

Add the Numerators

Now add the numerators (22 + 180 = 202) and keep the common denominator 440 unchanged.

22 + 180/440 = 202/440

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 202 and 440, which is 2. Divide both the numerator and denominator by 2.

202 ÷ 2/440 ÷ 2 = 101/220

Step 5

Decimal & Percentage Representation

Dividing the numerator 101 by denominator 220 produces a repeating decimal (approximately 0.459091, or 45.9091%).

101 ÷ 220 = 0.459091 (45.9091%)

Visual Representation

The diagram below illustrates 2/40 plus 9/22 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`101/220`
Mixed Number Form	`101/220`
Decimal Form	`0.459091`
Percentage	`45.9091%`

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Frequently Asked Questions

What is 2/40 plus 9/22 as a fraction?

2/40 + 9/22 in simplest fraction form is 101/220.

What is 2/40 plus 9/22 as a decimal?

2/40 + 9/22 converted to a decimal is 0.459091.

What is 2/40 plus 9/22 as a percentage?

2/40 + 9/22 expressed as a percentage is 45.9091%.

Does 2/40 plus 9/22 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.459091...) because the denominator contains prime factors other than 2 and 5.