What is 5/22 plus 3/4? (Answer: 43/44)

Exact Answer

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Problem: What is 5/22 plus 3/4?
Formula / Expression: 5/22 + 3/4
Final Answer: 43/44
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 22 and 4 share a common factor (GCD = 2). Finding their Least Common Multiple gives an LCD of 44 (which is smaller than their product 22 × 4 = 88, keeping the calculation simpler).
Working: LCD(22, 4) = 44

Step 2: Convert to Equivalent Fractions with Common Denominator 44
Multiply the numerator and denominator of 5/22 by 2, and multiply the numerator and denominator of 3/4 by 11 so both fractions share the common base 44.
Working: 5 × 2/22 × 2 = 10/44 and 3 × 11/4 × 11 = 33/44

Step 3: Add the Numerators
Now add the numerators (10 + 33 = 43) and keep the common denominator 44 unchanged.
Working: 10 + 33/44 = 43/44

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 43 and 44 is 1, confirming that 43/44 cannot be reduced further—it is already in its simplest irreducible form.
Working: 43/44

Step 5: Decimal & Percentage Representation
Dividing the numerator 43 by denominator 44 produces a repeating decimal (approximately 0.977273, or 97.7273%).
Working: 43 ÷ 44 = 0.977273 (97.7273%)

Key Values:
- Simplified Fraction: 43/44
- Mixed Number Form: 43/44
- Decimal Value: 0.977273
- Percentage: 97.7273%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-5-22-plus-3-4/
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5/22 + 3/4 = 43/44

Simplified Fraction

43/44

Mixed Number

Proper (43/44)

Decimal Value

0.977273

Percentage

97.7273%

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Step-by-Step Solution: 5/22 + 3/4

Step 1

Find the Least Common Denominator (LCD)

The denominators 22 and 4 share a common factor (GCD = 2). Finding their Least Common Multiple gives an LCD of 44 (which is smaller than their product 22 × 4 = 88, keeping the calculation simpler).

LCD(22, 4) = 44

Step 2

Convert to Equivalent Fractions with Common Denominator 44

Multiply the numerator and denominator of 5/22 by 2, and multiply the numerator and denominator of 3/4 by 11 so both fractions share the common base 44.

5 × 2/22 × 2 = 10/44 and 3 × 11/4 × 11 = 33/44

Step 3

Add the Numerators

Now add the numerators (10 + 33 = 43) and keep the common denominator 44 unchanged.

10 + 33/44 = 43/44

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 43 and 44 is 1, confirming that 43/44 cannot be reduced further—it is already in its simplest irreducible form.

43/44

Step 5

Decimal & Percentage Representation

Dividing the numerator 43 by denominator 44 produces a repeating decimal (approximately 0.977273, or 97.7273%).

43 ÷ 44 = 0.977273 (97.7273%)

Visual Representation

The diagram below illustrates 5/22 plus 3/4 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`43/44`
Mixed Number Form	`43/44`
Decimal Form	`0.977273`
Percentage	`97.7273%`

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Frequently Asked Questions

What is 5/22 plus 3/4 as a fraction?

5/22 + 3/4 in simplest fraction form is 43/44.

What is 5/22 plus 3/4 as a decimal?

5/22 + 3/4 converted to a decimal is 0.977273.

What is 5/22 plus 3/4 as a percentage?

5/22 + 3/4 expressed as a percentage is 97.7273%.

Does 5/22 plus 3/4 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.977273...) because the denominator contains prime factors other than 2 and 5.