What is 3/4 plus 9/10? (Answer: 33/20)

Exact Answer

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Problem: What is 3/4 plus 9/10?
Formula / Expression: 3/4 + 9/10
Final Answer: 1 13/20 (33/20)
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 4 and 10 share a common factor (GCD = 2). Finding their Least Common Multiple gives an LCD of 20 (which is smaller than their product 4 × 10 = 40, keeping the calculation simpler).
Working: LCD(4, 10) = 20

Step 2: Convert to Equivalent Fractions with Common Denominator 20
Multiply the numerator and denominator of 3/4 by 5, and multiply the numerator and denominator of 9/10 by 2 so both fractions share the common base 20.
Working: 3 × 5/4 × 5 = 15/20 and 9 × 2/10 × 2 = 18/20

Step 3: Add the Numerators
Now add the numerators (15 + 18 = 33) and keep the common denominator 20 unchanged.
Working: 15 + 18/20 = 33/20

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 33 and 20 is 1, confirming that 33/20 cannot be reduced further—it is already in its simplest irreducible form.
Working: 33/20

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (33) is greater than the denominator (20), divide 33 by 20: it goes in 1 whole time(s) with a remainder of 13, giving the mixed number 1 13/20.
Working: 33/20 = 1 13/20

Step 6: Decimal & Percentage Representation
Dividing the numerator 33 by denominator 20 yields an exact terminating decimal of 1.65 (or 165%).
Working: 33 ÷ 20 = 1.65 (165%)

Key Values:
- Simplified Fraction: 33/20
- Mixed Number Form: 1 13/20
- Decimal Value: 1.65
- Percentage: 165%

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Solved with FractionsCalc:
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3/4 + 9/10 = 33/20

Simplified Fraction

33/20

Mixed Number

1 13/20

Decimal Value

1.65

Percentage

165%

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Step-by-Step Solution: 3/4 + 9/10

Step 1

Find the Least Common Denominator (LCD)

The denominators 4 and 10 share a common factor (GCD = 2). Finding their Least Common Multiple gives an LCD of 20 (which is smaller than their product 4 × 10 = 40, keeping the calculation simpler).

LCD(4, 10) = 20

Step 2

Convert to Equivalent Fractions with Common Denominator 20

Multiply the numerator and denominator of 3/4 by 5, and multiply the numerator and denominator of 9/10 by 2 so both fractions share the common base 20.

3 × 5/4 × 5 = 15/20 and 9 × 2/10 × 2 = 18/20

Step 3

Add the Numerators

Now add the numerators (15 + 18 = 33) and keep the common denominator 20 unchanged.

15 + 18/20 = 33/20

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 33 and 20 is 1, confirming that 33/20 cannot be reduced further—it is already in its simplest irreducible form.

33/20

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (33) is greater than the denominator (20), divide 33 by 20: it goes in 1 whole time(s) with a remainder of 13, giving the mixed number 1 13/20.

33/20 = 113/20

Step 6

Decimal & Percentage Representation

Dividing the numerator 33 by denominator 20 yields an exact terminating decimal of 1.65 (or 165%).

33 ÷ 20 = 1.65 (165%)

Visual Representation

The diagram below illustrates 3/4 plus 9/10 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`33/20`
Mixed Number Form	`1 13/20`
Decimal Form	`1.65`
Percentage	`165%`

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Frequently Asked Questions

What is 3/4 plus 9/10 as a fraction?

3/4 + 9/10 in simplest fraction form is 33/20 (or 1 13/20 as a mixed number).

What is 3/4 plus 9/10 as a decimal?

3/4 + 9/10 converted to a decimal is 1.65.

What is 3/4 plus 9/10 as a percentage?

3/4 + 9/10 expressed as a percentage is 165%.

How do you write 3/4 plus 9/10 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 33/20 can be written as the mixed number 1 13/20.

Does 3/4 plus 9/10 result in a terminating or repeating decimal?

It results in an exact terminating decimal (1.65) because the denominator in simplest terms contains only prime factors 2 and/or 5.