What is 4/5 plus 9/10? (Answer: 17/10)

Exact Answer

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Problem: What is 4/5 plus 9/10?
Formula / Expression: 4/5 + 9/10
Final Answer: 1 7/10 (17/10)
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
Notice that 10 is an exact multiple of 5 (5 × 2 = 10). The Least Common Denominator (LCD) is simply 10, meaning we only need to scale one fraction.
Working: LCD(5, 10) = 10

Step 2: Convert to Equivalent Fractions with Common Denominator 10
Multiply the numerator and denominator of 4/5 by 2, and multiply the numerator and denominator of 9/10 by 1 so both fractions share the common base 10.
Working: 4 × 2/5 × 2 = 8/10 and 9 × 1/10 × 1 = 9/10

Step 3: Add the Numerators
Now add the numerators (8 + 9 = 17) and keep the common denominator 10 unchanged.
Working: 8 + 9/10 = 17/10

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 17 and 10 is 1, confirming that 17/10 cannot be reduced further—it is already in its simplest irreducible form.
Working: 17/10

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (17) is greater than the denominator (10), divide 17 by 10: it goes in 1 whole time(s) with a remainder of 7, giving the mixed number 1 7/10.
Working: 17/10 = 1 7/10

Step 6: Decimal & Percentage Representation
Dividing the numerator 17 by denominator 10 yields an exact terminating decimal of 1.7 (or 170%).
Working: 17 ÷ 10 = 1.7 (170%)

Key Values:
- Simplified Fraction: 17/10
- Mixed Number Form: 1 7/10
- Decimal Value: 1.7
- Percentage: 170%

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4/5 + 9/10 = 17/10

Simplified Fraction

17/10

Mixed Number

1 7/10

Decimal Value

1.7

Percentage

170%

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Step-by-Step Solution: 4/5 + 9/10

Step 1

Find the Least Common Denominator (LCD)

Notice that 10 is an exact multiple of 5 (5 × 2 = 10). The Least Common Denominator (LCD) is simply 10, meaning we only need to scale one fraction.

LCD(5, 10) = 10

Step 2

Convert to Equivalent Fractions with Common Denominator 10

Multiply the numerator and denominator of 4/5 by 2, and multiply the numerator and denominator of 9/10 by 1 so both fractions share the common base 10.

4 × 2/5 × 2 = 8/10 and 9 × 1/10 × 1 = 9/10

Step 3

Add the Numerators

Now add the numerators (8 + 9 = 17) and keep the common denominator 10 unchanged.

8 + 9/10 = 17/10

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 17 and 10 is 1, confirming that 17/10 cannot be reduced further—it is already in its simplest irreducible form.

17/10

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (17) is greater than the denominator (10), divide 17 by 10: it goes in 1 whole time(s) with a remainder of 7, giving the mixed number 1 7/10.

17/10 = 17/10

Step 6

Decimal & Percentage Representation

Dividing the numerator 17 by denominator 10 yields an exact terminating decimal of 1.7 (or 170%).

17 ÷ 10 = 1.7 (170%)

Visual Representation

The diagram below illustrates 4/5 plus 9/10 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`17/10`
Mixed Number Form	`1 7/10`
Decimal Form	`1.7`
Percentage	`170%`

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Frequently Asked Questions

What is 4/5 plus 9/10 as a fraction?

4/5 + 9/10 in simplest fraction form is 17/10 (or 1 7/10 as a mixed number).

What is 4/5 plus 9/10 as a decimal?

4/5 + 9/10 converted to a decimal is 1.7.

What is 4/5 plus 9/10 as a percentage?

4/5 + 9/10 expressed as a percentage is 170%.

How do you write 4/5 plus 9/10 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 17/10 can be written as the mixed number 1 7/10.

Does 4/5 plus 9/10 result in a terminating or repeating decimal?

It results in an exact terminating decimal (1.7) because the denominator in simplest terms contains only prime factors 2 and/or 5.