What is 1/2 plus 9/10? (Answer: 7/5)

Exact Answer

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Problem: What is 1/2 plus 9/10?
Formula / Expression: 1/2 + 9/10
Final Answer: 1 2/5 (7/5)
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Step-by-Step Solution:

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

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

Step 3: Add the Numerators
Now add the numerators (5 + 9 = 14) and keep the common denominator 10 unchanged.
Working: 5 + 9/10 = 14/10

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 14 and 10, which is 2. Divide both the numerator and denominator by 2.
Working: 14 ÷ 2/10 ÷ 2 = 7/5

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (7) is greater than the denominator (5), divide 7 by 5: it goes in 1 whole time(s) with a remainder of 2, giving the mixed number 1 2/5.
Working: 7/5 = 1 2/5

Step 6: Decimal & Percentage Representation
Dividing the numerator 7 by denominator 5 yields an exact terminating decimal of 1.4 (or 140%).
Working: 7 ÷ 5 = 1.4 (140%)

Key Values:
- Simplified Fraction: 7/5
- Mixed Number Form: 1 2/5
- Decimal Value: 1.4
- Percentage: 140%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-1-2-plus-9-10/
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1/2 + 9/10 = 7/5

Simplified Fraction

7/5

Mixed Number

1 2/5

Decimal Value

1.4

Percentage

140%

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Step-by-Step Solution: 1/2 + 9/10

Step 1

Find the Least Common Denominator (LCD)

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

LCD(2, 10) = 10

Step 2

Convert to Equivalent Fractions with Common Denominator 10

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

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

Step 3

Add the Numerators

Now add the numerators (5 + 9 = 14) and keep the common denominator 10 unchanged.

5 + 9/10 = 14/10

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 14 and 10, which is 2. Divide both the numerator and denominator by 2.

14 ÷ 2/10 ÷ 2 = 7/5

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (7) is greater than the denominator (5), divide 7 by 5: it goes in 1 whole time(s) with a remainder of 2, giving the mixed number 1 2/5.

7/5 = 12/5

Step 6

Decimal & Percentage Representation

Dividing the numerator 7 by denominator 5 yields an exact terminating decimal of 1.4 (or 140%).

7 ÷ 5 = 1.4 (140%)

Visual Representation

The diagram below illustrates 1/2 plus 9/10 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`7/5`
Mixed Number Form	`1 2/5`
Decimal Form	`1.4`
Percentage	`140%`

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Frequently Asked Questions

What is 1/2 plus 9/10 as a fraction?

1/2 + 9/10 in simplest fraction form is 7/5 (or 1 2/5 as a mixed number).

What is 1/2 plus 9/10 as a decimal?

1/2 + 9/10 converted to a decimal is 1.4.

What is 1/2 plus 9/10 as a percentage?

1/2 + 9/10 expressed as a percentage is 140%.

How do you write 1/2 plus 9/10 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 7/5 can be written as the mixed number 1 2/5.

Does 1/2 plus 9/10 result in a terminating or repeating decimal?

It results in an exact terminating decimal (1.4) because the denominator in simplest terms contains only prime factors 2 and/or 5.