What is 5/8 plus 9/10? (Answer: 61/40)

Exact Answer

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Problem: What is 5/8 plus 9/10?
Formula / Expression: 5/8 + 9/10
Final Answer: 1 21/40 (61/40)
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 8 and 10 share a common factor (GCD = 2). Finding their Least Common Multiple gives an LCD of 40 (which is smaller than their product 8 × 10 = 80, keeping the calculation simpler).
Working: LCD(8, 10) = 40

Step 2: Convert to Equivalent Fractions with Common Denominator 40
Multiply the numerator and denominator of 5/8 by 5, and multiply the numerator and denominator of 9/10 by 4 so both fractions share the common base 40.
Working: 5 × 5/8 × 5 = 25/40 and 9 × 4/10 × 4 = 36/40

Step 3: Add the Numerators
Now add the numerators (25 + 36 = 61) and keep the common denominator 40 unchanged.
Working: 25 + 36/40 = 61/40

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 61 and 40 is 1, confirming that 61/40 cannot be reduced further—it is already in its simplest irreducible form.
Working: 61/40

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (61) is greater than the denominator (40), divide 61 by 40: it goes in 1 whole time(s) with a remainder of 21, giving the mixed number 1 21/40.
Working: 61/40 = 1 21/40

Step 6: Decimal & Percentage Representation
Dividing the numerator 61 by denominator 40 yields an exact terminating decimal of 1.525 (or 152.5%).
Working: 61 ÷ 40 = 1.525 (152.5%)

Key Values:
- Simplified Fraction: 61/40
- Mixed Number Form: 1 21/40
- Decimal Value: 1.525
- Percentage: 152.5%

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Solved with FractionsCalc:
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5/8 + 9/10 = 61/40

Simplified Fraction

61/40

Mixed Number

1 21/40

Decimal Value

1.525

Percentage

152.5%

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Step-by-Step Solution: 5/8 + 9/10

Step 1

Find the Least Common Denominator (LCD)

The denominators 8 and 10 share a common factor (GCD = 2). Finding their Least Common Multiple gives an LCD of 40 (which is smaller than their product 8 × 10 = 80, keeping the calculation simpler).

LCD(8, 10) = 40

Step 2

Convert to Equivalent Fractions with Common Denominator 40

Multiply the numerator and denominator of 5/8 by 5, and multiply the numerator and denominator of 9/10 by 4 so both fractions share the common base 40.

5 × 5/8 × 5 = 25/40 and 9 × 4/10 × 4 = 36/40

Step 3

Add the Numerators

Now add the numerators (25 + 36 = 61) and keep the common denominator 40 unchanged.

25 + 36/40 = 61/40

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 61 and 40 is 1, confirming that 61/40 cannot be reduced further—it is already in its simplest irreducible form.

61/40

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (61) is greater than the denominator (40), divide 61 by 40: it goes in 1 whole time(s) with a remainder of 21, giving the mixed number 1 21/40.

61/40 = 121/40

Step 6

Decimal & Percentage Representation

Dividing the numerator 61 by denominator 40 yields an exact terminating decimal of 1.525 (or 152.5%).

61 ÷ 40 = 1.525 (152.5%)

Visual Representation

The diagram below illustrates 5/8 plus 9/10 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`61/40`
Mixed Number Form	`1 21/40`
Decimal Form	`1.525`
Percentage	`152.5%`

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Frequently Asked Questions

What is 5/8 plus 9/10 as a fraction?

5/8 + 9/10 in simplest fraction form is 61/40 (or 1 21/40 as a mixed number).

What is 5/8 plus 9/10 as a decimal?

5/8 + 9/10 converted to a decimal is 1.525.

What is 5/8 plus 9/10 as a percentage?

5/8 + 9/10 expressed as a percentage is 152.5%.

How do you write 5/8 plus 9/10 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 61/40 can be written as the mixed number 1 21/40.

Does 5/8 plus 9/10 result in a terminating or repeating decimal?

It results in an exact terminating decimal (1.525) because the denominator in simplest terms contains only prime factors 2 and/or 5.