What is 7/8 plus 9/10? (Answer: 71/40)

Exact Answer

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Problem: What is 7/8 plus 9/10?
Formula / Expression: 7/8 + 9/10
Final Answer: 1 31/40 (71/40)
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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 7/8 by 5, and multiply the numerator and denominator of 9/10 by 4 so both fractions share the common base 40.
Working: 7 × 5/8 × 5 = 35/40 and 9 × 4/10 × 4 = 36/40

Step 3: Add the Numerators
Now add the numerators (35 + 36 = 71) and keep the common denominator 40 unchanged.
Working: 35 + 36/40 = 71/40

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 71 and 40 is 1, confirming that 71/40 cannot be reduced further—it is already in its simplest irreducible form.
Working: 71/40

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (71) is greater than the denominator (40), divide 71 by 40: it goes in 1 whole time(s) with a remainder of 31, giving the mixed number 1 31/40.
Working: 71/40 = 1 31/40

Step 6: Decimal & Percentage Representation
Dividing the numerator 71 by denominator 40 yields an exact terminating decimal of 1.775 (or 177.5%).
Working: 71 ÷ 40 = 1.775 (177.5%)

Key Values:
- Simplified Fraction: 71/40
- Mixed Number Form: 1 31/40
- Decimal Value: 1.775
- Percentage: 177.5%

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Solved with FractionsCalc:
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7/8 + 9/10 = 71/40

Simplified Fraction

71/40

Mixed Number

1 31/40

Decimal Value

1.775

Percentage

177.5%

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Step-by-Step Solution: 7/8 + 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 7/8 by 5, and multiply the numerator and denominator of 9/10 by 4 so both fractions share the common base 40.

7 × 5/8 × 5 = 35/40 and 9 × 4/10 × 4 = 36/40

Step 3

Add the Numerators

Now add the numerators (35 + 36 = 71) and keep the common denominator 40 unchanged.

35 + 36/40 = 71/40

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 71 and 40 is 1, confirming that 71/40 cannot be reduced further—it is already in its simplest irreducible form.

71/40

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (71) is greater than the denominator (40), divide 71 by 40: it goes in 1 whole time(s) with a remainder of 31, giving the mixed number 1 31/40.

71/40 = 131/40

Step 6

Decimal & Percentage Representation

Dividing the numerator 71 by denominator 40 yields an exact terminating decimal of 1.775 (or 177.5%).

71 ÷ 40 = 1.775 (177.5%)

Visual Representation

The diagram below illustrates 7/8 plus 9/10 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`71/40`
Mixed Number Form	`1 31/40`
Decimal Form	`1.775`
Percentage	`177.5%`

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Frequently Asked Questions

What is 7/8 plus 9/10 as a fraction?

7/8 + 9/10 in simplest fraction form is 71/40 (or 1 31/40 as a mixed number).

What is 7/8 plus 9/10 as a decimal?

7/8 + 9/10 converted to a decimal is 1.775.

What is 7/8 plus 9/10 as a percentage?

7/8 + 9/10 expressed as a percentage is 177.5%.

How do you write 7/8 plus 9/10 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 71/40 can be written as the mixed number 1 31/40.

Does 7/8 plus 9/10 result in a terminating or repeating decimal?

It results in an exact terminating decimal (1.775) because the denominator in simplest terms contains only prime factors 2 and/or 5.