What is 3/4 plus 7/8?
3/4 plus 7/8 equals 13/8 (or 1 5/8 as a mixed number) (or 1.625 in decimal form). Learn the step-by-step solution to add 3/4 and 7/8 using Least Common Denominator and simplification.
Exact Answer
3/4 + 7/8 = 13/8
Simplified Fraction
13/8
Mixed Number
1 5/8
Decimal Value
1.625
Percentage
162.5%
Step-by-Step Solution: 3/4 + 7/8
Step 1
Find the Least Common Denominator (LCD)
Notice that 8 is an exact multiple of 4 (4 × 2 = 8). The Least Common Denominator (LCD) is simply 8, meaning we only need to scale one fraction.
LCD(4, 8) = 8
Step 2
Convert to Equivalent Fractions with Common Denominator 8
Multiply the numerator and denominator of 3/4 by 2, and multiply the numerator and denominator of 7/8 by 1 so both fractions share the common base 8.
3 × 2/4 × 2 = 6/8 and 7 × 1/8 × 1 = 7/8
Step 3
Add the Numerators
Now add the numerators (6 + 7 = 13) and keep the common denominator 8 unchanged.
6 + 7/8 = 13/8
Step 4
Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 13 and 8 is 1, confirming that 13/8 cannot be reduced further—it is already in its simplest irreducible form.
13/8
Step 5
Convert Improper Fraction to a Mixed Number
Since the numerator (13) is greater than the denominator (8), divide 13 by 8: it goes in 1 whole time(s) with a remainder of 5, giving the mixed number 1 5/8.
13/8 = 15/8
Step 6
Decimal & Percentage Representation
Dividing the numerator 13 by denominator 8 yields an exact terminating decimal of 1.625 (or 162.5%).
13 ÷ 8 = 1.625 (162.5%)
Visual Representation
The diagram below illustrates 3/4 plus 7/8 visually:
+
=
Summary & Alternative Representations
| Property / Format | Value |
|---|---|
| Lowest Terms Fraction | 13/8 |
| Mixed Number Form | 1 5/8 |
| Decimal Form | 1.625 |
| Percentage | 162.5% |
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Frequently Asked Questions
What is 3/4 plus 7/8 as a fraction?
3/4 + 7/8 in simplest fraction form is 13/8 (or 1 5/8 as a mixed number).
What is 3/4 plus 7/8 as a decimal?
3/4 + 7/8 converted to a decimal is 1.625.
What is 3/4 plus 7/8 as a percentage?
3/4 + 7/8 expressed as a percentage is 162.5%.
How do you write 3/4 plus 7/8 as a mixed number?
Because the numerator is greater than the denominator, the improper fraction 13/8 can be written as the mixed number 1 5/8.
Does 3/4 plus 7/8 result in a terminating or repeating decimal?
It results in an exact terminating decimal (1.625) because the denominator in simplest terms contains only prime factors 2 and/or 5.