What is 3/8 plus 7/10?
3/8 plus 7/10 equals 43/40 (or 1 3/40 as a mixed number) (or 1.075 in decimal form). Learn the step-by-step solution to add 3/8 and 7/10 using Least Common Denominator and simplification.
Exact Answer
3/8 + 7/10 = 43/40
Simplified Fraction
43/40
Mixed Number
1 3/40
Decimal Value
1.075
Percentage
107.5%
Step-by-Step Solution: 3/8 + 7/10
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 3/8 by 5, and multiply the numerator and denominator of 7/10 by 4 so both fractions share the common base 40.
3 × 5/8 × 5 = 15/40 and 7 × 4/10 × 4 = 28/40
Step 3
Add the Numerators
Now add the numerators (15 + 28 = 43) and keep the common denominator 40 unchanged.
15 + 28/40 = 43/40
Step 4
Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 43 and 40 is 1, confirming that 43/40 cannot be reduced further—it is already in its simplest irreducible form.
43/40
Step 5
Convert Improper Fraction to a Mixed Number
Since the numerator (43) is greater than the denominator (40), divide 43 by 40: it goes in 1 whole time(s) with a remainder of 3, giving the mixed number 1 3/40.
43/40 = 13/40
Step 6
Decimal & Percentage Representation
Dividing the numerator 43 by denominator 40 yields an exact terminating decimal of 1.075 (or 107.5%).
43 ÷ 40 = 1.075 (107.5%)
Visual Representation
The diagram below illustrates 3/8 plus 7/10 visually:
+
=
Summary & Alternative Representations
| Property / Format | Value |
|---|---|
| Lowest Terms Fraction | 43/40 |
| Mixed Number Form | 1 3/40 |
| Decimal Form | 1.075 |
| Percentage | 107.5% |
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Frequently Asked Questions
What is 3/8 plus 7/10 as a fraction?
3/8 + 7/10 in simplest fraction form is 43/40 (or 1 3/40 as a mixed number).
What is 3/8 plus 7/10 as a decimal?
3/8 + 7/10 converted to a decimal is 1.075.
What is 3/8 plus 7/10 as a percentage?
3/8 + 7/10 expressed as a percentage is 107.5%.
How do you write 3/8 plus 7/10 as a mixed number?
Because the numerator is greater than the denominator, the improper fraction 43/40 can be written as the mixed number 1 3/40.
Does 3/8 plus 7/10 result in a terminating or repeating decimal?
It results in an exact terminating decimal (1.075) because the denominator in simplest terms contains only prime factors 2 and/or 5.