What is 4/10 plus 7/8?
4/10 plus 7/8 equals 51/40 (or 1 11/40 as a mixed number) (or 1.275 in decimal form). Learn the step-by-step solution to add 4/10 and 7/8 using Least Common Denominator and simplification.
Exact Answer
4/10 + 7/8 = 51/40
Simplified Fraction
51/40
Mixed Number
1 11/40
Decimal Value
1.275
Percentage
127.5%
Step-by-Step Solution: 4/10 + 7/8
Step 1
Find the Least Common Denominator (LCD)
The denominators 10 and 8 share a common factor (GCD = 2). Finding their Least Common Multiple gives an LCD of 40 (which is smaller than their product 10 × 8 = 80, keeping the calculation simpler).
LCD(10, 8) = 40
Step 2
Convert to Equivalent Fractions with Common Denominator 40
Multiply the numerator and denominator of 4/10 by 4, and multiply the numerator and denominator of 7/8 by 5 so both fractions share the common base 40.
4 × 4/10 × 4 = 16/40 and 7 × 5/8 × 5 = 35/40
Step 3
Add the Numerators
Now add the numerators (16 + 35 = 51) and keep the common denominator 40 unchanged.
16 + 35/40 = 51/40
Step 4
Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 51 and 40 is 1, confirming that 51/40 cannot be reduced further—it is already in its simplest irreducible form.
51/40
Step 5
Convert Improper Fraction to a Mixed Number
Since the numerator (51) is greater than the denominator (40), divide 51 by 40: it goes in 1 whole time(s) with a remainder of 11, giving the mixed number 1 11/40.
51/40 = 111/40
Step 6
Decimal & Percentage Representation
Dividing the numerator 51 by denominator 40 yields an exact terminating decimal of 1.275 (or 127.5%).
51 ÷ 40 = 1.275 (127.5%)
Visual Representation
The diagram below illustrates 4/10 plus 7/8 visually:
+
=
Summary & Alternative Representations
| Property / Format | Value |
|---|---|
| Lowest Terms Fraction | 51/40 |
| Mixed Number Form | 1 11/40 |
| Decimal Form | 1.275 |
| Percentage | 127.5% |
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Frequently Asked Questions
What is 4/10 plus 7/8 as a fraction?
4/10 + 7/8 in simplest fraction form is 51/40 (or 1 11/40 as a mixed number).
What is 4/10 plus 7/8 as a decimal?
4/10 + 7/8 converted to a decimal is 1.275.
What is 4/10 plus 7/8 as a percentage?
4/10 + 7/8 expressed as a percentage is 127.5%.
How do you write 4/10 plus 7/8 as a mixed number?
Because the numerator is greater than the denominator, the improper fraction 51/40 can be written as the mixed number 1 11/40.
Does 4/10 plus 7/8 result in a terminating or repeating decimal?
It results in an exact terminating decimal (1.275) because the denominator in simplest terms contains only prime factors 2 and/or 5.