What is 4/9 plus 7/10?
4/9 plus 7/10 equals 103/90 (or 1 13/90 as a mixed number) (or 1.144444 in decimal form). Learn the step-by-step solution to add 4/9 and 7/10 using Least Common Denominator and simplification.
Exact Answer
4/9 + 7/10 = 103/90
Simplified Fraction
103/90
Mixed Number
1 13/90
Decimal Value
1.144444
Percentage
114.4444%
Step-by-Step Solution: 4/9 + 7/10
Step 1
Find the Least Common Denominator (LCD)
The denominators 9 and 10 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 9 × 10 = 90.
LCD(9, 10) = 90
Step 2
Convert to Equivalent Fractions with Common Denominator 90
Multiply the numerator and denominator of 4/9 by 10, and multiply the numerator and denominator of 7/10 by 9 so both fractions share the common base 90.
4 × 10/9 × 10 = 40/90 and 7 × 9/10 × 9 = 63/90
Step 3
Add the Numerators
Now add the numerators (40 + 63 = 103) and keep the common denominator 90 unchanged.
40 + 63/90 = 103/90
Step 4
Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 103 and 90 is 1, confirming that 103/90 cannot be reduced further—it is already in its simplest irreducible form.
103/90
Step 5
Convert Improper Fraction to a Mixed Number
Since the numerator (103) is greater than the denominator (90), divide 103 by 90: it goes in 1 whole time(s) with a remainder of 13, giving the mixed number 1 13/90.
103/90 = 113/90
Step 6
Decimal & Percentage Representation
Dividing the numerator 103 by denominator 90 produces a repeating decimal (approximately 1.144444, or 114.4444%).
103 ÷ 90 = 1.144444 (114.4444%)
Visual Representation
The diagram below illustrates 4/9 plus 7/10 visually:
+
=
Summary & Alternative Representations
| Property / Format | Value |
|---|---|
| Lowest Terms Fraction | 103/90 |
| Mixed Number Form | 1 13/90 |
| Decimal Form | 1.144444 |
| Percentage | 114.4444% |
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Frequently Asked Questions
What is 4/9 plus 7/10 as a fraction?
4/9 + 7/10 in simplest fraction form is 103/90 (or 1 13/90 as a mixed number).
What is 4/9 plus 7/10 as a decimal?
4/9 + 7/10 converted to a decimal is 1.144444.
What is 4/9 plus 7/10 as a percentage?
4/9 + 7/10 expressed as a percentage is 114.4444%.
How do you write 4/9 plus 7/10 as a mixed number?
Because the numerator is greater than the denominator, the improper fraction 103/90 can be written as the mixed number 1 13/90.
Does 4/9 plus 7/10 result in a terminating or repeating decimal?
It results in a repeating decimal (approximately 1.144444...) because the denominator contains prime factors other than 2 and 5.