What is 4/10 plus 7/9?
4/10 plus 7/9 equals 53/45 (or 1 8/45 as a mixed number) (or 1.177778 in decimal form). Learn the step-by-step solution to add 4/10 and 7/9 using Least Common Denominator and simplification.
Exact Answer
4/10 + 7/9 = 53/45
Simplified Fraction
53/45
Mixed Number
1 8/45
Decimal Value
1.177778
Percentage
117.7778%
Step-by-Step Solution: 4/10 + 7/9
Step 1
Find the Least Common Denominator (LCD)
The denominators 10 and 9 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 10 × 9 = 90.
LCD(10, 9) = 90
Step 2
Convert to Equivalent Fractions with Common Denominator 90
Multiply the numerator and denominator of 4/10 by 9, and multiply the numerator and denominator of 7/9 by 10 so both fractions share the common base 90.
4 × 9/10 × 9 = 36/90 and 7 × 10/9 × 10 = 70/90
Step 3
Add the Numerators
Now add the numerators (36 + 70 = 106) and keep the common denominator 90 unchanged.
36 + 70/90 = 106/90
Step 4
Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 106 and 90, which is 2. Divide both the numerator and denominator by 2.
106 ÷ 2/90 ÷ 2 = 53/45
Step 5
Convert Improper Fraction to a Mixed Number
Since the numerator (53) is greater than the denominator (45), divide 53 by 45: it goes in 1 whole time(s) with a remainder of 8, giving the mixed number 1 8/45.
53/45 = 18/45
Step 6
Decimal & Percentage Representation
Dividing the numerator 53 by denominator 45 produces a repeating decimal (approximately 1.177778, or 117.7778%).
53 ÷ 45 = 1.177778 (117.7778%)
Visual Representation
The diagram below illustrates 4/10 plus 7/9 visually:
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Summary & Alternative Representations
| Property / Format | Value |
|---|---|
| Lowest Terms Fraction | 53/45 |
| Mixed Number Form | 1 8/45 |
| Decimal Form | 1.177778 |
| Percentage | 117.7778% |
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Frequently Asked Questions
What is 4/10 plus 7/9 as a fraction?
4/10 + 7/9 in simplest fraction form is 53/45 (or 1 8/45 as a mixed number).
What is 4/10 plus 7/9 as a decimal?
4/10 + 7/9 converted to a decimal is 1.177778.
What is 4/10 plus 7/9 as a percentage?
4/10 + 7/9 expressed as a percentage is 117.7778%.
How do you write 4/10 plus 7/9 as a mixed number?
Because the numerator is greater than the denominator, the improper fraction 53/45 can be written as the mixed number 1 8/45.
Does 4/10 plus 7/9 result in a terminating or repeating decimal?
It results in a repeating decimal (approximately 1.177778...) because the denominator contains prime factors other than 2 and 5.