What is 9/21 plus 5/8?
9/21 plus 5/8 equals 59/56 (or 1 3/56 as a mixed number) (or 1.053571 in decimal form). Learn the step-by-step solution to add 9/21 and 5/8 using Least Common Denominator and simplification.
Exact Answer
9/21 + 5/8 = 59/56
Simplified Fraction
59/56
Mixed Number
1 3/56
Decimal Value
1.053571
Percentage
105.3571%
Step-by-Step Solution: 9/21 + 5/8
Step 1
Find the Least Common Denominator (LCD)
The denominators 21 and 8 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 21 × 8 = 168.
LCD(21, 8) = 168
Step 2
Convert to Equivalent Fractions with Common Denominator 168
Multiply the numerator and denominator of 9/21 by 8, and multiply the numerator and denominator of 5/8 by 21 so both fractions share the common base 168.
9 × 8/21 × 8 = 72/168 and 5 × 21/8 × 21 = 105/168
Step 3
Add the Numerators
Now add the numerators (72 + 105 = 177) and keep the common denominator 168 unchanged.
72 + 105/168 = 177/168
Step 4
Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 177 and 168, which is 3. Divide both the numerator and denominator by 3.
177 ÷ 3/168 ÷ 3 = 59/56
Step 5
Convert Improper Fraction to a Mixed Number
Since the numerator (59) is greater than the denominator (56), divide 59 by 56: it goes in 1 whole time(s) with a remainder of 3, giving the mixed number 1 3/56.
59/56 = 13/56
Step 6
Decimal & Percentage Representation
Dividing the numerator 59 by denominator 56 produces a repeating decimal (approximately 1.053571, or 105.3571%).
59 ÷ 56 = 1.053571 (105.3571%)
Visual Representation
The diagram below illustrates 9/21 plus 5/8 visually:
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Summary & Alternative Representations
| Property / Format | Value |
|---|---|
| Lowest Terms Fraction | 59/56 |
| Mixed Number Form | 1 3/56 |
| Decimal Form | 1.053571 |
| Percentage | 105.3571% |
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Frequently Asked Questions
What is 9/21 plus 5/8 as a fraction?
9/21 + 5/8 in simplest fraction form is 59/56 (or 1 3/56 as a mixed number).
What is 9/21 plus 5/8 as a decimal?
9/21 + 5/8 converted to a decimal is 1.053571.
What is 9/21 plus 5/8 as a percentage?
9/21 + 5/8 expressed as a percentage is 105.3571%.
How do you write 9/21 plus 5/8 as a mixed number?
Because the numerator is greater than the denominator, the improper fraction 59/56 can be written as the mixed number 1 3/56.
Does 9/21 plus 5/8 result in a terminating or repeating decimal?
It results in a repeating decimal (approximately 1.053571...) because the denominator contains prime factors other than 2 and 5.