What is 22/42 plus 12/21?
22/42 plus 12/21 equals 23/21 (or 1 2/21 as a mixed number) (or 1.095238 in decimal form). Learn the step-by-step solution to add 22/42 and 12/21 using Least Common Denominator and simplification.
Exact Answer
22/42 + 12/21 = 23/21
Simplified Fraction
23/21
Mixed Number
1 2/21
Decimal Value
1.095238
Percentage
109.5238%
Step-by-Step Solution: 22/42 + 12/21
Step 1
Find the Least Common Denominator (LCD)
Notice that 42 is an exact multiple of 21 (21 × 2 = 42). The Least Common Denominator (LCD) is simply 42, meaning we only need to scale one fraction.
LCD(42, 21) = 42
Step 2
Convert to Equivalent Fractions with Common Denominator 42
Multiply the numerator and denominator of 22/42 by 1, and multiply the numerator and denominator of 12/21 by 2 so both fractions share the common base 42.
22 × 1/42 × 1 = 22/42 and 12 × 2/21 × 2 = 24/42
Step 3
Add the Numerators
Now add the numerators (22 + 24 = 46) and keep the common denominator 42 unchanged.
22 + 24/42 = 46/42
Step 4
Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 46 and 42, which is 2. Divide both the numerator and denominator by 2.
46 ÷ 2/42 ÷ 2 = 23/21
Step 5
Convert Improper Fraction to a Mixed Number
Since the numerator (23) is greater than the denominator (21), divide 23 by 21: it goes in 1 whole time(s) with a remainder of 2, giving the mixed number 1 2/21.
23/21 = 12/21
Step 6
Decimal & Percentage Representation
Dividing the numerator 23 by denominator 21 produces a repeating decimal (approximately 1.095238, or 109.5238%).
23 ÷ 21 = 1.095238 (109.5238%)
Visual Representation
The diagram below illustrates 22/42 plus 12/21 visually:
+
=
Summary & Alternative Representations
| Property / Format | Value |
|---|---|
| Lowest Terms Fraction | 23/21 |
| Mixed Number Form | 1 2/21 |
| Decimal Form | 1.095238 |
| Percentage | 109.5238% |
Was this solution helpful?
Help us improve our free step-by-step tools
Frequently Asked Questions
What is 22/42 plus 12/21 as a fraction?
22/42 + 12/21 in simplest fraction form is 23/21 (or 1 2/21 as a mixed number).
What is 22/42 plus 12/21 as a decimal?
22/42 + 12/21 converted to a decimal is 1.095238.
What is 22/42 plus 12/21 as a percentage?
22/42 + 12/21 expressed as a percentage is 109.5238%.
How do you write 22/42 plus 12/21 as a mixed number?
Because the numerator is greater than the denominator, the improper fraction 23/21 can be written as the mixed number 1 2/21.
Does 22/42 plus 12/21 result in a terminating or repeating decimal?
It results in a repeating decimal (approximately 1.095238...) because the denominator contains prime factors other than 2 and 5.