What is 22/42 plus 15/21?
22/42 plus 15/21 equals 26/21 (or 1 5/21 as a mixed number) (or 1.238095 in decimal form). Learn the step-by-step solution to add 22/42 and 15/21 using Least Common Denominator and simplification.
Exact Answer
22/42 + 15/21 = 26/21
Simplified Fraction
26/21
Mixed Number
1 5/21
Decimal Value
1.238095
Percentage
123.8095%
Step-by-Step Solution: 22/42 + 15/21
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 15/21 by 2 so both fractions share the common base 42.
22 × 1/42 × 1 = 22/42 and 15 × 2/21 × 2 = 30/42
Step 3
Add the Numerators
Now add the numerators (22 + 30 = 52) and keep the common denominator 42 unchanged.
22 + 30/42 = 52/42
Step 4
Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 52 and 42, which is 2. Divide both the numerator and denominator by 2.
52 ÷ 2/42 ÷ 2 = 26/21
Step 5
Convert Improper Fraction to a Mixed Number
Since the numerator (26) is greater than the denominator (21), divide 26 by 21: it goes in 1 whole time(s) with a remainder of 5, giving the mixed number 1 5/21.
26/21 = 15/21
Step 6
Decimal & Percentage Representation
Dividing the numerator 26 by denominator 21 produces a repeating decimal (approximately 1.238095, or 123.8095%).
26 ÷ 21 = 1.238095 (123.8095%)
Visual Representation
The diagram below illustrates 22/42 plus 15/21 visually:
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=
Summary & Alternative Representations
| Property / Format | Value |
|---|---|
| Lowest Terms Fraction | 26/21 |
| Mixed Number Form | 1 5/21 |
| Decimal Form | 1.238095 |
| Percentage | 123.8095% |
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Frequently Asked Questions
What is 22/42 plus 15/21 as a fraction?
22/42 + 15/21 in simplest fraction form is 26/21 (or 1 5/21 as a mixed number).
What is 22/42 plus 15/21 as a decimal?
22/42 + 15/21 converted to a decimal is 1.238095.
What is 22/42 plus 15/21 as a percentage?
22/42 + 15/21 expressed as a percentage is 123.8095%.
How do you write 22/42 plus 15/21 as a mixed number?
Because the numerator is greater than the denominator, the improper fraction 26/21 can be written as the mixed number 1 5/21.
Does 22/42 plus 15/21 result in a terminating or repeating decimal?
It results in a repeating decimal (approximately 1.238095...) because the denominator contains prime factors other than 2 and 5.