The Ultimate Math Test: Add Fractions With Unlike Denominators

Explanation
To add fractions, we need to have a common denominator. In this case, the common denominator is 10. So, we need to convert 1/2 to an equivalent fraction with a denominator of 10, which is 5/10. Now, we can add the fractions: 5/10 + 2/10 = 7/10. Therefore, the correct answer is 7/10.

Explanation
When adding fractions, the denominators must be the same. In this case, the denominators are 4 and 8. To make the denominators the same, we need to find a common multiple of 4 and 8, which is 8. We then convert 1/4 to an equivalent fraction with a denominator of 8 by multiplying the numerator and denominator by 2. This gives us 2/8. Now we can add 2/8 and 3/8 together, which equals 5/8. Therefore, the correct answer is 5/8.

Explanation
The given expression involves adding two fractions, 5/6 and 2/12. To add fractions, we need to have a common denominator. In this case, the common denominator is 12. We can convert 5/6 to 10/12 by multiplying the numerator and denominator by 2. Now, we can add 10/12 and 2/12 to get 12/12, which simplifies to 1. Therefore, the correct answer is 1.

Explanation
The given expression is a sum of two fractions. To add fractions, we need to have a common denominator. In this case, the common denominator is 15. When we convert 4/5 to have a denominator of 15, we get 12/15. Adding this to 4/15 gives us a total of 16/15. This can be simplified to the mixed number 1 1/15.

Explanation
The given expression is a sum of two fractions. To add fractions, we need to find a common denominator. In this case, the common denominator is 21. We then convert the fractions to have the same denominator and add the numerators. The result is 11/21. Since the numerator is greater than the denominator, we have a mixed number. Dividing the numerator by the denominator, we get 11 ÷ 21 = 0 with a remainder of 11. Therefore, the answer is 1 2/21.

Explanation
The given question asks for the sum of two mixed numbers. To add mixed numbers, we first add the whole numbers together, which gives us 3. Then, we add the fractions together. The fractions have different denominators, so we need to find a common denominator. The least common multiple of 5 and 7 is 35. We convert the fractions to have a denominator of 35 and add them together. The sum of 2/5 and 4/7 is 34/35. Therefore, the correct answer is 3 34/35.

Explanation
To add mixed numbers, we first add the whole numbers together and then add the fractions together. In this case, 1 + 2 = 3 for the whole numbers. Then, we add the fractions 1/2 and 1/3 together. To do this, we need to find a common denominator, which is 6. Converting 1/2 to have a denominator of 6 gives us 3/6, and converting 1/3 to have a denominator of 6 gives us 2/6. Adding 3/6 and 2/6 together gives us 5/6. Therefore, the answer is 3 5/6.

Explanation
The given expression involves adding two fractions with different denominators. To add fractions, we need to have a common denominator. In this case, the common denominator is 12. To convert 5/6 into a fraction with a denominator of 12, we multiply the numerator and denominator by 2, resulting in 10/12. Now we can add 10/12 and 4/12, which equals 14/12. Simplifying this fraction gives us 1 1/6, which is the final answer.

Explanation
The given expression is a sum of two fractions. To add fractions, we need to find a common denominator. The least common multiple of 12 and 3 is 12. So, we can rewrite the fractions with a common denominator of 12. 5/12 becomes 5/12 and 2/3 becomes 8/12. Now, we can add the fractions by adding their numerators and keeping the denominator the same. 5/12 + 8/12 = 13/12. Since the numerator is greater than the denominator, we have a mixed number. Dividing 13 by 12 gives us a quotient of 1 and a remainder of 1. So, the final answer is 1 1/12.

Explanation
The given expression involves adding two fractions: 9/20 and 3/5. To add these fractions, we need to find a common denominator. The least common multiple of 20 and 5 is 20. We can convert 9/20 to an equivalent fraction with a denominator of 20 by multiplying the numerator and denominator by 1, resulting in 9/20. Similarly, we can convert 3/5 to an equivalent fraction with a denominator of 20 by multiplying the numerator and denominator by 4, resulting in 12/20. Adding the two fractions, we get 9/20 + 12/20 = 21/20. This can be simplified to 1 1/20, which is the correct answer.