Mixed Fractions: Multiply And Divide

Explanation
The correct answer is 10.5 or 10 1/2. This is because when you multiply 5 1/4 by 3, you can find the product by multiplying the whole numbers (5 and 3) and then multiplying the fractions (1/4 and 3). The product of the whole numbers is 15, and the product of the fractions is 3/4. Adding these two products together gives us 15 3/4, which can be simplified to 10 1/2 or expressed as a decimal as 10.5. Therefore, both 10.5 and 10 1/2 are correct answers.

Explanation
To find the product of 3½ and 2⅓, we can convert the mixed numbers into improper fractions. 3½ is equal to 7/2 and 2⅓ is equal to 7/3. Then, we can multiply the numerators (7 x 7) to get 49 and multiply the denominators (2 x 3) to get 6. Therefore, the product of 3½ and 2⅓ is 49/6.

Explanation
The given expression involves multiplying a mixed number (4½) by a mixed fraction (3⅖). To multiply mixed numbers, we first convert them to improper fractions. 4½ can be written as 9/2 and 3⅖ can be written as 17/5. Multiplying these fractions gives us (9/2) * (17/5) = 153/10. Therefore, the correct answer is 153/10. Alternatively, we can convert the mixed fraction to a decimal by dividing the numerator (17) by the denominator (5), which gives us 3.4. Multiplying 4.5 by 3.4 also gives us 15.3, so the answer can be expressed as 15.3 as well.

Explanation
The correct answer is 22 11/20. This is the result of multiplying 5⅛ by 4⅖.

Explanation
When dividing a whole number by a fraction, we can convert the whole number into a fraction by placing it over 1. In this case, 5⅓ can be written as 16/3. To divide by a fraction, we can multiply the numerator by the reciprocal of the fraction. The reciprocal of ½ is 2/1. So, we multiply 16/3 by 2/1, which gives us 32/3 as the result. Therefore, the correct answer is 32/3.

Explanation
To divide a mixed number by a fraction, we first convert the mixed number into an improper fraction. In this case, 12¾ can be written as 51/4. Then, we invert the divisor (⅖ becomes 5/2) and multiply it by the dividend. So, 51/4 ÷ 5/2 is the same as 51/4 * 2/5. Simplifying this gives us 255/20. Finally, we reduce the fraction to its simplest form, which is 255/8. Additionally, 255/8 can also be expressed as a mixed number, which is 31 7/8. Therefore, the correct answers are 255/8, 31.875, and 31 7/8.

Explanation
The given expression can be simplified by converting the mixed numbers into improper fractions. 16⅚ can be written as 86/5 and 3½ can be written as 7/2. To divide fractions, we multiply the first fraction by the reciprocal of the second fraction. Therefore, 86/5 ÷ 7/2 is equal to (86/5) * (2/7), which simplifies to 172/35. However, 172/35 is not one of the answer choices provided. Therefore, the correct answer is not available.

Explanation
The correct answer is 180/184, 90/92, 45/46, and 0.9783 because when we divide 4⅝ by 5¾, we can convert both fractions to improper fractions and then divide the numerators. The result is 180/184, which can be simplified to 90/92 and further simplified to 45/46. Alternatively, we can convert the mixed numbers to decimals and divide them, which gives us 0.9783. Therefore, all four options are equivalent and correct.