Converting Decimals, Improper Fractions, and Mixed Numbers

A mixed number is a whole number along with a proper fraction next to it.

Step 1. Convert the decimal number to an improper fraction by multiplying it by some form of one, so the value of the decimal does not change. The number 8 after the decimal is in the tenths place, so we can multiply our decimal number by $\frac{10}{10}$ to convert it to an improper fraction.

$6.8\times \frac{10}{10}=\frac{68}{10}$

Step 2. Reduce the improper fraction by completely factoring the numerator and denominator, then cancel out any common factors between them.

$\frac{68}{10}=\frac{2\times 2\times 17}{2\times 5}=\frac{34}{5}$

Step 3. Convert the improper fraction, in reduced form, to a mixed number by dividing the numerator by the denominator.

 
The mixed number is written using the quotient, any remainder, and the divisor. The whole number for our mixed number is the quotient of $6$. The numerator of the proper fraction is the remainder of $4$, and the denominator is the divisor of $5$. So, $\frac{34}{5}=6\frac{4}{5}$.

Thus, $6.8=6\frac{4}{5}$.

A mixed number is a whole number along with a proper fraction next to it.

Step 1. Convert the decimal number to an improper fraction by multiplying it by some form of one, so the value of the decimal does not change. The number 5 after the decimal is in the hundredths place, so we can multiply our decimal number by $\frac{100}{100}$ to convert it to an improper fraction.

$3.25\times \frac{100}{100}=\frac{325}{100}$

Step 2. Reduce the improper fraction by completely factoring the numerator and denominator, then cancel out any common factors between them.

$\frac{325}{100}=\frac{5\times 5\times 13}{2\times 2\times \times 5}=\frac{13}{4}$

Step 3. Convert the improper fraction, in reduced form, to a mixed number by dividing the numerator by the denominator.

 
The mixed number is written using the quotient, any remainder, and the divisor. The whole number for our mixed number is the quotient of 3. The numerator of the proper fraction is the remainder of 1, and the denominator is the divisor of 4. So, $\frac{13}{4}=3\frac{1}{4}$.

Thus, $3.25=3\frac{1}{4}$.

A mixed number is a whole number along with a proper fraction next to it.

Step 1. Convert the decimal number to an improper fraction by multiplying it by some form of one, so the value of the decimal does not change. The number 5 after the decimal is in the thousandths place, so we can multiply our decimal number by $\frac{\mathrm{1,000}}{\mathrm{1,000}}$ to convert it to an improper fraction.

$8.275\times \frac{\mathrm{1,000}}{\mathrm{1,000}}=\frac{\mathrm{8,275}}{\mathrm{1,000}}$

Step 2. Reduce the improper fraction by completely factoring the numerator and denominator, then cancel out any common factors between them.

$\frac{\mathrm{8,275}}{\mathrm{1,000}}=\frac{5\times 5\times 331}{2\times 2\times 2\times 5\times 5\times 5}=\frac{331}{40}$

Step 3. Convert the improper fraction, in reduced form, to a mixed number by dividing the numerator by the denominator.

 
The mixed number is written using the quotient, any remainder, and the divisor. The whole number for our mixed number is the quotient of 8. The numerator of the proper fraction is the remainder of 11, and the denominator is the divisor of 40. So, $\frac{331}{40}=8\frac{11}{40}$.

Thus, $8.275=8\frac{11}{40}$.

We need to combine the amounts of water, apple juice, and lemon juice to find the total amount of liquid needed to mix into the fruit drink. We will convert the amounts of apple juice and lemon juice to mixed numbers first before combining all of the amounts of liquid. A mixed number is a whole number along with a proper fraction next to it.

Step 1. Convert the decimal number of 10.2 to an improper fraction by multiplying it by some form of one, so the value of the decimal does not change, before converting it to a mixed number. The number 2 after the decimal is in the tenths place, so we can multiply our decimal number by $\frac{10}{10}$ to convert it to an improper fraction.

$10.2\times \frac{10}{10}=\frac{102}{10}$

Step 2. Reduce the improper fraction by completely factoring the numerator and denominator, then cancel out any common factors between them.

$\frac{102}{10}=\frac{2\times 51}{2\times 5}=\frac{51}{5}$

Step 3. Convert the improper fraction, in reduced form, to a mixed number by dividing the numerator by the denominator.

 
The mixed number is written using the quotient, any remainder, and the divisor. The whole number for our mixed number is the quotient of 10. The numerator of the proper fraction is the remainder of 1, and the denominator is the divisor of 5. So, $\frac{51}{5}=10\frac{1}{5}$.

Step 4. Next, convert $\frac{13}{5}$ to a mixed number by dividing the numerator by the denominator.

The mixed number is written using the quotient, any remainder, and the divisor. The whole number for our mixed number is the quotient of 2. The numerator of the proper fraction is the remainder of 3, and the denominator is the divisor of 5. So, $\frac{13}{5}=2\frac{3}{5}$.

Step 5. Now that we have converted the amounts of apple juice and lemon juice to mixed numbers, we can combine the 3 amounts by adding the proper fractions for the mixed numbers, then adding the whole numbers for each mixed number.

$20+10\frac{1}{5}+2\frac{3}{5}=32\frac{4}{5}$

So, there is a total of $32\frac{4}{5}$ ounces of liquid needed for the fruit drink recipe.

We will combine the total weight of the 2 fish you caught using mixed numbers and compare it with the daily weight limit to determine if one of the fish needs to be released. A mixed number is a whole number along with a proper fraction next to it.

Step 1. Convert the weight of the fish given as a decimal number to an improper fraction by multiplying it by some form of one, so the value of the decimal does not change, before converting it to a mixed number. The number 5 after the decimal is in the hundredths place value, so we can multiply our decimal number by $\frac{100}{100}$ to convert it to an improper fraction.

$4.75\times \frac{100}{100}=\frac{475}{100}$

Step 2. Reduce the improper fraction by completely factoring the numerator and denominator, then cancel out any common factors between them.

$\frac{475}{100}=\frac{5\times 5\times 19}{2\times 2\times 5\times 5}=\frac{19}{4}$

Next, convert the improper fraction, in reduced form, to a mixed number by dividing the numerator by the denominator.

 
The mixed number is written using the quotient, any remainder, and the divisor. The whole number for our mixed number is the quotient of 4. The numerator of the proper fraction is the remainder of 3, and the denominator is the divisor of 4. So, $4.75=\frac{19}{4}=4\frac{3}{4}$.

Step 3. Convert the weight of the fish given as an improper fraction to a mixed number by dividing the numerator by the denominator.

The mixed number is written using the quotient, any remainder, and the divisor. The whole number for our mixed number is the quotient of 4. The numerator of the proper fraction is the remainder of 1, and the denominator is the divisor of 2. So, $\frac{9}{2}=4\frac{1}{2}$.

Step 4. Now that we have converted the weights of the two fish caught to mixed numbers, we can combine them by adding the proper fractions for each mixed number, then adding the whole numbers for each mixed number.

$4\frac{3}{4}+4\frac{1}{2}=4\frac{3}{4}+4\frac{2}{4}=8\frac{5}{4}$

Since the fractional part of the mixed number is an improper fraction, we need to convert it to a mixed number and add it to 8 to determine the total weight of the fish caught as a proper mixed number.

We can convert $\frac{5}{4}$ to a mixed number by dividing the numerator by the denominator.

 
The mixed number is written using the quotient, any remainder, and the divisor. The whole number for our mixed number is the quotient of 1. The numerator of the proper fraction is the remainder of 1, and the denominator is the divisor of 4. So, $\frac{5}{4}=1\frac{1}{4}$.

Therefore, the proper mixed number is:

$8\frac{5}{4}=8+1\frac{1}{4}=9\frac{1}{4}$

The total weight of the two game fish you caught is $9\frac{1}{4}$ pounds. The daily weight limit for the game fish is $9\frac{1}{2}$ pounds, or $9\frac{2}{4}$ pounds. Since your total weight for the fish caught is less than the daily weight limit, you do not need to release any of the fish.