Mixed Numbers: Practice

Writing a whole number directly beside a fraction is shorthand for adding the two. The space between them means plus.

$2\tfrac{1}{3} = 2 + \tfrac{1}{3}$

It does not mean $2 \times \tfrac{1}{3}$.

A mixed number is read as the whole number, then "and," then the fraction. The "and" stands for the plus sign you do not write.

$4\tfrac{2}{5} = 4 + \tfrac{2}{5}$

So it is read "four and two fifths."

The bar means divide, so work out $7 \div 3$ with a remainder. Three goes into $7$ twice, using $6$, leaving $1$.

$7 \div 3 = 2 \text{ remainder } 1$

The quotient $2$ is the whole part and the remainder $1$ over $3$ is the fraction part, so $\tfrac{7}{3} = 2\tfrac{1}{3}$.

Multiply the whole number by the denominator, add the numerator, and keep the denominator.

$1 \times 2 + 1 = 3$

So $1\tfrac{1}{2} = \tfrac{3}{2}$. The denominator stays $2$.

Multiply the whole number by the denominator and add the numerator, keeping the denominator $4$.

$2 \times 4 + 1 = 9$

So $2\tfrac{1}{4} = \tfrac{9}{4}$.

Divide $5$ by $2$. Two goes into $5$ twice, using $4$, leaving $1$.

$5 \div 2 = 2 \text{ remainder } 1$

The quotient $2$ is the whole part and the remainder $1$ over $2$ is the fraction, so $\tfrac{5}{2} = 2\tfrac{1}{2}$.

Multiply the whole number by the denominator and add the numerator, keeping the denominator $3$.

$3 \times 3 + 1 = 10$

So $3\tfrac{1}{3} = \tfrac{10}{3}$.

Divide $13$ by $6$. Six goes into $13$ twice, using $12$, leaving $1$.

$13 \div 6 = 2 \text{ remainder } 1$

The quotient $2$ is the whole part and the remainder $1$ over $6$ is the fraction, so $\tfrac{13}{6} = 2\tfrac{1}{6}$.

A mixed number is a whole number plus a proper fraction. The fraction part is the fraction written after the whole number.

$5\tfrac{3}{8} = 5 + \tfrac{3}{8}$

So the fraction part is $\tfrac{3}{8}$.

Multiply the whole number by the denominator and add the numerator, keeping the denominator $2$.

$4 \times 2 + 1 = 9$

So $4\tfrac{1}{2} = \tfrac{9}{2}$.

Multiply the whole number by the denominator and add the numerator, keeping the denominator $3$.

$2 \times 3 + 2 = 8$

So $2\tfrac{2}{3} = \tfrac{8}{3}$.

An improper fraction equals a whole number exactly when the division comes out even, with remainder $0$. Check each by dividing.

$12 \div 3 = 4 \text{ remainder } 0$

The others leave a remainder, so $\tfrac{12}{3} = 4$ is the only whole number.