Mixed Numbers: Additional Practice (Set 2)

The fraction being subtracted is larger, so convert to improper fractions: $5\tfrac14 = \tfrac{21}{4}$ and $2\tfrac23 = \tfrac{8}{3}$. The least common denominator is $12$.

$\tfrac{63}{12} - \tfrac{32}{12} = \tfrac{31}{12} = 2\tfrac{7}{12}$

So $5\tfrac14 - 2\tfrac23 = 2\tfrac{7}{12}$.

Convert both to improper fractions: $2\tfrac12 = \tfrac{5}{2}$ and $2\tfrac25 = \tfrac{12}{5}$. Multiply across and cancel.

$\tfrac{5}{2} \times \tfrac{12}{5} = \tfrac{60}{10} = 6$

So the product is the whole number $6$.

Convert both to improper fractions: $2\tfrac23 = \tfrac{8}{3}$ and $3\tfrac34 = \tfrac{15}{4}$. Multiply across and cancel.

$\tfrac{8}{3} \times \tfrac{15}{4} = \tfrac{8 \times 15}{3 \times 4} = \tfrac{120}{12} = 10$

Multiplying the whole and fraction parts separately would give the wrong answer.

Convert both to improper fractions: $5\tfrac13 = \tfrac{16}{3}$ and $1\tfrac13 = \tfrac{4}{3}$. Multiply by the reciprocal of the divisor and cancel.

$\tfrac{16}{3} \times \tfrac{3}{4} = \tfrac{48}{12} = 4$

Only the divisor is flipped.

The fraction being subtracted is larger, so convert to improper fractions: $7\tfrac12 = \tfrac{15}{2}$ and $3\tfrac56 = \tfrac{23}{6}$. The least common denominator is $6$, so $\tfrac{15}{2} = \tfrac{45}{6}$.

$\tfrac{45}{6} - \tfrac{23}{6} = \tfrac{22}{6} = \tfrac{11}{3} = 3\tfrac{2}{3}$

The last step simplifies by the common factor $2$, then converts to a mixed number.

Convert both to improper fractions: $3\tfrac34 = \tfrac{15}{4}$ and $1\tfrac15 = \tfrac{6}{5}$. Multiply across and cancel.

$\tfrac{15}{4} \times \tfrac{6}{5} = \tfrac{90}{20} = \tfrac{9}{2} = 4\tfrac{1}{2}$

The last step simplifies by the common factor $10$, then converts to a mixed number.

Doubling means multiplying by $2$. Convert the mixed number first: $2\tfrac34 = \tfrac{11}{4}$, and $2 = \tfrac{2}{1}$.

$\tfrac{11}{4} \times \tfrac{2}{1} = \tfrac{22}{4} = \tfrac{11}{2} = 5\tfrac{1}{2}$

So you need $5\tfrac12$ cups.

The word "of" means multiply. Convert the mixed number: $6\tfrac23 = \tfrac{20}{3}$, and multiply by $\tfrac38$.

$\tfrac{3}{8} \times \tfrac{20}{3} = \tfrac{60}{24} = \tfrac{5}{2} = 2\tfrac{1}{2}$

The last step simplifies by the common factor $12$, then converts to a mixed number.

"How many fourths fit" is a division: $2\tfrac12 \div \tfrac14$. Convert: $2\tfrac12 = \tfrac{5}{2}$, and multiply by the reciprocal of $\tfrac14$.

$\tfrac{5}{2} \times \tfrac{4}{1} = \tfrac{20}{2} = 10$

So $10$ people can be served.

Put both in the same form. Convert the mixed number: $4 \times 7 + 3 = 31$, so $4\tfrac37 = \tfrac{31}{7}$.

$\tfrac{31}{7} = \tfrac{31}{7}$

The two are exactly the same value, so the correct symbol is $=$.

Convert the mixed number: $4\tfrac12 = \tfrac{9}{2}$, and multiply by $\tfrac23$.

$\tfrac{2}{3} \times \tfrac{9}{2} = \tfrac{18}{6} = 3$

So the product is $3$.

The amount is the rate times the time: $\tfrac34 \times 2\tfrac13$. Convert: $2\tfrac13 = \tfrac{7}{3}$.

$\tfrac{3}{4} \times \tfrac{7}{3} = \tfrac{21}{12} = \tfrac{7}{4} = 1\tfrac{3}{4}$

The last step simplifies by the common factor $3$, then converts to a mixed number, so it pours $1\tfrac34$ gallons.