Question

practice & problem solving leveled practice in 14-25, find each quotient. 14. $10 \div 2\frac{1}{4} = \frac{10}{1} \div \square = \frac{10}{1} \times \square = \square$ 15. $9\frac{1}{3} \div 6 = \frac{28}{3} \div \square = \frac{28}{3} \times \square = \square$ 16. $1\frac{3}{8} \div 4\frac{1}{8} = \frac{11}{8} \div \square = \frac{11}{8} \times \square = \square$ 17. $2\frac{2}{3} \div 8 = \frac{8}{3} \div \square = \square \times \square = \square$ 18. $4\frac{1}{3} \div 3\frac{1}{4} = \frac{13}{3} \div \square = \square \times \square = \square$ 19. $1 \div 8\frac{5}{9} = \frac{1}{1} \div \square = \square \times \square = \square$ 20. $3\frac{5}{6} \div 9\frac{5}{6}$ 21. $16 \div 2\frac{2}{3}$ 22. $2\frac{5}{8} \div 13$ 23. $3\frac{6}{7} \div 6\frac{3}{4}$ 24. $2\frac{1}{3} \div 1\frac{1}{3}$ 25. $3\frac{3}{4} \div 1\frac{1}{2}$ analyze and persevere luna is making a rope ladder. each step of the ladder is $2\frac{1}{3}$ feet wide and uses an additional $\frac{1}{2}$ foot of rope on each end of the step for the knot. luna has a rope that is 30 feet long. how many steps can she make from the rope? 27. the area of this rectangle is $257\frac{1}{4}$ in.². find the width $w$.

Explanation:

Let's solve problem 24: \( 2\frac{1}{3} \div 1\frac{1}{3} \)

Step 1: Convert mixed numbers to improper fractions

To divide mixed numbers, first convert them to improper fractions.
For \( 2\frac{1}{3} \), we have \( 2\frac{1}{3}=\frac{2\times3 + 1}{3}=\frac{7}{3} \)
For \( 1\frac{1}{3} \), we have \( 1\frac{1}{3}=\frac{1\times3+1}{3}=\frac{4}{3} \)
So the division becomes \( \frac{7}{3}\div\frac{4}{3} \)

Step 2: Divide the fractions

Dividing by a fraction is the same as multiplying by its reciprocal. The reciprocal of \( \frac{4}{3} \) is \( \frac{3}{4} \)
So \( \frac{7}{3}\div\frac{4}{3}=\frac{7}{3}\times\frac{3}{4} \)

Step 3: Multiply the fractions

Multiply the numerators and denominators: \( \frac{7\times3}{3\times4}=\frac{21}{12} \)
Simplify the fraction: \( \frac{21}{12}=\frac{7}{4}=1\frac{3}{4} \)

Answer:

\( 1\frac{3}{4} \) (or \( \frac{7}{4} \))