Question

practice & problem solving
leveled practice in 14 - 25, find each quotient.

1. 10÷2 1/4=
2. 9 1/3÷6=
3. 1 3/8÷4 1/8=
4. 2 2/3÷8=
5. 4 1/3÷3 1/4=
6. 1÷8 5/9=
7. 3 5/6÷9 5/6
8. 16÷2 2/3
9. 2 5/8÷13
10. 3 6/7÷6 3/4
11. 2 1/3÷1 1/3
12. 3 3/4÷1 1/2
13. analyze and persevere luna is making a rope ladder. each step of the ladder is 2 1/3 feet wide and uses an additional 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?
14. the area of this rectangle is 257 1/4 in.². find side length w.

Explanation:

Step1: Convert mixed - numbers to improper fractions

For example, for \(2\frac{1}{3}=\frac{2\times3 + 1}{3}=\frac{7}{3}\), \(1\frac{1}{2}=\frac{1\times2+1}{2}=\frac{3}{2}\), etc.

Step2: Recall division rule for fractions

\(a\div b=a\times\frac{1}{b}\), where \(b
eq0\).

Step3: Calculate each quotient

Problem 20:

\(3\frac{5}{6}\div9\frac{5}{6}=\frac{3\times6 + 5}{6}\div\frac{9\times6+5}{6}=\frac{23}{6}\div\frac{59}{6}=\frac{23}{6}\times\frac{6}{59}=\frac{23}{59}\)

Problem 21:

\(16\div2\frac{2}{3}=16\div\frac{2\times3 + 2}{3}=16\div\frac{8}{3}=16\times\frac{3}{8}=6\)

Problem 22:

\(2\frac{5}{8}\div13=\frac{2\times8 + 5}{8}\div13=\frac{21}{8}\div13=\frac{21}{8}\times\frac{1}{13}=\frac{21}{104}\)

Problem 23:

\(3\frac{6}{7}\div6\frac{3}{4}=\frac{3\times7+6}{7}\div\frac{6\times4 + 3}{4}=\frac{27}{7}\div\frac{27}{4}=\frac{27}{7}\times\frac{4}{27}=\frac{4}{7}\)

Problem 24:

\(2\frac{1}{3}\div1\frac{1}{3}=\frac{2\times3+1}{3}\div\frac{1\times3 + 1}{3}=\frac{7}{3}\div\frac{4}{3}=\frac{7}{3}\times\frac{3}{4}=\frac{7}{4} = 1\frac{3}{4}\)

Problem 25:

\(3\frac{3}{4}\div1\frac{1}{2}=\frac{3\times4+3}{4}\div\frac{1\times2+1}{2}=\frac{15}{4}\div\frac{3}{2}=\frac{15}{4}\times\frac{2}{3}=\frac{5}{2}=2\frac{1}{2}\)

Problem 26:

The length of rope used for each step is \(l = 2\frac{1}{3}+2\times\frac{1}{2}=\frac{7}{3}+1=\frac{7 + 3}{3}=\frac{10}{3}\) feet.
The number of steps \(n=\frac{30}{\frac{10}{3}}=30\times\frac{3}{10}=9\)

Problem 27:

The area of a rectangle \(A = lw\). Given \(A = 257\frac{1}{4}=\frac{257\times4+1}{4}=\frac{1029}{4}\) in² and \(l = 10\frac{1}{2}=\frac{10\times2+1}{2}=\frac{21}{2}\) in.
\(w=\frac{A}{l}=\frac{\frac{1029}{4}}{\frac{21}{2}}=\frac{1029}{4}\times\frac{2}{21}=\frac{1029\times2}{4\times21}=\frac{2058}{84}=24.5\) in.

Answer:

1. \(\frac{23}{59}\)
2. \(6\)
3. \(\frac{21}{104}\)
4. \(\frac{4}{7}\)
5. \(1\frac{3}{4}\)
6. \(2\frac{1}{2}\)
7. \(9\) steps
8. \(24.5\) in.