Question

8 assessment practice

1. which rectangle has the greater area, a rectangle with length $\frac{1}{12}$ foot and width $\frac{3}{4}$ foot or a rectangle with length $\frac{1}{6}$ foot and width $\frac{4}{5}$ foot?
2. alberto runs $3\frac{1}{4}$ miles each day.

n total miles
$3\frac{1}{4}$ $3\frac{1}{4}$ $3\frac{1}{4}$ $3\frac{1}{4}$ $3\frac{1}{4}$ $3\frac{1}{4}$ $3\frac{1}{4}$
a. write an equation using the variable n to model how far he runs in 7 days.
b. how far does he run in 7 days?
c. explain how to estimate how far he would run in 11 days.

1. is the following equation true? explain.

$\frac{5}{6} \times \frac{8}{4} = \frac{5}{3}$

1. complete the equation. show your work.

$16 \times \frac{5}{8} = ?$

1. select all the expressions that are equal to $\frac{4}{7} \times 6$.

$4 \div 6 \times 7 = \frac{14}{3}$
$\frac{6}{7} \times 4 = \frac{24}{7}$
$6 \div 4 \times 7 = 10\frac{1}{2}$
$4 \times 6 \div 7 = 3\frac{3}{7}$
$7 \div 4 \times 6 = \frac{21}{2}$

1. tracy took a test that had 24 questions. she got $\frac{5}{6}$ of the questions correct. how many questions did she answer correctly? write an equation to model your work.

Explanation:

Step1: Calculate Area of Rectangle 1

Area = length × width = $\frac{1}{12} \times \frac{3}{4} = \frac{1 \times 3}{12 \times 4} = \frac{3}{48} = \frac{1}{16}$ square feet

Step2: Calculate Area of Rectangle 2

Area = length × width = $\frac{1}{16} \times \frac{4}{5} = \frac{1 \times 4}{16 \times 5} = \frac{4}{80} = \frac{1}{20}$ square feet

Step3: Compare the Two Areas

$\frac{1}{16} > \frac{1}{20}$

Part A: Model Total Miles

Total miles = daily miles × days
$n = 3\frac{1}{4} \times 7$

Part B: Calculate Total Miles

Convert mixed number to improper fraction: $3\frac{1}{4} = \frac{13}{4}$
$n = \frac{13}{4} \times 7 = \frac{91}{4} = 22\frac{3}{4}$ miles

Part C: Estimate for 11 Days

Round $3\frac{1}{4}$ to 3, multiply by 11: $3 \times 11 = 33$ miles (or round to 3.25, $3.25 \times 11 \approx 35.75$; the whole number estimate is standard)

Step1: Calculate Left-Hand Side

$\frac{5}{6} \times \frac{8}{4} = \frac{5 \times 8}{6 \times 4} = \frac{40}{24} = \frac{5}{3}$

Step2: Compare to Right-Hand Side

Right-hand side = $\frac{5}{3}$, so both sides are equal.

Step1: Rewrite 16 as a Fraction

$16 = \frac{16}{1}$

Step2: Multiply Fractions

$\frac{16}{1} \times \frac{5}{8} = \frac{16 \times 5}{1 \times 8} = \frac{80}{8} = 10$

Answer:

The rectangle with length $\frac{1}{12}$ foot and width $\frac{3}{4}$ foot has the greater area.

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