Question

week 17
monday
use the model to solve.
\\(\frac{3\text{ cars}}{12\text{ people}} = \frac{5\text{ cars}}{\\_\text{people}}\\)
how many people can fit into 5 cars?
plot and label the given points on the number line.
a) -3
b) 0
c) 6

tuesday
use <, >, or = to make each statement true.
-9 ______ -6
12 ______ 7
-4 ______ -1
-2 ______ 2
convert each to an improper fraction.
\\(1\frac{3}{4}=\\)
\\(7\frac{4}{6}=\\)

Explanation:

Step1: Solve the proportion

Let $x$ = people for 5 cars.
$\frac{3}{12} = \frac{5}{x}$
Cross multiply: $3x = 12 \times 5$
$3x = 60$
$x = \frac{60}{3} = 20$

Step2: Compare integers (negative/positive)

• For $-9$ and $-6$: On number line, left < right. $-9 < -6$
• For $12$ and $7$: Positive numbers, larger value > smaller. $12 > 7$
• For $-4$ and $-1$: Left < right on number line. $-4 < -1$
• For $-2$ and $2$: Negative < positive. $-2 < 2$

Step3: Convert mixed to improper fractions

For $1\frac{3}{4}$: $1\times4 + 3 = 7$, so $\frac{7}{4}$
For $7\frac{4}{6}$: $7\times6 + 4 = 46$, so $\frac{46}{6} = \frac{23}{3}$

Step4: Plot points on number line

• a) Mark $-3$ at the -3 tick
• b) Mark $0$ at the 0 tick
• c) Mark $6$ at the 6 tick

Answer:

Monday Proportion:

20 people

Tuesday Comparisons:

$-9 < -6$
$12 > 7$
$-4 < -1$
$-2 < 2$

Monday Number Line:

a) Point labeled 'a' at -3, b) Point labeled 'b' at 0, c) Point labeled 'c' at 6

Tuesday Improper Fractions:

$1\frac{3}{4} = \frac{7}{4}$
$7\frac{4}{6} = \frac{23}{3}$