Question

6.3a (l)

1. which expression is equivalent to $6 \div \frac{7}{8}$?

a $\frac{1}{6} \times \frac{7}{8}$
b $6 \div \frac{8}{7}$
c $6 \times \frac{8}{7}$
d $\frac{1}{6} \div \frac{8}{7}$

6.3d (m)

1. tyrone’s older brother is saving his money until he has $100. he currently has $60 but needs to put $15 worth of gas in his car. after spending this amount, how much more money will tyrone’s brother need to save to reach his goal of $100?

a $25
b $40
c $55
d $75

6.4b (l)

1. margie usually drinks 12.25 liters of water in one week (7 days). if she continues drink water at the same rate, what is the total amount of water margie will drink during a 4 - week period?

a 35 l
b 49 l
c 55 l
d 343 l

Explanation:

Question 1

Step1: Recall division of fractions rule

To divide by a fraction, we multiply by its reciprocal. The reciprocal of $\frac{7}{8}$ is $\frac{8}{7}$. So, $6\div\frac{7}{8}=6\times\frac{8}{7}$.

Step2: Compare with options

Option A: $\frac{1}{6}\times\frac{7}{8}$ is not equivalent. Option B: $6\div\frac{8}{7}=6\times\frac{7}{8}$, not equivalent. Option C: $6\times\frac{8}{7}$, which matches our result. Option D: $\frac{1}{6}\div\frac{8}{7}=\frac{1}{6}\times\frac{7}{8}$, not equivalent.

Step1: Find remaining after gas

First, find how much money he has after buying gas. He has $60$ and spends $15$, so $60 - 15 = 45$.

Step2: Find amount needed to reach 100

His goal is $100$, so the amount needed is $100 - 45 = 55$? Wait, no, wait. Wait, the problem says "how much more money will Tyrone’s brother need to save to reach his goal of $100$" after spending $15$ on gas. Wait, initial amount: $60$. He spends $15$ on gas, so his current amount is $60 - 15 = 45$. Then, to reach $100$, he needs $100 - 45 = 55$? Wait, but let's check the options. Option C is $55$. Wait, but let's re - read the problem: "Tyrone’s older brother is saving his money until he has $100$. He currently has $60$ but needs to put $15$ worth of gas in his car. After spending this amount, how much more money will Tyrone’s brother need to save to reach his goal of $100$?" So current amount: $60$. Spends $15$: $60 - 15 = 45$. Goal: $100$. So needed: $100 - 45 = 55$. So the answer is C.

Step1: Calculate money after gas

Amount after gas: $60 - 15 = 45$

Step2: Calculate money needed to reach 100

Money needed: $100 - 45 = 55$

Step1: Recall the rate

Margie drinks $12.25$ liters per week.

Step2: Calculate for 4 weeks

To find the total for 4 weeks, multiply the weekly amount by 4: $12.25\times4 = 49$.

Answer:

C. $6 \times \frac{8}{7}$

Question 2