lesson check
1. tina has $\frac{3}{5}$ pound of rice. she will use $\frac{2}{3}$ of it to make fried rice for her family. how much rice will tina use to make fried rice?
$\boldsymbol{\text{a}}$ $\frac{5}{8}$ pound
$\boldsymbol{\text{b}}$ $\frac{3}{5}$ pound
$\boldsymbol{\text{c}}$ $\frac{2}{5}$ pound
$\boldsymbol{\text{d}}$ $\frac{1}{3}$ pound

2. the waterfall trail is $\frac{3}{4}$ mile long. at $\frac{1}{6}$ of the distance from the trailhead, there is a lookout. in miles, how far is the lookout from the trailhead?
$\boldsymbol{\text{a}}$ $\frac{1}{8}$ mile
$\boldsymbol{\text{b}}$ $\frac{1}{4}$ mile
$\boldsymbol{\text{c}}$ $\frac{4}{10}$ mile
$\boldsymbol{\text{d}}$ $\frac{24}{3}$ miles

spiral review
3. hayden bought 48 new trading cards. three - fourths of the new cards are baseball cards. how many baseball cards did hayden buy? (lesson 7.1)
$\boldsymbol{\text{a}}$ 12
$\boldsymbol{\text{b}}$ 16
$\boldsymbol{\text{c}}$ 24
$\boldsymbol{\text{d}}$ 36

4. yesterday, annie walked $\frac{9}{10}$ mile to her friend’s house. together, they walked $\frac{1}{3}$ mile to the library. which is the best estimate for how far annie walked yesterday? (lesson 6.3)
$\boldsymbol{\text{a}}$ about $\frac{1}{2}$ mile
$\boldsymbol{\text{b}}$ about 1 mile
$\boldsymbol{\text{c}}$ about $1\frac{1}{2}$ miles
$\boldsymbol{\text{d}}$ about 2 miles

5. erin is going to sew a jacket and a skirt. she needs $2\frac{3}{4}$ yards of material for the jacket and $1\frac{1}{2}$ yards of material for the skirt. altogether, how many yards of material does erin need? (lesson 6.6)
$\boldsymbol{\text{a}}$ $2\frac{3}{8}$ yards
$\boldsymbol{\text{b}}$ $3\frac{1}{4}$ yards
$\boldsymbol{\text{c}}$ $3\frac{7}{8}$ yards
$\boldsymbol{\text{d}}$ $4\frac{1}{4}$ yards

6. which of the following expressions simplifies to 4? (lesson 1.12)
$\boldsymbol{\text{a}}$ $(3\times6)-(5\times2) + 7$
$\boldsymbol{\text{b}}$ $(3\times6)+(5\times2)\div7$
$\boldsymbol{\text{c}}$ $(3\times6)+(5 + 2)-7$
$\boldsymbol{\text{d}}$ $(3\times6)-(5\times2)\times7$

Question

lesson check
1. tina has $\frac{3}{5}$ pound of rice. she will use $\frac{2}{3}$ of it to make fried rice for her family. how much rice will tina use to make fried rice?
$\boldsymbol{\text{a}}$ $\frac{5}{8}$ pound
$\boldsymbol{\text{b}}$ $\frac{3}{5}$ pound
$\boldsymbol{\text{c}}$ $\frac{2}{5}$ pound
$\boldsymbol{\text{d}}$ $\frac{1}{3}$ pound

2. the waterfall trail is $\frac{3}{4}$ mile long. at $\frac{1}{6}$ of the distance from the trailhead, there is a lookout. in miles, how far is the lookout from the trailhead?
$\boldsymbol{\text{a}}$ $\frac{1}{8}$ mile
$\boldsymbol{\text{b}}$ $\frac{1}{4}$ mile
$\boldsymbol{\text{c}}$ $\frac{4}{10}$ mile
$\boldsymbol{\text{d}}$ $\frac{24}{3}$ miles

spiral review
3. hayden bought 48 new trading cards. three - fourths of the new cards are baseball cards. how many baseball cards did hayden buy? (lesson 7.1)
$\boldsymbol{\text{a}}$ 12
$\boldsymbol{\text{b}}$ 16
$\boldsymbol{\text{c}}$ 24
$\boldsymbol{\text{d}}$ 36

4. yesterday, annie walked $\frac{9}{10}$ mile to her friend’s house. together, they walked $\frac{1}{3}$ mile to the library. which is the best estimate for how far annie walked yesterday? (lesson 6.3)
$\boldsymbol{\text{a}}$ about $\frac{1}{2}$ mile
$\boldsymbol{\text{b}}$ about 1 mile
$\boldsymbol{\text{c}}$ about $1\frac{1}{2}$ miles
$\boldsymbol{\text{d}}$ about 2 miles

5. erin is going to sew a jacket and a skirt. she needs $2\frac{3}{4}$ yards of material for the jacket and $1\frac{1}{2}$ yards of material for the skirt. altogether, how many yards of material does erin need? (lesson 6.6)
$\boldsymbol{\text{a}}$ $2\frac{3}{8}$ yards
$\boldsymbol{\text{b}}$ $3\frac{1}{4}$ yards
$\boldsymbol{\text{c}}$ $3\frac{7}{8}$ yards
$\boldsymbol{\text{d}}$ $4\frac{1}{4}$ yards

6. which of the following expressions simplifies to 4? (lesson 1.12)
$\boldsymbol{\text{a}}$ $(3\times6)-(5\times2) + 7$
$\boldsymbol{\text{b}}$ $(3\times6)+(5\times2)\div7$
$\boldsymbol{\text{c}}$ $(3\times6)+(5 + 2)-7$
$\boldsymbol{\text{d}}$ $(3\times6)-(5\times2)\times7$

Accepted Answer

### Question 1
# Explanation:
## Step1: Identify the operation
To find the amount of rice Tina uses, we multiply the total amount of rice by the fraction she uses. So we calculate $\frac{3}{5} 	imes \frac{2}{3}$.
## Step2: Multiply the fractions
When multiplying fractions, we multiply the numerators and the denominators: $\frac{3	imes2}{5	imes3}=\frac{6}{15}$.
## Step3: Simplify the fraction
Simplify $\frac{6}{15}$ by dividing both the numerator and denominator by their greatest common divisor, which is 3. So $\frac{6\div3}{15\div3}=\frac{2}{5}$.
# Answer: C. $\frac{2}{5}$ pound

### Question 2
# Explanation:
## Step1: Identify the operation
To find the distance of the lookout from the trailhead, we multiply the length of the trail by the fraction of the distance from the trailhead. So we calculate $\frac{3}{4} 	imes \frac{1}{6}$.
## Step2: Multiply the fractions
Multiply the numerators and denominators: $\frac{3	imes1}{4	imes6}=\frac{3}{24}$.
## Step3: Simplify the fraction
Simplify $\frac{3}{24}$ by dividing both by 3: $\frac{3\div3}{24\div3}=\frac{1}{8}$.
# Answer: A. $\frac{1}{8}$ mile

### Question 3
# Explanation:
## Step1: Identify the operation
To find the number of baseball cards, we multiply the total number of new cards by the fraction that are baseball cards. So we calculate $48	imes\frac{3}{4}$.
## Step2: Multiply the whole number and the fraction
We can rewrite 48 as $\frac{48}{1}$, then multiply: $\frac{48}{1}	imes\frac{3}{4}=\frac{48	imes3}{1	imes4}=\frac{144}{4}$.
## Step3: Simplify the fraction
Simplify $\frac{144}{4}=36$? Wait, no, wait. Wait, $48	imes\frac{3}{4}$: 48 divided by 4 is 12, 12 times 3 is 36? Wait, no, the options have 36 as D. Wait, let's check again. Wait, 48 new cards, three - fourths are baseball cards. So $48	imes\frac{3}{4}=\frac{48	imes3}{4}=12	imes3 = 36$.
# Answer: D. 36

### Question 4
# Explanation:
## Step1: Estimate the distances
First, $\frac{9}{10}$ is close to 1, and $\frac{1}{3}$ is about $\frac{1}{3}$. When we add them together, $1+\frac{1}{3}\approx1\frac{1}{3}$, but we can also estimate $\frac{9}{10}\approx1$ and $\frac{1}{3}\approx0$, but a better estimate is that $\frac{9}{10}$ is almost 1 and $\frac{1}{3}$ is about a third. So $1+\frac{1}{3}\approx1$, but more accurately, $\frac{9}{10}+\frac{1}{3}=\frac{27 + 10}{30}=\frac{37}{30}\approx1.23$, which is about 1 mile? Wait, no, $\frac{9}{10}$ is 0.9 and $\frac{1}{3}\approx0.333$, so $0.9 + 0.333\approx1.23$, which is about $1\frac{1}{2}$? Wait, no, $1\frac{1}{2}$ is 1.5. Wait, maybe the question is to estimate. $\frac{9}{10}$ is close to 1, and $\frac{1}{3}$ is close to 0, but when we add them, 0.9+0.333≈1.23, which is about 1 mile? Wait, no, the options: A is about 0.5, B is about 1, C is about 1.5, D is about 2. Let's calculate $\frac{9}{10}+\frac{1}{3}=\frac{27 + 10}{30}=\frac{37}{30}\approx1.23$, which is closer to 1 mile? Wait, no, 1.23 is closer to $1\frac{1}{2}$? Wait, maybe I made a mistake. Wait, $\frac{9}{10}$ is 0.9, $\frac{1}{3}\approx0.33$, so 0.9 + 0.33 = 1.23, which is about 1 mile? Wait, no, 1.23 is closer to 1 than to 1.5? Wait, 1.23 - 1 = 0.23, 1.5 - 1.23 = 0.27. So it's closer to 1. But let's check the options again. Wait, maybe the intended estimate is that $\frac{9}{10}$ is almost 1, and $\frac{1}{3}$ is about a third, so 1 + 0.33≈1.33, which is about 1 mile? Wait, the answer is B? Wait, no, let's see the options. The question is "which is the best estimate". $\frac{9}{10}$ is 0.9, $\frac{1}{3}\approx0.33$, sum is≈1.23, which is about 1 mile (since 1.23 is closer to 1 than to 1.5 or 0.5 or 2). So the best estimate is about 1 mile.
# Answer: B. about 1 mile

### Question 5
# Explanation:
## Step1: Convert the mixed numbers to improper fractions
$2\frac{3}{4}=\frac{2	imes4 + 3}{4}=\frac{11}{4}$ and $1\frac{1}{2}=\frac{1	imes2+1}{2}=\frac{3}{2}$.
## Step2: Find a common denominator
The common denominator of 4 and 2 is 4. So rewrite $\frac{3}{2}$ as $\frac{6}{4}$.
## Step3: Add the fractions
$\frac{11}{4}+\frac{6}{4}=\frac{11 + 6}{4}=\frac{17}{4}$.
## Step4: Convert back to a mixed number
$\frac{17}{4}=4\frac{1}{4}$? Wait, no, $\frac{17}{4}=4.25$, and $4\frac{1}{4}$ is 4.25. Wait, but let's check the options. Wait, the options are A: $2\frac{3}{8}$, B: $3\frac{1}{4}$, C: $3\frac{7}{8}$, D: $4\frac{1}{4}$. Wait, maybe I made a mistake in conversion. Wait, $2\frac{3}{4}$ is 2.75 and $1\frac{1}{2}$ is 1.5. So 2.75+1.5 = 4.25, which is $4\frac{1}{4}$. So the answer is D.
# Answer: D. $4\frac{1}{4}$ yards

### Question 6
# Explanation:
## Step1: Calculate each option
- Option A: $[(3	imes6)-(5	imes2)] + 7=[18 - 10]+7=8 + 7 = 15$
- Option B: $[(3	imes6)+(5	imes2)]\div7=[18 + 10]\div7=28\div7 = 4$
- Option C: $[(3	imes6)+(5 + 2)]-7=[18+7]-7=25 - 7 = 18$
- Option D: $[(3	imes6)-(5	imes2)]	imes7=[18 - 10]	imes7=8	imes7 = 56$
# Answer: B. $[(3	imes6)+(5	imes2)]\div7$

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Question 1

Step1: Identify the operation

Step2: Multiply the fractions

Step3: Simplify the fraction

Step1: Identify the operation

Step2: Multiply the fractions

Step3: Simplify the fraction

Step1: Identify the operation

Step2: Multiply the whole number and the fraction

Step3: Simplify the fraction

Answer:

Question 2