1 dariush ate $\frac{3}{8}$ of the coffee cake while eton ate $\frac{4}{8}$. how much of the coffee cake did the boys eat? $\underline{\quad\quad}$ of the coffee cake 2 the maximum weight allowed at one time on a walking bridge is 400,000 grams. can these people safely stand on the bridge together? $\underline{\quad\quad}$ kyle 71 kg cara 59 kg betty 66 kg roge 79 kg devin 86 kg how many grams do they weigh all together? $\underline{\quad\quad}$ grams 3 multiply. show your work. $\begin{array}{r}483\\*\quad 9\\\hline\end{array}$ estimate: $\underline{\quad\quad}$ answer: $\underline{\quad\quad}$ 4 use your fraction circle pieces to solve this problem. if $\triangle$ is $\frac{1}{4}$, then what is the whole? $\underline{\quad\quad}$ 5 writing/reasoning solve problem 3 using a different strategy. show your work.

Question

Accepted Answer

### Problem 1
# Explanation:
## Step1: Add the two fractions
To find the total amount of the coffee cake the boys ate, we add the fractions of the cake each boy ate. The fractions are $\frac{3}{8}$ and $\frac{4}{8}$. When adding fractions with the same denominator, we add the numerators and keep the denominator the same. So, $\frac{3}{8}+\frac{4}{8}=\frac{3 + 4}{8}$.
## Step2: Calculate the sum of numerators
$3+4 = 7$, so the result is $\frac{7}{8}$.
# Answer:
$\frac{7}{8}$

### Problem 2
#### Part 1: Check if they can stand on the bridge
# Explanation:
## Step1: Convert kilograms to grams
We know that $1\space kg=1000\space grams$. So we convert each person's weight from kilograms to grams:
- Kyle: $71\times1000 = 71000$ grams
- Betty: $66\times1000=66000$ grams
- Devin: $86\times1000 = 86000$ grams
- Cara: $59\times1000=59000$ grams
- Roge: $79\times1000 = 79000$ grams
## Step2: Find the total weight in grams
Add all the weights together: $71000+66000 + 86000+59000+79000$.
First, $71000+66000=137000$; $137000+86000 = 223000$; $223000+59000=282000$; $282000+79000 = 361000$ grams.
## Step3: Compare with maximum weight
The maximum weight allowed is $400000$ grams. Since $361000<400000$, they can safely stand on the bridge together.

#### Part 2: Total weight in grams
# Explanation:
As calculated above, the total weight is the sum of all their weights in grams.
# Answer:
- Can they safely stand on the bridge together? Yes.
- How many grams do they weigh all together? $361000$ grams

### Problem 3
# Explanation:
## Step1: Estimate the product
To estimate $483\times9$, we can round $483$ to the nearest hundred, which is $500$. Then $500\times9 = 4500$. (We could also round to the nearest ten: $480\times9=4320$, but rounding to the nearest hundred is a common estimation method here.)
## Step2: Calculate the actual product
We multiply $483$ by $9$:
$$
\begin{align*}
483\times9&=(400 + 80+3)\times9\
&=400\times9+80\times9 + 3\times9\
&=3600+720+27\
&=3600 + 720=4320;4320+27 = 4347
\end{align*}
$$
# Answer:
- Estimate: $4500$ (or $4320$ depending on rounding method)
- Answer: $4347$

### Problem 4
# Explanation:
If a part is $\frac{1}{4}$ of the whole, then the whole is 4 times that part. Since the given part is $\frac{1}{4}$ of the whole, to find the whole, we multiply the part by 4. If the part is represented by the given fraction circle piece (which is $\frac{1}{4}$), then the whole is 4 of those pieces. So the whole is 1 (because 4 times $\frac{1}{4}$ is $4\times\frac{1}{4}=1$).
# Answer:
The whole is 1 (or 4 of the given fraction circle pieces, which make up a whole circle, representing 1).

### Problem 5
# Explanation:
We can use the distributive property in a different way or break down the number further. Let's use the fact that $483 = 480+3$. Then $483\times9=(480 + 3)\times9=480\times9+3\times9$. We know that $480\times9 = 4320$ and $3\times9 = 27$. Then $4320+27 = 4347$, which matches the previous result. Another way: We can do long multiplication:
```
  483
×   9
------
  4347
```
(We multiply 9 by 3 to get 27, write down 7 and carry over 2. Then 9 times 8 is 72, plus 2 is 74, write down 4 and carry over 7. Then 9 times 4 is 36, plus 7 is 43. So we get 4347.)
# Answer:
Using long multiplication (or another distributive method) we still get $4347$ as shown above.

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Problem 1

Step1: Add the two fractions

Step2: Calculate the sum of numerators

Step1: Convert kilograms to grams

Step2: Find the total weight in grams

Step3: Compare with maximum weight

Part 2: Total weight in grams

Answer:

Problem 2

Part 1: Check if they can stand on the bridge