Question
What is the least common denominator for 68 and 56 ?
(1 point)
Responses
24
24
36
36
48
48
14
14
Question 2
Jose is baking a cake. The recipe calls for 24
cup of sugar for the cake and 35
cup of sugar for the frosting. How many cups of sugar will he need in all?(1 point)
Responses
2 220
2 220
159
15 ninths
1110
11 tenth
Question 3
True or False: When adding or subtracting fractions, you must always have a common denominator.(1 point)
Responses
True
True
False
False
Question 4
Find the difference: 34 − 26
(1 point)
Responses
512
5 over 12
12
1 half
510
5 tenths
112
1 over 12
Question 5
Find the sum: 46 + 23
(1 point)
Responses
69
6 ninths
23
2 thirds
1 59
1 59
1 13
1 13
Skip to navigation
(1 point)
Responses
24
24
36
36
48
48
14
14
Question 2
Jose is baking a cake. The recipe calls for 24
cup of sugar for the cake and 35
cup of sugar for the frosting. How many cups of sugar will he need in all?(1 point)
Responses
2 220
2 220
159
15 ninths
1110
11 tenth
Question 3
True or False: When adding or subtracting fractions, you must always have a common denominator.(1 point)
Responses
True
True
False
False
Question 4
Find the difference: 34 − 26
(1 point)
Responses
512
5 over 12
12
1 half
510
5 tenths
112
1 over 12
Question 5
Find the sum: 46 + 23
(1 point)
Responses
69
6 ninths
23
2 thirds
1 59
1 59
1 13
1 13
Skip to navigation
Answers
GPT-4o mini
Let's address each question one by one.
**Question 1: What is the least common denominator for 68 and 56?**
To find the least common denominator (LCD), we need to find the least common multiple (LCM) of 68 and 56.
- The prime factorization of 68 is \(2^2 \times 17\).
- The prime factorization of 56 is \(2^3 \times 7\).
To find the LCM, we take the highest power of each prime factor:
- \(2^3\) (from 56)
- \(7\) (from 56)
- \(17\) (from 68)
So, the LCM is \(2^3 \times 7 \times 17 = 8 \times 7 \times 17 = 952\).
Therefore, the least common denominator is **952**. However, since this value is not in the provided options, it appears there might be a misunderstanding with the question. The correct LCD for fractions involving 68 and 56 should actually be 56, which can be used for most simple fractions from these numbers.
**Question 2: Jose is baking a cake. The recipe calls for \( \frac{2}{4} \) cup of sugar for the cake and \( \frac{3}{5} \) cup of sugar for the frosting. How many cups of sugar will he need in all?**
We need a common denominator to add these fractions:
- The least common denominator for 4 and 5 is 20.
- \( \frac{2}{4} = \frac{10}{20} \)
- \( \frac{3}{5} = \frac{12}{20} \)
Now, add them together:
\[
\frac{10}{20} + \frac{12}{20} = \frac{22}{20} = 1 \frac{2}{20} = 1 \frac{1}{10}
\]
Thus, Jose will need **1 1/10 cups of sugar**.
**Question 3: True or False: When adding or subtracting fractions, you must always have a common denominator.**
The answer is **True**. You need to have a common denominator to add or subtract fractions.
**Question 4: Find the difference: \( \frac{3}{4} - \frac{2}{6} \)**
First, find a common denominator. The least common denominator of 4 and 6 is 12.
- Convert \( \frac{3}{4} \) to \( \frac{9}{12} \)
- Convert \( \frac{2}{6} \) to \( \frac{4}{12} \)
Now, subtract:
\[
\frac{9}{12} - \frac{4}{12} = \frac{5}{12}
\]
So the answer is **\( \frac{5}{12} \)**.
**Question 5: Find the sum: \( \frac{4}{6} + \frac{2}{3} \)**
To add these fractions, convert \( \frac{2}{3} \) to sixths:
- \( \frac{2}{3} = \frac{4}{6} \)
Now add:
\[
\frac{4}{6} + \frac{4}{6} = \frac{8}{6} = \frac{4}{3} = 1 \frac{1}{3}
\]
So the answer is **\( 1 \frac{1}{3} \)**.
If you need further clarifications or assistance, feel free to ask!
**Question 1: What is the least common denominator for 68 and 56?**
To find the least common denominator (LCD), we need to find the least common multiple (LCM) of 68 and 56.
- The prime factorization of 68 is \(2^2 \times 17\).
- The prime factorization of 56 is \(2^3 \times 7\).
To find the LCM, we take the highest power of each prime factor:
- \(2^3\) (from 56)
- \(7\) (from 56)
- \(17\) (from 68)
So, the LCM is \(2^3 \times 7 \times 17 = 8 \times 7 \times 17 = 952\).
Therefore, the least common denominator is **952**. However, since this value is not in the provided options, it appears there might be a misunderstanding with the question. The correct LCD for fractions involving 68 and 56 should actually be 56, which can be used for most simple fractions from these numbers.
**Question 2: Jose is baking a cake. The recipe calls for \( \frac{2}{4} \) cup of sugar for the cake and \( \frac{3}{5} \) cup of sugar for the frosting. How many cups of sugar will he need in all?**
We need a common denominator to add these fractions:
- The least common denominator for 4 and 5 is 20.
- \( \frac{2}{4} = \frac{10}{20} \)
- \( \frac{3}{5} = \frac{12}{20} \)
Now, add them together:
\[
\frac{10}{20} + \frac{12}{20} = \frac{22}{20} = 1 \frac{2}{20} = 1 \frac{1}{10}
\]
Thus, Jose will need **1 1/10 cups of sugar**.
**Question 3: True or False: When adding or subtracting fractions, you must always have a common denominator.**
The answer is **True**. You need to have a common denominator to add or subtract fractions.
**Question 4: Find the difference: \( \frac{3}{4} - \frac{2}{6} \)**
First, find a common denominator. The least common denominator of 4 and 6 is 12.
- Convert \( \frac{3}{4} \) to \( \frac{9}{12} \)
- Convert \( \frac{2}{6} \) to \( \frac{4}{12} \)
Now, subtract:
\[
\frac{9}{12} - \frac{4}{12} = \frac{5}{12}
\]
So the answer is **\( \frac{5}{12} \)**.
**Question 5: Find the sum: \( \frac{4}{6} + \frac{2}{3} \)**
To add these fractions, convert \( \frac{2}{3} \) to sixths:
- \( \frac{2}{3} = \frac{4}{6} \)
Now add:
\[
\frac{4}{6} + \frac{4}{6} = \frac{8}{6} = \frac{4}{3} = 1 \frac{1}{3}
\]
So the answer is **\( 1 \frac{1}{3} \)**.
If you need further clarifications or assistance, feel free to ask!