What is the least common denominator for 68 and 56 ? (1 point)

Question

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

Answer 1

Let's go through each question one by one.

Question 1

To find the least common denominator (LCD) for 68 and 56, we can find their prime factors.

• 68: \( 2^2 \times 17 \)
• 56: \( 2^3 \times 7 \)

The LCD is found by taking the highest power of each prime factor:

• For 2, the highest power is \( 2^3 \)
• For 7, the highest power is \( 7^1 \)
• For 17, the highest power is \( 17^1 \)

So, the LCD = \( 2^3 \times 7 \times 17 = 8 \times 7 \times 17 = 56 \times 17 = 952 \)

However, none of the options provided are correct for the least common denominator. Let's double-check.

The correct answer should be 68 because \( 68 \) is a multiple of \( 56 \).

None of the given responses are correct.

Question 2

Jose is baking a cake and needs:

• \( \frac{2}{4} \) cup of sugar for the cake.
• \( \frac{3}{5} \) cup of sugar for the frosting.

We convert to a common denominator to add these fractions:

The least common denominator (LCD) of 4 and 5 is 20.

Convert the fractions:

• \( \frac{2}{4} = \frac{10}{20} \)
• \( \frac{3}{5} = \frac{12}{20} \)

Now add them: \[ \frac{10}{20} + \frac{12}{20} = \frac{22}{20} = 1 \frac{2}{20} = 1 \frac{1}{10} \] So the answer is 1 1/10 (which is equivalent to 11/10).

Final answer: 11/10.

Question 3

True or False: When adding or subtracting fractions, you must always have a common denominator.

True.

Question 4

Find the difference: \( \frac{3}{4} - \frac{2}{6} \).

To subtract these fractions, convert them to a common denominator.

The least common denominator of 4 and 6 is 12.

Convert fractions:

• \( \frac{3}{4} = \frac{9}{12} \)
• \( \frac{2}{6} = \frac{4}{12} \)

Now subtract: \[ \frac{9}{12} - \frac{4}{12} = \frac{5}{12} \]

So the answer is 5/12.

Question 5

Find the sum: \( \frac{4}{6} + \frac{2}{3} \).

To find the sum, convert to a common denominator.

The least common denominator of 6 and 3 is 6.

Convert:

• \( \frac{2}{3} = \frac{4}{6} \)

Now add: \[ \frac{4}{6} + \frac{4}{6} = \frac{8}{6} = 1 \frac{2}{6} = 1 \frac{1}{3} \]

So, the answer is 1 1/3.

Summary of Answers:

1. None of the given responses are correct.
2. 1 1/10
3. True
4. 5/12
5. 1 1/3