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Which of the following numbers should replace the missing denominator in order to add the fractions? 2582 + 13?

(1 point)
Responses

82
82

13
13

28
28

25

11 answers

To add the fractions \( \frac{2582}{?} + \frac{13}{?} \), we need both fractions to have a common denominator. This means the denominators must be the same.

Given the options:

  • 82
  • 13
  • 28
  • 25

We can see that the denominator could fulfill the requirement if it allows us to express both fractions correctly.

However, the number 13 can also be a denominator since both fractions would be expressed as \( \frac{2582}{13} + \frac{13}{13} \).

To simplify the addition, selecting 13 as the common denominator would yield:

\[ \text{Option: } 13 \]

This means the missing denominator can reasonably be 13 to successfully add the fractions. Thus, the answer is:

13

Find the least common multiple of 2 and 12.(1 point)
Responses

36
36

24
24

2
2

12
12

To find the least common multiple (LCM) of 2 and 12, we can list the multiples of each number:

  • Multiples of 2: 2, 4, 6, 8, 10, 12, 14, 16, …
  • Multiples of 12: 12, 24, 36, 48, …

The smallest common multiple from both lists is 12.

Therefore, the least common multiple of 2 and 12 is:

12

Jiani gets paid for a job every 9 weeks and Rosa gets paid for a job every 12 weeks. How many weeks will it take for them to get paid at the same time?

To find out when Jiani and Rosa will get paid at the same time, we need to determine the least common multiple (LCM) of their pay periods, which are 9 weeks and 12 weeks.

Step 1: List the multiples of each number.

  • Multiples of 9:

    • 9, 18, 27, 36, 45, 54, ...

  • Multiples of 12:

    • 12, 24, 36, 48, 60, ...

Step 2: Identify the smallest common multiple.

From the lists above, the smallest common multiple is 36.

Conclusion:

Jiani and Rosa will get paid at the same time after 36 weeks.

Add the following fractions: 2 1/5 + 1/3

To add the fractions \(2 \frac{1}{5}\) and \(\frac{1}{3}\), we first need to convert the mixed number into an improper fraction.

Step 1: Convert \(2 \frac{1}{5}\) to an improper fraction.

\[ 2 \frac{1}{5} = \frac{2 \times 5 + 1}{5} = \frac{10 + 1}{5} = \frac{11}{5} \]

Step 2: Find a common denominator for \(\frac{11}{5}\) and \(\frac{1}{3}\).

The denominators are 5 and 3. The least common multiple (LCM) of 5 and 3 is 15.

Step 3: Convert each fraction to have the common denominator of 15.

  • For \(\frac{11}{5}\): \[ \frac{11}{5} \times \frac{3}{3} = \frac{33}{15} \]

  • For \(\frac{1}{3}\): \[ \frac{1}{3} \times \frac{5}{5} = \frac{5}{15} \]

Step 4: Add the two fractions.

Now add \(\frac{33}{15} + \frac{5}{15}\):

\[ \frac{33 + 5}{15} = \frac{38}{15} \]

Step 5: Convert back to a mixed number, if desired.

\(\frac{38}{15}\) can be converted to a mixed number:

\[ 38 \div 15 = 2 \quad \text{(whole number: 2)} \] \[ 38 - (15 \times 2) = 8 \quad \text{(remainder: 8)} \]

So,

\[ \frac{38}{15} = 2 \frac{8}{15} \]

Final Answer:

The sum of \(2 \frac{1}{5} + \frac{1}{3}\) is \(\frac{38}{15}\) or \(2 \frac{8}{15}\).

i meant Add the following fractions: 21/5 + 1/3

To add the fractions \( \frac{21}{5} \) and \( \frac{1}{3} \), we need to find a common denominator.

Step 1: Find the least common denominator (LCD)

The denominators are 5 and 3. The least common multiple (LCM) of 5 and 3 is 15.

Step 2: Convert each fraction to have the common denominator of 15.

  • For \( \frac{21}{5} \): \[ \frac{21}{5} \times \frac{3}{3} = \frac{63}{15} \]

  • For \( \frac{1}{3} \): \[ \frac{1}{3} \times \frac{5}{5} = \frac{5}{15} \]

Step 3: Add the two fractions.

Now we can add:

\[ \frac{63}{15} + \frac{5}{15} = \frac{63 + 5}{15} = \frac{68}{15} \]

Final Answer:

The sum of \( \frac{21}{5} + \frac{1}{3} \) is \( \frac{68}{15} \).

If you want to convert it to a mixed number:

\[ 68 \div 15 = 4 \quad \text{(whole number: 4)} \] \[ 68 - (15 \times 4) = 8 \quad \text{(remainder: 8)} \]

So,

\[ \frac{68}{15} = 4 \frac{8}{15} \]

Thus, the final answer can be expressed as \( \frac{68}{15} \) or \( 4 \frac{8}{15} \).

which do i put?

You can choose to write the answer in either form depending on what is required. Here are your options:

  1. As an improper fraction: \[ \frac{68}{15} \]

  2. As a mixed number: \[ 4 \frac{8}{15} \]

If you need to submit a single answer, you can choose either \( \frac{68}{15} \) (improper fraction) or \( 4 \frac{8}{15} \) (mixed number). If the instructions do not specify, using the improper fraction \( \frac{68}{15} \) is often acceptable in mathematical contexts.