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Determine the lowest common denominator for each sum or difference.

1. [tex]\(\frac{13}{24} + \frac{7}{12}\)[/tex]
A. Common Denominator: 10
B. Common Denominator: 12
C. Common Denominator: 24

2. [tex]\(\frac{7}{6} + \left(-\frac{5}{12}\right)\)[/tex]

3. [tex]\(-\frac{3}{4} + \left(-\frac{2}{3}\right)\)[/tex]

4. [tex]\(5 - \frac{7}{10}\)[/tex]

5. [tex]\(\frac{1}{8} - \frac{5}{3}\)[/tex]

6. [tex]\(32 - \frac{4}{5}\)[/tex]



Answer :

GinnyAnswer
Sure! Let's determine the lowest common denominator (LCD) for each given sum or difference in the fractions.

### Problem 1: [tex]\( \frac{13}{24} + \frac{7}{12} \)[/tex]

To find the lowest common denominator:

1. Identify the denominators: 24 and 12.
2. Find the LCD of 24 and 12.

The lowest common denominator (LCD) of 24 and 12 is 24.

### Problem 2: [tex]\( \frac{7}{6} + \left( -\frac{5}{12} \right) \)[/tex]

To find the lowest common denominator:

1. Identify the denominators: 6 and 12.
2. Find the LCD of 6 and 12.

The lowest common denominator (LCD) of 6 and 12 is 12.

### Problem 3: [tex]\( -\frac{3}{4} + \left( -\frac{2}{3} \right) \)[/tex]

To find the lowest common denominator:

1. Identify the denominators: 4 and 3.
2. Find the LCD of 4 and 3.

The lowest common denominator (LCD) of 4 and 3 is 12.

### Problem 4: [tex]\( 5 - \frac{7}{10} \)[/tex]

To find the lowest common denominator:

1. Represent 5 as a fraction: [tex]\( \frac{5}{1} \)[/tex].
2. Identify the denominators: 1 and 10.
3. Find the LCD of 1 and 10.

The lowest common denominator (LCD) of 1 and 10 is 10.

### Problem 5: [tex]\( \frac{1}{8} - \frac{5}{3} \)[/tex]

To find the lowest common denominator:

1. Identify the denominators: 8 and 3.
2. Find the LCD of 8 and 3.

The lowest common denominator (LCD) of 8 and 3 is 24.

### Problem 6: [tex]\( 32 - \frac{4}{5} \)[/tex]

To find the lowest common denominator:

1. Represent 32 as a fraction: [tex]\( \frac{32}{1} \)[/tex].
2. Identify the denominators: 1 and 5.
3. Find the LCD of 1 and 5.

The lowest common denominator (LCD) of 1 and 5 is 5.

### Summary

Here are the lowest common denominators for each given sum or difference:

1. [tex]\( \frac{13}{24} + \frac{7}{12} \)[/tex]: 24
2. [tex]\( \frac{7}{6} + \left( -\frac{5}{12} \right) \)[/tex]: 12
3. [tex]\( -\frac{3}{4} + \left( -\frac{2}{3} \right) \)[/tex]: 12
4. [tex]\( 5 - \frac{7}{10} \)[/tex]: 10
5. [tex]\( \frac{1}{8} - \frac{5}{3} \)[/tex]: 24
6. [tex]\( 32 - \frac{4}{5} \)[/tex]: 5

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