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Determine if the fraction is greater than or equal to 1.

1. [tex]\frac{42}{37}[/tex] (42 > 37)
2. [tex]\frac{14}{9}[/tex] (14 > 9)
3. [tex]\frac{13}{8}[/tex] (13 > 8)
4. [tex]\frac{20}{19}[/tex]
5. [tex]\frac{12}{12}[/tex] (12 = 12)
6. [tex]\frac{27}{27}[/tex] (27 = 27)

Which fractions are greater than 1? Select all that apply.

- [tex]\frac{15}{10}[/tex]
- [tex]\frac{21}{20}[/tex]
- [tex]\frac{1}{2}[/tex]
- [tex]\frac{3}{3}[/tex]
- [tex]\frac{2}{13}[/tex]
- [tex]\frac{48}{12}[/tex]

Write each fraction as a whole number or mixed number in simplest form.

1. [tex]\frac{8}{5}[/tex]
2. [tex]\frac{11}{7}[/tex]
3. [tex]\frac{28}{3}[/tex]
4. [tex]\frac{26}{7}[/tex]
5. [tex]\frac{10}{10}[/tex]
6. [tex]\frac{24}{7}[/tex]
7. [tex]\frac{20}{16}[/tex]
8. [tex]\frac{16}{4}[/tex]
9. [tex]\frac{40}{15}[/tex]
10. [tex]\frac{55}{20}[/tex]
11. [tex]\frac{30}{14}[/tex]
12. [tex]\frac{65}{26}[/tex]

Answer :

Sure! Let's go through the process of solving this problem step-by-step:

### Step 1: Identify Fractions Greater Than or Equal to 1

To determine which fractions are greater than or equal to 1, we need to compare the numerators and denominators:

- If the numerator is greater than or equal to the denominator, the fraction is greater than or equal to 1.

Here are the fractions given and their evaluations:

1. [tex]\(\frac{42}{37}\)[/tex]: 42 > 37 → Greater than 1
2. [tex]\(\frac{14}{9}\)[/tex]: 14 > 9 → Greater than 1
3. [tex]\(\frac{13}{8}\)[/tex]: 13 > 8 → Greater than 1
4. [tex]\(\frac{20}{19}\)[/tex]: 20 > 19 → Greater than 1
5. [tex]\(\frac{12}{12}\)[/tex]: 12 = 12 → Equals 1
6. [tex]\(\frac{27}{27}\)[/tex]: 27 = 27 → Equals 1
7. [tex]\(\frac{15}{10}\)[/tex]: 15 > 10 → Greater than 1
8. [tex]\(\frac{21}{20}\)[/tex]: 21 > 20 → Greater than 1
9. [tex]\(\frac{1}{2}\)[/tex]: 1 < 2 → Less than 1
10. [tex]\(\frac{3}{3}\)[/tex]: 3 = 3 → Equals 1
11. [tex]\(\frac{2}{13}\)[/tex]: 2 < 13 → Less than 1
12. [tex]\(\frac{48}{12}\)[/tex]: 48 > 12 → Greater than 1

The fractions greater than or equal to 1 are:
[tex]\(\frac{42}{37}\)[/tex], [tex]\(\frac{14}{9}\)[/tex], [tex]\(\frac{13}{8}\)[/tex], [tex]\(\frac{20}{19}\)[/tex], [tex]\(\frac{12}{12}\)[/tex], [tex]\(\frac{27}{27}\)[/tex], [tex]\(\frac{15}{10}\)[/tex], [tex]\(\frac{21}{20}\)[/tex], [tex]\(\frac{3}{3}\)[/tex], [tex]\(\frac{48}{12}\)[/tex].

### Step 2: Convert Fractions to Whole or Mixed Numbers

For each fraction, we'll find the whole number part and, if necessary, express the remainder as a fraction:

1. [tex]\(\frac{8}{5}\)[/tex]:
- Whole number part: 8 // 5 = 1
- Remainder: 8 % 5 = 3
- Simplified form: [tex]\(1\frac{3}{5}\)[/tex]

2. [tex]\(\frac{11}{7}\)[/tex]:
- Whole number part: 11 // 7 = 1
- Remainder: 11 % 7 = 4
- Simplified form: [tex]\(1\frac{4}{7}\)[/tex]

3. [tex]\(\frac{28}{3}\)[/tex]:
- Whole number part: 28 // 3 = 9
- Remainder: 28 % 3 = 1
- Simplified form: [tex]\(9\frac{1}{3}\)[/tex]

4. [tex]\(\frac{26}{7}\)[/tex]:
- Whole number part: 26 // 7 = 3
- Remainder: 26 % 7 = 5
- Simplified form: [tex]\(3\frac{5}{7}\)[/tex]

9. [tex]\(\frac{10}{10}\)[/tex]:
- Whole number part: 10 // 10 = 1
- No remainder.
- Simplified form: 1

20. [tex]\(\frac{24}{7}\)[/tex]:
- Whole number part: 24 // 7 = 3
- Remainder: 24 % 7 = 3
- Simplified form: [tex]\(3\frac{3}{7}\)[/tex]

21. [tex]\(\frac{20}{16}\)[/tex]:
- Whole number part: 20 // 16 = 1
- Remainder: 20 % 16 = 4
- Simplified form: [tex]\(1\frac{4}{16}\)[/tex] or [tex]\(1\frac{1}{4}\)[/tex]

22. [tex]\(\frac{16}{4}\)[/tex]:
- Whole number part: 16 // 4 = 4
- No remainder.
- Simplified form: 4

[tex]\(\frac{40}{15}\)[/tex]:
- Whole number part: 40 // 15 = 2
- Remainder: 40 % 15 = 10
- Simplified form: [tex]\(2\frac{10}{15}\)[/tex] or [tex]\(2\frac{2}{3}\)[/tex]

25. [tex]\(\frac{55}{20}\)[/tex]:
- Whole number part: 55 // 20 = 2
- Remainder: 55 % 20 = 15
- Simplified form: [tex]\(2\frac{15}{20}\)[/tex] or [tex]\(2\frac{3}{4}\)[/tex]

26. [tex]\(\frac{30}{14}\)[/tex]:
- Whole number part: 30 // 14 = 2
- Remainder: 30 % 14 = 2
- Simplified form: [tex]\(2\frac{2}{14}\)[/tex] or [tex]\(2\frac{1}{7}\)[/tex]

27. [tex]\(\frac{65}{26}\)[/tex]:
- Whole number part: 65 // 26 = 2
- Remainder: 65 % 26 = 13
- Simplified form: [tex]\(2\frac{13}{26}\)[/tex] or [tex]\(2\frac{1}{2}\)[/tex]

This concludes the process! Please feel free to ask if you need further explanations.

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