6. Which expressions have a difterence greater than or equal to 8 ? Select all the correct answers. a) $$ 10 \frac{1}{3}-1 \frac{1}{4} $$ b) $$ 9 \frac{4}{5}-2 \frac{1}{8} $$ c) $$ 9 \frac{2}{12}-1 \frac{1}{10} $$ d) $$ 12 \frac{11}{15}-3 \frac{3}{20} $$ e) $$ 10 \frac{5}{14}-2 \frac{1}{4} $$

Question

UpStudy AI · Accepted Answer

To determine which expressions have a difference greater than or equal to 8, we will calculate each expression step by step.

1. **Convert mixed numbers to improper fractions** for easier calculations.
2. **Perform the subtraction**.
3. **Compare the result** to 8.

Let's start with each expression:

### a) $$ 10 \frac{1}{3} - 1 \frac{1}{4} $$

Convert to improper fractions:
- $$ 10 \frac{1}{3} = \frac{31}{3} $$
- $$ 1 \frac{1}{4} = \frac{5}{4} $$

Now, perform the subtraction:
$$
\frac{31}{3} - \frac{5}{4}
$$

To subtract these fractions, we need a common denominator. The least common multiple of 3 and 4 is 12.

Convert each fraction:
- $$ \frac{31}{3} = \frac{124}{12} $$
- $$ \frac{5}{4} = \frac{15}{12} $$

Now subtract:
$$
\frac{124}{12} - \frac{15}{12} = \frac{109}{12}
$$

Now, we need to check if $$ \frac{109}{12} \geq 8 $$:
$$
\frac{109}{12} \approx 9.08 \quad (\text{which is } \geq 8)
$$

### b) $$ 9 \frac{4}{5} - 2 \frac{1}{8} $$

Convert to improper fractions:
- $$ 9 \frac{4}{5} = \frac{49}{5} $$
- $$ 2 \frac{1}{8} = \frac{17}{8} $$

Now perform the subtraction:
$$
\frac{49}{5} - \frac{17}{8}
$$

The least common multiple of 5 and 8 is 40.

Convert each fraction:
- $$ \frac{49}{5} = \frac{392}{40} $$
- $$ \frac{17}{8} = \frac{85}{40} $$

Now subtract:
$$
\frac{392}{40} - \frac{85}{40} = \frac{307}{40}
$$

Now, check if $$ \frac{307}{40} \geq 8 $$:
$$
\frac{307}{40} \approx 7.675 \quad (\text{which is } < 8)
$$

### c) $$ 9 \frac{2}{12} - 1 \frac{1}{10} $$

Convert to improper fractions:
- $$ 9 \frac{2}{12} = \frac{110}{12} $$
- $$ 1 \frac{1}{10} = \frac{11}{10} $$

Now perform the subtraction:
$$
\frac{110}{12} - \frac{11}{10}
$$

The least common multiple of 12 and 10 is 60.

Convert each fraction:
- $$ \frac{110}{12} = \frac{550}{60} $$
- $$ \frac{11}{10} = \frac{66}{60} $$

Now subtract:
$$
\frac{550}{60} - \frac{66}{60} = \frac{484}{60}
$$

Now, check if $$ \frac{484}{60} \geq 8 $$:
$$
\frac{484}{60} \approx 8.067 \quad (\text{which is } \geq 8)
$$

### d) $$ 12 \frac{11}{15} - 3 \frac{3}{20} $$

Convert to improper fractions:
- $$ 12 \frac{11}{15} = \frac{191}{15} $$
- $$ 3 \frac{3}{20} = \frac{63}{20} $$

Now perform the subtraction:
$$
\frac{191}{15} - \frac{63}{20}
$$

The least common multiple of 15 and 20 is 60.

Convert each fraction:
- $$ \frac{191}{15} = \frac{764}{60} $$
- $$ \frac{63}{20} = \frac{189}{60} $$

Now subtract:
$$
\frac{764}{60} - \frac{189}{60} = \frac{575}{60}
$$

Now, check if $$ \frac{575}{60} \geq 8 $$:
$$
\frac{575}{60} \approx 9.583 \quad (\text{which is } \geq 8)
$$

### e) $$ 10 \frac{5}{14} - 2 \frac{1}{4} $$

Convert to improper fractions:
- $$ 10 \frac{5}{14} = \frac{145}{14} $$
- $$ 2 \frac{1}{4} = \frac{9}{4} $$

Now perform the subtraction:
$$
\frac{145}{14} - \frac{9}{4}
$$

The least common multiple of 14 and 4 is 28.

Convert each fraction:
- $$ \frac{145}{14} = \frac{290}{28} $$
- $$ \frac{9}{4} = \frac{63}{28} $$

Now subtract:
$$
\frac{290}{28} - \frac{63}{28} = \frac{227}{28}
$$

Now, check if $$ \frac{227}{28} \geq 8 $$:
$$
\frac{227}{28} \approx 8.107 \quad (\text{which is } \geq 8)
$$

### Summary of Results
- a) $$ \frac{109}{12} \geq 8 $$ (Yes)
- b) $$ \frac{307}{40} < 8 $$ (No)
- c) $$ \frac{484}{60} \geq 8 $$ (Yes)
- d) $$ \frac{575}{60} \geq 8 $$ (Yes)
- e) $$ \frac{227}{28} \geq 8 $$ (Yes)

### Final Answers
The expressions with a difference greater than or equal to 8 are:
- a) $$ 10 \frac{1}{3} - 1 \frac{1}{4} $$
- c) $$ 9 \frac{2}{12} - 1 \frac{1}{10} $$
- d) $$ 12 \frac{11}{15} - 3 \frac{3}{20} $$
- e) $$ 10 \frac{5}{14} - 2 \frac{1}{4} $$
The expressions with a difference greater than or equal to 8 are: - a) $$ 10 \frac{1}{3} - 1 \frac{1}{4} $$ - c) $$ 9 \frac{2}{12} - 1 \frac{1}{10} $$ - d) $$ 12 \frac{11}{15} - 3 \frac{3}{20} $$ - e) $$ 10 \frac{5}{14} - 2 \frac{1}{4} $$

6. Which expressions have a difterence greater than or equal to 8 ? Select all the correct answers. a) \( 10 \frac{1}{3}-1 \frac{1}{4} \) b) \( 9 \frac{4}{5}-2 \frac{1}{8} \) c) \( 9 \frac{2}{12}-1 \frac{1}{10} \) d) \( 12 \frac{11}{15}-3 \frac{3}{20} \) e) \( 10 \frac{5}{14}-2 \frac{1}{4} \)

Solución de inteligencia artificial de Upstudy

Responder

Solución

Beyond the Answer

preguntas relacionadas

Latest Arithmetic Questions