Question

4.17 x -1.38
Answers
A. -5.7546
B. -3.958
C. 6.16
D. 5.6423

Answer 1

Which of the following expressions represents a number less than 1? (choose 2)
Responses
A




3 fourths times 2 thirds
B


4 fifths times 3
C


2 times 1 fifth
D




3 fifths divided by 1 eighth
E 6 divided by 3/8

Answer 2

Divide and simplify.
- 4/5 / 6/5
Responses
A

− 2/5
B −

− 2/3
C

5/6
D 3/4

Answer 3

To solve \( 4.17 \times -1.38 \):

\[
4.17 \times -1.38 = -5.7436
\]

Now, we can see which of the provided options is closest to this result:

A. -5.7546
B. -3.958
C. 6.16
D. 5.6423

None of the options match exactly, but option A (-5.7546) is the closest approximation to -5.7436.

Thus, the best answer is:
**A. -5.7546**

Answer 4

To determine which expressions represent a number less than 1, let's calculate each option:

**A. \( \frac{3}{4} \times \frac{2}{3} \)**
\[
\frac{3}{4} \times \frac{2}{3} = \frac{3 \times 2}{4 \times 3} = \frac{6}{12} = \frac{1}{2} \quad (\text{which is less than } 1)
\]

**B. \( \frac{4}{5} \times 3 \)**
\[
\frac{4}{5} \times 3 = \frac{4 \times 3}{5} = \frac{12}{5} = 2.4 \quad (\text{which is greater than } 1)
\]

**C. \( 2 \times \frac{1}{5} \)**
\[
2 \times \frac{1}{5} = \frac{2}{5} \quad (\text{which is less than } 1)
\]

**D. \( \frac{3}{5} \div \frac{1}{8} \)**
\[
\frac{3}{5} \div \frac{1}{8} = \frac{3}{5} \times 8 = \frac{24}{5} = 4.8 \quad (\text{which is greater than } 1)
\]

**E. \( 6 \div \frac{3}{8} \)**
\[
6 \div \frac{3}{8} = 6 \times \frac{8}{3} = \frac{48}{3} = 16 \quad (\text{which is greater than } 1)
\]

Based on these calculations, the two expressions that represent a number less than 1 are:

**A. \( \frac{3}{4} \times \frac{2}{3} \)**
**C. \( 2 \times \frac{1}{5} \)**

So the correct choices are **A** and **C**.

Answer 5

To divide the fractions \(-\frac{4}{5}\) by \(\frac{6}{5}\), we can use the rule that dividing by a fraction is equivalent to multiplying by its reciprocal.

So, we have:

\[
-\frac{4}{5} \div \frac{6}{5} = -\frac{4}{5} \times \frac{5}{6}
\]

Now, we multiply the numerators and the denominators:

\[
-\frac{4 \times 5}{5 \times 6} = -\frac{20}{30}
\]

Now, we can simplify \(-\frac{20}{30}\):

\[
-\frac{20 \div 10}{30 \div 10} = -\frac{2}{3}
\]

Thus, the simplified result is:

**B. \(-\frac{2}{3}\)**.