Answers
A. -5.7546
B. -3.958
C. 6.16
D. 5.6423
5 answers
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
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.
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. \(-\frac{2}{3}\).
