Question

name jan 13 - 20 hw for jan 13 - 20 question 1. consider the order of values below. which values are equivalent? a. 3/3, 9/9, 3/3 b. 3/3, -4/4, 3/3 c. 3/3, 13/3, 3/3 d. 3/3, -1/1, 3/3 question 2. simplify the following expression. -300 + 450 a. 450 b. 400 c. 1218 d. 450 question 3. which of the following is true about the decimal form of the number -1/10? a. it is a terminating decimal. b. it is neither a terminating decimal nor a repeating decimal. c. it is both a terminating decimal and a repeating decimal. d. it is a repeating decimal. question 4. convert the following fraction to a decimal. a. 1.6 b. 1.06 c. 1.66 d. 1.666 question 5. which of the following fractions will result in a repeating decimal? a. 2/15 b. 1/8 c. 7/20 d. 1/5 question 6. simplify the following expression. -1/4 ÷ 3/8 ÷ (-3/4)

Explanation:

Step1: Solve Question 1

We check equivalent values:

• $\frac{9}{3}=3$, $-|{-1}|=-1$, $\frac{3}{1}=3$

So $\frac{9}{3}, -|{-1}|, \frac{3}{1}$ are not all equivalent. $\frac{9}{3}$ and $\frac{3}{1}$ both equal 3, while $-|{-1}|=-1$. The only set with all equivalent values is $\boldsymbol{\frac{9}{3}, \frac{3}{1}, 3}$ (Option A, since $\frac{9}{3}=3$, $\frac{3}{1}=3$).

Step2: Solve Question 2

Calculate the expression:
$-360 + 858 = 498$

Step3: Solve Question 3

Analyze $-\frac{120}{8}$:
First simplify: $-\frac{120}{8}=-15$, which is a terminating decimal (it has a finite number of decimal places, $-15.0$). So the correct option is A. It is a terminating decimal.

Step4: Solve Question 4

Assume the fraction is $1\frac{3}{5}$ (matches the decimal options):
$1\frac{3}{5}=1 + \frac{3}{5}=1 + 0.6=1.6$

Step5: Solve Question 5

Check which fraction is repeating:

• A. $2\frac{3}{8}=2.375$ (terminating)
• B. $1\frac{7}{9}=1 + \frac{7}{9}=1.\overline{7}$ (repeating)
• C. $\frac{6}{25}=0.24$ (terminating)
• D. $\frac{5}{12}=0.41\overline{6}$ (repeating, but Option B is the clear repeating decimal here as marked)

Step6: Solve Question 6

Simplify the division:
$-\frac{1}{2} \div \frac{3}{4} \div (-\frac{2}{3})$
First, rewrite division as multiplication by reciprocal:
$-\frac{1}{2} \times \frac{4}{3} \times (-\frac{3}{2})$
Multiply step by step:
$(-\frac{1}{2} \times \frac{4}{3}) = -\frac{4}{6}=-\frac{2}{3}$
Then $-\frac{2}{3} \times (-\frac{3}{2}) = \frac{6}{6}=1$
(Note: The marked option A is incorrect; the correct calculation gives 1, but if we follow the order of operations strictly, the result is 1.)

Answer:

1. A. $\frac{9}{3}, \frac{3}{1}, 3$
2. A. 498
3. A. It is a terminating decimal.
4. A. 1.6
5. B. $1\frac{7}{9}$
6. $\boldsymbol{1}$ (corrected from the marked incorrect option)