Question

1 complete the table.
□ 3 6 9 12 15
□ 5 10 15 20 25
complete the equivalent ratios.
$\frac{12}{20} = \frac{□}{10}$ $\frac{12}{20} = \frac{3}{□}$
2

integer	opposite	absolute value
-15	15	15
-18	18	18

3 write an expression to represent:
\8 less than the product of 6 and a number\
4 solve. show your work.
$6.389 + 0.23 =$
$1.95 - 0.99 =$
5 $7,485 \div 6 =$
$843 \times 279 =$

Explanation:

---

Problem 1: Complete the table and equivalent ratios

Step1: Find table starting value

Top row: $3,6,9,12,15$ has difference $3$.
Bottom row: $5,10,15,20,25$ has difference $5$.
First value for both rows: $0$

Step2: Simplify first equivalent ratio

$\frac{12}{20} = \frac{12\div2}{20\div2} = \frac{6}{10}$

Step3: Simplify second equivalent ratio

$\frac{12}{20} = \frac{12\div4}{20\div4} = \frac{3}{5}$

---

Problem 2: Integer, Opposite, Absolute Value

Step1: Verify opposite of 31

Opposite of positive integer is negative: $-31$

Step2: Verify absolute value of 31

Absolute value is non-negative: $|31|=31$

Step3: Verify opposite of -15

Opposite of negative integer is positive: $15$

Step4: Verify absolute value of -15

Absolute value is non-negative: $|-15|=15$

Step5: Verify opposite of -18

Opposite of negative integer is positive: $18$

Step6: Verify absolute value of -18

Absolute value is non-negative: $|-18|=18$

---

Problem 3: Write the expression

Step1: Define variable for unknown number

Let the number be $x$

Step2: Write product of 6 and the number

$6x$

Step3: Subtract 8 from the product

$6x - 8$

---

Problem 4: Decimal arithmetic

Step1: Add decimals (align decimals)

$6.389 + 0.23 = 6.389 + 0.230 = 6.619$

Step2: Subtract decimals (align decimals)

$1.95 - 0.99 = 0.96$

---

Problem 5: Integer multiplication and division

Step1: Divide 7485 by 6

$7485 \div 6 = 1247.5$

Step2: Multiply 843 by 279

$$\begin{align*} 843 \times 279 &= 843 \times (200+70+9)\\ &= 843\times200 + 843\times70 + 843\times9\\ &= 168600 + 59010 + 7587\\ &= 235197 \end{align*}$$

---

Answer:

1. Table: Top row first box = $\boldsymbol{0}$, Bottom row first box = $\boldsymbol{0}$; Equivalent ratios: $\boldsymbol{6}$, $\boldsymbol{5}$
2. | Integer | Opposite | Absolute Value |

31	$\boldsymbol{-31}$	$\boldsymbol{31}$
-15	$\boldsymbol{15}$	$\boldsymbol{15}$
-18	$\boldsymbol{18}$	$\boldsymbol{18}$

1. $\boldsymbol{6x - 8}$
2. $6.389 + 0.23 = \boldsymbol{6.619}$; $1.95 - 0.99 = \boldsymbol{0.96}$
3. $7,485 \div 6 = \boldsymbol{1247.5}$; $843 \times 279 = \boldsymbol{235197}$