10.1: Which One Doesn’t Belong: Expressions
Which expression doesn’t belong?
$7.9x$
$7.9\boldcdot (\text- 10)$
$7.9 + x$
$\text-79$
Lesson 10: Multiply!
Let’s get more practice multiplying signed numbers.
10.2: Matching Expressions
Match expressions that are equal to each other.
| row 1 | $(\text-1) \boldcdot 12$ | $(\text-64)\boldcdot \frac18$ | $1 \boldcdot 15$ |
|---|---|---|---|
| row 2 | $(\text-1) \boldcdot (\text-3) \boldcdot (\text-5)$ | $(\text-1) \boldcdot (\text-2) \boldcdot 6$ | $(\text-1) \boldcdot (\text-12)$ |
| row 3 | $1 \boldcdot (\text-3) \boldcdot (\text-5)$ | $(\text-\frac{1}{4}) \boldcdot (\text-32)$ | $(\text-2) \boldcdot 6$ |
| row 4 | $(\text-\frac{1}{2}) \boldcdot (\text-16)$ | $(\text-3) \boldcdot 5$ | $2\boldcdot (\text-4)$ |
| row 5 | $(\text-\frac12)\boldcdot 16$ | $(\text-1) \boldcdot (\text-3) \boldcdot (\text-4)$ | $2\boldcdot 4$ |
| row 6 | $(\text-1) \boldcdot (\text-3) \boldcdot 4$ | $(\text-3) \boldcdot (\text-5)$ | $1 \boldcdot (\text-15)$ |
10.3: Row Game: Multiplying Rational Numbers
Evaluate the expressions in one of the columns. Your partner will work on the other column. Check in with your partner after you finish each row. Your answers in each row should be the same. If your answers aren’t the same, work together to find the error.
| column A | column B | |
|---|---|---|
| row 1 | $790\div 10$ | $(7.9)\boldcdot 10$ |
| row 2 | $\left(\text- \frac67\right) \boldcdot 7$ | $(0.1) \boldcdot (\text- 60)$ |
| row 3 | $(2.1) \boldcdot (\text- 2)$ | $(\text-8.4) \boldcdot\frac12$ |
| row 4 | \((2.5) \boldcdot (\text-3.25)\) | $\left(\text{-} \frac52 \right)\boldcdot \frac{13}{4}$ |
| row 5 | \((\text-10) \boldcdot (3.2) \boldcdot (\text-7.3)\) | \(5\boldcdot (\text-1.6) \boldcdot (\text-29.2)\) |
A sequence of rational numbers is made by starting with 1, and from then on, each term is one more than the reciprocal of the previous term. Evaluate the first few expressions in the sequence. Can you find any patterns? Find the 10th term in this sequence.
$$1\qquad\quad 1+\frac{1}{1}\qquad\quad 1+\frac{1}{1+1}\qquad\quad 1+\frac{1}{1+\frac{1}{1+1}} \qquad \quad 1+\frac{1}{1+\frac{1}{1+\frac{1}{1+1}}}\qquad\quad \dots$$
Summary
A positive times a positive is always positive. For example, $\frac35 \boldcdot \frac78 = \frac{21}{40}$.
A negative times a negative is also positive. For example, $\text-\frac35 \boldcdot \text-\frac78 = \frac{21}{40}$.
A negative times a positive or a positive times a negative is always negative. For example, $\frac35 \boldcdot \text-\frac78 = \text-\frac35 \boldcdot \frac78 = \text-\frac{21}{40}$.
A negative times a negative times a negative is also negative. For example, $\text-3 \boldcdot \text-4 \boldcdot \text-5 = \text-60$.