Multiply and Divide Rational Numbers Guided Notes online exercise ... - Free Printable

Here is the completed worksheet with explanations for each answer.

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Multiplying & Dividing Rational Numbers

1. You can _multiply_ and _divide_ rational numbers by using the same rules to multiply and divide integers.

> Explanation: Rational numbers include fractions, decimals, and integers. The sign rules (positive/negative) and basic operations are consistent across all rational numbers, just like with integers.

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2. The product or quotient of two numbers with the same sign is _positive_.

> Explanation:
> - (+) × (+) = (+)
> - (–) × (–) = (+)
> - (+) ÷ (+) = (+)
> - (–) ÷ (–) = (+)

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3. The product or quotient of two numbers with different signs is _negative_.

> Explanation:
> - (+) × (–) = (–)
> - (–) × (+) = (–)
> - (+) ÷ (–) = (–)
> - (–) ÷ (+) = (–)

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Multiplying and Dividing Fractions

4. To multiply two fractions, multiply the _numerators_ and then multiply the _denominators_.

> Example:
> \(\frac{2}{3} \times \frac{4}{5} = \frac{2 \times 4}{3 \times 5} = \frac{8}{15}\)

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5. To divide two fractions, keep the dividend the same, change division to _multiplication_, and change the divisor to its _reciprocal_.

> Example:
> \(\frac{2}{3} \div \frac{4}{5} = \frac{2}{3} \times \frac{5}{4} = \frac{10}{12} = \frac{5}{6}\)

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Multiplying and Dividing Decimals

4. To multiply decimals, multiply as if both factors are _whole_ numbers. Then count the number of decimal places in both factors to find out how many places are needed in the _product_.

> Example:
> \(1.2 \times 0.3\) → Multiply 12 × 3 = 36.
> Count decimal places: 1 + 1 = 2 → Answer: 0.36

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5. To divide a decimal by a whole number, bring up the _decimal point_ into the quotient. Then, _divide_ as you normally would.

> Example:
> \(4.8 ÷ 2\) → Bring decimal up: 2.4

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6. To divide a decimal by another decimal, _convert_ the divisor as a whole number. Move the decimal in the dividend the same number of spaces to the _right_.

> Example:
> \(4.8 ÷ 0.2\) → Move decimal one place right in both: \(48 ÷ 2 = 24\)

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7. Evaluate each expression:

#### Left Box:
\( -\frac{1}{4} \div \frac{2}{7} \)

> Step 1: Change division to multiplication and flip the second fraction (reciprocal).
> \( -\frac{1}{4} \times \frac{7}{2} \)

> Step 2: Multiply numerators and denominators.
> Numerator: \(-1 \times 7 = -7\)
> Denominator: \(4 \times 2 = 8\)
> Result: \( -\frac{7}{8} \)

✔ Answer: \( \boxed{-\frac{7}{8}} \)

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#### Right Box:
\( -1.2 \cdot -3 \)

> Step 1: Multiply the absolute values: \(1.2 \times 3 = 3.6\)

> Step 2: Apply sign rule: negative × negative = positive
> So, result is positive.

✔ Answer: \( \boxed{3.6} \)

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✔ Final Completed Worksheet Answers:

1. multiply, divide
2. positive
3. negative
4. numerators, denominators
5. multiplication, reciprocal
4. whole, product
5. decimal point, divide
6. convert, right

Expression 1: \( -\frac{1}{4} \div \frac{2}{7} = \boxed{-\frac{7}{8}} \)
Expression 2: \( -1.2 \cdot -3 = \boxed{3.6} \)

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