7th Grade Multiplying and Dividing Rational Numbers Lesson (Free PDF)
This multiply divide rationals lesson for 7th Grade covers multiplying and dividing rational numbers (Common Core 7.NS.A.2), with a free PDF to print.
To multiply or divide rational numbers, multiply or divide the absolute values and then decide the sign. Same signs give a positive result, and different signs give a negative result. Division by 0 is undefined. Every rational number can be written as a decimal that either terminates or repeats.
Grade 7 · Common Core State Standards: 7.NS.A.2
Key facts in this multiply divide rationals lesson
- Same signs: positive. Different signs: negative.
- An even number of negative factors gives a positive product; an odd number gives a negative product.
- Divide by a fraction by multiplying by its reciprocal.
- Division by 0 is undefined.
- A fraction is a terminating decimal or a repeating decimal, found by long division.
How do you multiply signed numbers?
Multiply the absolute values first, then decide the sign. If the factors have the same sign, the product is positive. If the signs are different, the product is negative.
One way to see why: multiplication is repeated addition, so \(4 \times (-3) = (-3) + (-3) + (-3) + (-3) = -12\).
How do you divide signed numbers?
Division follows the same sign rules because every division fact comes from a multiplication fact. Since \((-4) \times 3 = -12\), we know \(-12 \div 3 = -4\) and \(-12 \div (-4) = 3\).
Dividing by a fraction means multiplying by its reciprocal: \(-\frac{3}{4} \div \frac{1}{2} = -\frac{3}{4} \times 2 = -\frac{3}{2}\).
- Rewrite division as multiplication by the reciprocal (for fractions).
- Count the negative factors.
- Multiply the absolute values and simplify.
- Attach the sign: an even number of negatives gives a positive answer.
Example. \((-\frac{2}{3}) \times (-\frac{9}{10})\): two negatives, so the result is positive. \(\frac{2}{3} \times \frac{9}{10} = \frac{18}{30} = \frac{3}{5}\).
How do you turn a fraction into a decimal?
Divide the numerator by the denominator with long division. The decimal either terminates (stops) or repeats a block of digits forever. A bar over the repeating block shows it: \(\frac{5}{11} = 0.\overline{45}\).
Every rational number is one of these two kinds. A fraction in lowest terms terminates only when the denominator has no prime factors other than 2 and 5.
Multiply divide rationals lesson: questions and answers
Why is a negative times a negative positive?
Multiplying by a negative reverses direction. Doing it twice sends you back the original way. In patterns, \(-3 \times 2 = -6\), \(-3 \times 1 = -3\), \(-3 \times 0 = 0\), \(-3 \times (-1) = 3\).
What is the sign of a product with five negative factors?
It is negative. An odd number of negative factors gives a negative product.
How do you divide by a negative fraction?
Multiply by its reciprocal, which keeps the negative sign. For example, \(-\frac{2}{5} \div (-\frac{4}{15}) = -\frac{2}{5} \times (-\frac{15}{4}) = \frac{3}{2}\).
How do you know if a decimal terminates?
Write the fraction in lowest terms. If the denominator has only the prime factors 2 and 5, the decimal terminates. Otherwise it repeats.
Why can’t you divide by zero?
There is no number that multiplies by 0 to give a nonzero result, so \(6 \div 0\) has no answer. We say it is undefined.
How to use this multiply divide rationals lesson
Read the definitions first, then follow the worked method line by line and redo the example on paper without looking. When every step makes sense, move on to the worksheet, then check yourself with the quiz.
Download the multiply divide rationals lesson as a PDF with the button below and keep it with your notes.
All Grade 7 chapters: Grade 7 math.
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