Multiplying & Dividing Rational Numbers
More Lessons for Grade 6
Math Worksheets
Examples, solutions, videos, and worksheets to help Grade 6 students learn how to multiply and divide rational numbers.
Rational numbers include fractions, integers, and decimals. Here’s how to multiply and divide them:
How to multiply Rational Numbers?
- Fraction Form
Multiply the top numbers (numerators), multiply the bottom numbers (denominators) and simplify the answer when needed.
As a shortcut, we can cancel factors first before we multiply. Identify any common factors between any numerator and any denominator. It doesn’t have to be a numerator and denominator of the same fraction. You can cancel factors diagonally or vertically.
When working with fractions, a negative sign can be in the numerator, the denominator, or in front of the entire fraction, and they all represent the same negative value (e.g., ( \( \frac{-p}{q} \) = \( \frac{p}{-q} \) = \( -\frac{p}{q} \))
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Mixed Numbers
Convert mixed numbers to improper fractions before multiplying. -
Decimal Form
Ignore decimals and multiply as whole numbers.
Count total decimal places in both numbers.
Place the decimal in the answer.
Determine the sign of the product:
Positive × Positive = Positive
Negative × Negative = Positive
Positive × Negative = Negative
Negative × Positive = Negative
The following diagram gives some examples of multiplying rational numbers. Scroll down the page for more examples and solutions.
Fraction, Decimal & Rational Number Worksheets
Practice your skills with the following worksheets:
Online & Printable Fraction Worksheets
Online & Printable Decimal Worksheets
Online & Printable Rational Number Worksheets
How to divide Rational Numbers?
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Fraction Form:
To divide rational numbers, we replace the divisor with its reciprocal and then multiply to get the answer. -
Mixed Numbers:
Convert mixed numbers to improper fractions before dividing. -
Decimal Form:
Move the decimal point in the divisor to the right until it becomes a whole number.
Move the decimal point in the dividend the same number of places to the right. You may need to add trailing zeros to the dividend if it doesn’t have enough decimal places.
Perform the division as you would with whole numbers.
Place the decimal point in the quotient directly above the new position of the decimal point in the dividend.
Determine the sign of the quotient:
Positive ÷ Positive = Positive
Negative ÷ Negative = Positive
Positive ÷ Negative = Negative
Negative ÷ Positive = Negative
Multiplying Rational Numbers
Multiplying Rational Numbers
Dividing Rational Numbers
Dividing Rational Numbers
Try out our new and fun Fraction Concoction Game.
Add and subtract fractions to make exciting fraction concoctions following a recipe. There are four levels of difficulty: Easy, medium, hard and insane. Practice the basics of fraction addition and subtraction or challenge yourself with the insane level.
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