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Algebra Foundations
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Divide Rational Numbers

Divide Rational Numbers Worksheet

Algebra 1
Algebra Foundations

Total questions - 6

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How Will This Worksheet on "Divide Rational Numbers" Benefit Your Students' Learning?

`1`. The division of rational numbers helps the student to get the basic knowledge of fundamental mathematical concepts, fractions, decimal calculation, and arithmetic problems.

`2`. This Mathematics can help the student enhance critical thinking and analytical power. It helps to learn the division techniques to solve real-life mathematical problems.

`3`. It can help the student to solve highly complex mathematical concepts like algebra, geometry, statistics, etc.

`4`. It can boost students' confidence in solving mathematical problems, and strengthen them to solve mathematical challenges easily.

 

How to Divide Rational Numbers?

The following procedures can be used to divide rational numbers into fractions or decimals:

Division of Fractional:

  • The divisor will first be reversed as the numerator and denominator are switched.
  • Dividends will be multiplied by the inverted divisor.
  • The outcome will be as simplified as possible.

 

Division of Decimals:

  • Initially, the divisor will be made into a whole number by shifting the decimal point.
  • The dividend will be multiplied by this converted divisor.
  • Place the decimal point in the quotient appropriately.
  • Simplify the result as much as possible.

Solved Example

Q. Divide. \newline58÷14=\frac{5}{8}\div\frac{1}{4}=_____
Solution:
  1. Divide and Multiply: What is the multiplication form of 58÷14\frac{5}{8} \div \frac{1}{4}?\newlineDividing by a number is the same as multiplying by its reciprocal.\newline58÷14=58×41\frac{5}{8} \div \frac{1}{4} = \frac{5}{8} \times \frac{4}{1} =(5×48×1)=208= \left(\frac{5 \times 4}{8 \times 1}\right)= \frac{20}{8}
  2. Simplify Fraction: Simplify the fraction 208\frac{20}{8}. \newline208\frac{20}{8} can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 44. \newline20÷4=520 \div 4 = 5 \newline8÷4=28 \div 4 = 2\newlineSo, 208\frac{20}{8} simplifies to 52\frac{5}{2}.
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About Worksheet

Algebra 1
Algebra Foundations

To divide rational numbers, the reciprocal of the second fraction is multiplied by the first fraction. By switching the second fraction's numerator and denominator, the reciprocal can be obtained. If you can, simplify the resulting fraction. 

As an example, to divide `\frac{2}{3}` by  `\frac{4}{5}`.

`\frac{2}{3} \times \frac{5}{4} = \frac{2 \times 5}{3 \times 4} = \frac{10}{12}`, which simplifies to `\frac{5}{6}`. As an example, to divide `\frac{2}{3}` by `\frac{4}{5}`.

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