Divide rational numbers practice
Sure, here are a few practice problems to help you divide rational numbers:
1) \(\frac{3}{4} \div \frac{5}{6}\)
To divide rational numbers, you must multiply by the reciprocal of the second number. So, \(\frac{3}{4} \div \frac{5}{6}\) becomes \(\frac{3}{4} \times \frac{6}{5}\). Simplifying this expression, we get \(\frac{18}{20}\), which can be further simplified to \(\frac{9}{10}\).
2) \(\frac{2}{5} \div \frac{4}{3}\)
Similarly, \(\frac{2}{5} \div \frac{4}{3}\) can be expressed as \(\frac{2}{5} \times \frac{3}{4}\). Simplifying this expression, we get \(\frac{6}{20}\), which can be further simplified to \(\frac{3}{10}\).
3) \(\frac{7}{8} \div \frac{2}{9}\)
Again, to divide rational numbers, multiply by the reciprocal of the second number. So, \(\frac{7}{8} \div \frac{2}{9}\) becomes \(\frac{7}{8} \times \frac{9}{2}\). Simplifying this expression, we get \(\frac{63}{16}\).
4) \(\frac{11}{3} \div \frac{7}{2}\)
Similar to the previous examples, \(\frac{11}{3} \div \frac{7}{2}\) can be expressed as \(\frac{11}{3} \times \frac{2}{7}\). Simplifying this expression, we get \(\frac{22}{21}\).
Remember to always simplify your fractions if possible.
Sure! Here's a step-by-step guide on how to divide rational numbers:
Step 1: Write down the division problem. For example, let's say we have the rational numbers 2/3 and 4/5, and we want to divide them: (2/3) ÷ (4/5).
Step 2: To divide rational numbers, we need to multiply the first number by the reciprocal of the second number. The reciprocal of a number is obtained by switching the numerator and denominator. In this case, the reciprocal of 4/5 is 5/4.
Step 3: Now, rewrite the division problem as a multiplication problem using the reciprocal. So, (2/3) ÷ (4/5) becomes (2/3) * (5/4).
Step 4: Multiply the numerators together. In this case, multiply 2 and 5 to get 10.
Step 5: Multiply the denominators together. In this case, multiply 3 and 4 to get 12.
Step 6: Write the result as a fraction. So, (2/3) * (5/4) is equal to 10/12.
Step 7: Simplify the fraction if possible. In this case, we can simplify the fraction by dividing both the numerator and denominator by their greatest common divisor, which is 2. Dividing 10/2 and 12/2, we get 5/6.
Step 8: The final answer is 5/6.
So, when dividing the rational numbers 2/3 and 4/5, the result is 5/6.
To practice dividing rational numbers, you can follow these steps:
1. Understand the concept: Rational numbers are numbers that can be expressed as a fraction of two integers, where the denominator is not zero. Dividing rational numbers involves dividing one fraction by another.
2. Simplify the fractions: Before dividing, simplify the fractions involved to their lowest terms, if possible. To do this, find the greatest common divisor (GCD) of the numerator and denominator, and divide both by the GCD.
3. Invert and multiply: To divide a fraction, invert (flip) the second fraction and multiply it by the first fraction. For example, to divide a/b by c/d, multiply (a/b) * (d/c) = (ad)/(bc).
4. Perform the multiplication: Multiply the numerators together to get the resulting numerator, and multiply the denominators together to get the resulting denominator.
5. Simplify the result (if needed): If the resulting fraction can be simplified further, find the GCD of the numerator and denominator, and divide both by it.
6. Finalize the answer: The final result is the simplified fraction obtained from the multiplication.
Example:
Divide 2/3 by 4/5.
1. Simplify the fractions (already simplified).
2. Invert and multiply: (2/3) * (5/4).
3. Multiply the numerators: 2 * 5 = 10.
4. Multiply the denominators: 3 * 4 = 12.
5. Simplify: No further simplification possible.
6. Final result: 10/12, which reduces to 5/6.
Remember to always check your answer by performing a quick mental calculation or using a calculator.