Learn how to multiply and divide rational numbers through these examples.
Example 1: Multiplying Rational Numbers
Calculate: 23x45
Step 1: To multiply rational numbers (fractions), multiply the numerators together and multiply the denominators together.
abxcd=a * cb * d
Step 2: Multiply the numerators (2 and 4) and the denominators (3 and 5).
23x45=2 * 43 * 5
Step 3: Calculate the products in the numerator and denominator.
2 * 43 * 5=815
Step 4: Simplify the resulting fraction if possible (in this case, 8/15 cannot be simplified further).
Result: The product is 815.
Example 2: Multiplying with Negatives
Calculate: -34x56
Step 1: Multiply the numerators (-3 and 5) and the denominators (4 and 6). Remember the rules for multiplying integers: negative multiplied by positive is negative.
-34x56=-3 * 54 * 6
Step 2: Calculate the products.
-3 * 54 * 6=-1524
Step 3: Simplify the resulting fraction. Both 15 and 24 are divisible by 3.
-1524=-15 / 324 / 3=-58
Result: The product is -58.
Example 3: Dividing Rational Numbers
Calculate: 12÷34
Step 1: To divide by a rational number, multiply by its reciprocal. The reciprocal of a fraction is obtained by swapping the numerator and the denominator.
The reciprocal of 34 is 43.
Step 2: Rewrite the division problem as a multiplication problem using the reciprocal of the second fraction.
12÷34=12x43
Step 3: Multiply the fractions as learned in the previous examples: multiply numerators and multiply denominators.
12x43=1 * 42 * 3=46
Step 4: Simplify the resulting fraction. Both 4 and 6 are divisible by 2.
46=4 / 26 / 2=23
Result: The quotient is 23.
Example 4: Dividing with Negatives
Calculate: -25÷-47
Step 1: Find the reciprocal of the second fraction. The reciprocal of -47 is 7-4 (or -74).
Step 2: Rewrite the division problem as a multiplication problem using the reciprocal.
-25÷-47=-25x-74
Step 3: Multiply the fractions. Remember the rules for multiplying integers: negative multiplied by negative is positive.
-25x-74=-2 * -75 * 4=1420
Step 4: Simplify the resulting fraction. Both 14 and 20 are divisible by 2.
1420=14 / 220 / 2=710
Result: The quotient is 710.
Practice Mode
Enter the numerators and denominators below to solve a problem.
Related Concepts
Explore these related mathematical concepts to deepen your understanding of rational number operations.
Fractions
Numbers representing parts of a whole.
Integers
Whole numbers (positive, negative, and zero).
Numerator
The top number in a fraction.
Denominator
The bottom number in a fraction (cannot be zero).
Reciprocal
A fraction flipped upside down (used in division).