Math with Mr. J: Solving Proportions with Cross Multiplication

Key Concepts

• Proportions are two ratios that are equivalent.
• Cross Multiplication is a method used to solve for the missing value in a proportion.
  • It involves multiplying across the equal sign diagonally and setting the products equal.

Solving Proportions Step-by-Step

Example 1: Solving 4/10 = n/25

1. Cross Multiply:
   • Multiply 25 and 4: ( 25 \times 4 = 100 )
   • Multiply 10 and n: ( 10n )
   • Set the products equal: ( 100 = 10n )
2. Solve for n:
   • Divide both sides by 10: ( n = \frac{100}{10} = 10 )
3. Conclusion:
   • 4/10 is equivalent to 10/25.

Example 2: Solving x/8 = 15/20

1. Cross Multiply:
   • Multiply 20 and x: ( 20x )
   • Multiply 15 and 8: ( 120 )
   • Set the products equal: ( 20x = 120 )
2. Solve for x:
   • Divide both sides by 20: ( x = \frac{120}{20} = 6 )
3. Conclusion:
   • x/8 is equivalent to 15/20.

Example 3: Solving 9/12 = 6/m

1. Cross Multiply:
   • Multiply 9 and m: ( 9m )
   • Multiply 12 and 6: ( 72 )
   • Set the products equal: ( 9m = 72 )
2. Solve for m:
   • Divide both sides by 9: ( m = \frac{72}{9} = 8 )
3. Conclusion:
   • 9/12 is equivalent to 6/8.

Example 4: Solving 10/W = 5/9

1. Cross Multiply:
   • Multiply 9 and 10: ( 90 )
   • Multiply 5 and W: ( 5W )
   • Set the products equal: ( 90 = 5W )
2. Solve for W:
   • Divide both sides by 5: ( W = \frac{90}{5} = 18 )
3. Conclusion:
   • 10/18 is equivalent to 5/9.

Final Notes

• Cross multiplication is a straightforward technique to solve proportions if done step-by-step.
• Always check your final answer by substituting it back into the original proportion to ensure both sides are equal.

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Thanks for learning with Mr. J! Feel free to review these steps and practice with additional problems for better understanding.