Cross Solve

This worksheet moves students into the full cross-multiplication process by introducing a variable, x, into each proportion. Problems include arrangements such as 3/5 = x/20, x/18 = 2/3, and 7/8 = 21/x. Students must cross multiply, create an equation, and then solve for x. This is an important step because the variable appears in different positions, so students cannot simply memorize one visual pattern. They have to understand that the same cross-product rule works no matter where the unknown is located.

For a parent, the process is easiest to think of as two stages. First, cross multiply to turn the proportion into an ordinary multiplication equation. Second, solve that equation by dividing. For example, if 3/5 = x/20, cross multiplication gives 3 × 20 = 5x. That becomes 60 = 5x. Divide both sides by 5, and x = 12. The fraction setup may look intimidating at first, but once the cross multiplication is done, the problem becomes a much more familiar equation.

Learning Goals

• Solve Proportions with Variables: Students find the missing value represented by x.
• Write Cross-Product Equations: Learners correctly multiply the diagonal pairs.
• Use Division to Isolate x: Students solve the resulting one-step equation.
• Handle Different Variable Positions: Learners see that x may appear in any numerator or denominator.
• Check Reasonableness: Students can substitute the answer back into the proportion to see whether the ratios match.

Parent-Friendly Teaching Tips

Use this routine:

1. Draw the imaginary X.
2. Multiply across both diagonals.
3. Write the multiplication equation.
4. Divide to get x alone.
5. Check the answer if needed.

For example:

3/5 = x/20

Cross multiply:

3 × 20 = 5 × x

So:

60 = 5x

Divide by 5:

x = 12

The important part is not where x appears. The same diagonal rule still works.

Why This Worksheet Helps

• Turns Fractions into Simpler Equations: Cross multiplication removes the fraction bars and creates a familiar algebra problem.
• Builds Flexibility: Students see variables in several different positions.
• Strengthens Algebra Skills: Learners practice isolating x after setting up the cross products.
• Connects Ratios and Equations: Students see that proportions can be solved using ordinary equation reasoning.
• Prepares for Real Applications: This method will later be used with rates, scale drawings, recipes, prices, and similar figures.

Classroom & Home Use

• Excellent for Guided Practice: A teacher or parent can model one full example, then let students repeat the process.
• Helpful for Parents: The two-stage idea-cross multiply, then divide-keeps the method manageable.
• Good for Intervention: Students can show the cross-product equation before solving, making mistakes easier to locate.
• Strong for Algebra Readiness: Solving for x is an important middle-school skill.
• Useful for Independent Practice: Once the routine is established, students can work through the different variable placements confidently.

The main value of this worksheet is that it connects proportions with equation solving. Ratios, fractions, cross products, multiplication, division, and variables all work together. For parents, the best coaching reminder is: “Cross multiply first, then solve the equation you created.” In classroom and homeschool settings, this worksheet is the point where the cross-multiplication method becomes a true problem-solving tool rather than just a pattern students recognize.