Cross Product Practice

This worksheet introduces students to the structure behind cross multiplication without immediately asking them to solve for a missing number. Each problem shows two equal ratios, such as 2/3 = 8/12 or 5/7 = 15/21, and students are asked to write the cross-product equation only. That means they multiply the numerator of one fraction by the denominator of the other fraction, then show that the two diagonal products are equal. The worksheet deliberately stops before solving because the goal is to help students understand what cross multiplication actually means before adding variables and multi-step algebra.

For a parent who may not remember proportions very well, think of a proportion as two fractions that are supposed to represent the same relationship. Cross multiplication gives us a quick way to test that relationship. If a/b = c/d, then multiplying across the diagonals gives a × d = b × c. For example, with 2/3 = 8/12, the cross products are 2 × 12 and 3 × 8. Both products equal 24, which is why the two ratios are proportional. On this worksheet, though, students only need to write the equation, such as 2 × 12 = 3 × 8.

Learning Goals

• Recognize the Structure of a Proportion: Students see how two ratios are written as equal fractions.
• Identify the Diagonals: Learners practice pairing the top-left number with the bottom-right number and the bottom-left with the top-right.
• Write Cross-Product Equations: Students translate a proportion into a multiplication equation.
• Build Accuracy Before Solving: Learners focus on setting up the method correctly without the distraction of finding an unknown.
• Prepare for Algebraic Proportions: This becomes the setup students will use later when a variable replaces one of the numbers.

Parent-Friendly Teaching Tips

A simple way to explain the method is:

“Draw an X through the fractions and multiply along each diagonal.”

For example:

2/3 = 8/12

The diagonals are:

2 × 12
3 × 8

So the cross-product equation is:

2 × 12 = 3 × 8

On this worksheet, students should stop there because the directions specifically say do not solve.

Why This Worksheet Helps

• Slows the Process Down: Students learn setup before trying to solve equations.
• Prevents Diagonal Mix-Ups: Repeated practice helps students remember which numbers multiply together.
• Builds a Strong Foundation: Later proportion problems become easier when the cross-product pattern is automatic.
• Helps Parents See the Method: The visual “X” idea makes the process easier to explain at home.
• Supports Algebra Readiness: Students are practicing the exact structure they will later use to isolate variables.

The main value of this worksheet is that it teaches students the mechanics of cross multiplication without rushing ahead. Ratios, equivalent fractions, diagonal products, multiplication, and proportional relationships all work together. For parents, the best coaching phrase is: “Multiply across both diagonals and write the two products as equal.” In classroom and homeschool settings, this page is a strong first step before students begin solving proportions with missing values.