If you’re helping a student with fraction homework, comparison problems can be tricky. Two fractions sit side by side, the denominators don’t match, and the student isn’t sure what to do next.
A simple fraction comparison method can clear that up. The criss-cross method gives you a fast way to decide which fraction is greater, which is smaller, or whether the two are equal. In this video, I will review how and why this strategy works every time.
Why the criss-cross method is so useful
When you compare fractions, the hard part is often the unlike denominators. A student might know that common denominators matter, but finding them can slow the whole problem down. That is why this shortcut helps. You still rely on the same math idea, but you skip extra writing.
You may hear this strategy called criss-cross, butterfly, x marks the spot, or even the McDonald’s or Golden Arches method. The name does not matter. What matters is that you multiply across the fractions diagonally, then compare the two products.
Under the surface, you are doing the same work you would do if you rewrote both fractions with a common denominator. For example, to compare a/b and c/d, you could rewrite them as ad/bd and bc/bd. Because the new denominators match, you only need to compare ad and bc. The criss-cross method skips the step of writing bd, because it is the same on both sides.
That is why this method feels short, but it is not random. It has a clear mathematical reason behind it.
A few features make it especially helpful when you’re teaching or reviewing at home:
- It is fast for comparing two fractions.
- It works when denominators are different.
- It also shows when fractions are equal.
- It gives students a repeatable pattern they can remember.
You are still comparing fractions with like denominators, you are simply not writing those denominators out.
If a student is struggling with fractions, this kind of repeatable structure often reduces guesswork. Instead of staring at the fractions and hoping one “looks bigger,” you can follow a sequence and reach a clear answer.
How to do the criss-cross method step by step
You can teach this method in three small moves. Start by placing the two fractions side by side. Then focus on the bottom number of one fraction and the top number of the other.
Cross multiply diagonally from the first denominator to the second numerator
Begin with the denominator of the fraction on the left. Multiply it by the numerator of the fraction on the right.
If your fractions are 3/4 and 1/2, you start with 4 and cross to 1. Then you multiply 4 x 1 = 4.
Many students like to draw a slanted arrow from the bottom of the first fraction to the top of the second. That visual cue helps them keep the direction straight. In the lesson from MyTutoringBee, the product is written on the side where the arrow lands, so the first product goes on the right side.
Cross back the other way
Next, move from the denominator of the fraction on the right to the numerator of the fraction on the left.
Using the same example, you cross from 2 to 3. Then you multiply 2 x 3 = 6. Write that product on the left side.
At this point, you have two products. You have not changed the fractions themselves. You have only created two numbers that help you compare them.
Compare the products
Now compare the two results. The larger product points to the larger fraction.
With 3/4 and 1/2, you got 6 and 4. Because 6 is greater than 4, 3/4 is greater than 1/2.
This rule stays consistent:
- If the left-side product is larger, the left fraction is larger.
- If the right-side product is larger, the right fraction is larger.
- If the products match, the fractions are equal.
That last case matters because students often think the method only works for “greater than” or “less than” problems. It also works when the fractions name the same amount.
There are many names for this method, so it is important to choose one and stick with it. I like to use the “criss-cross” method and draw arrows from each denominator to the other numerator that “criss-cross” each other to keep things consistent.
Work through the examples from the lesson
Examples make this method easier to teach because students can watch the pattern stay the same, even when the numbers change. The lesson uses three examples, and each one shows a different outcome.
The examples below show the cross products side by side.
Fractions | Cross product 1 | Cross product 2 | Comparison | Result
3/4 and 1/2 | 4 x 1 = 4 | 2 x 3 = 6 | 6 > 4 | 3/4 > 1/2
3/20 and 5/12 | 20 x 5 = 100 | 12 x 3 = 36 | 100 > 36 | 5/12 > 3/20
6/15 and 2/5 | 15 x 2 = 30 | 5 x 6 = 30 | 30 = 30 | 6/15 = 2/5
The pattern never changes. Only the numbers do.
Example 1: Comparing 3/4 and 1/2
Start with the two fractions: 3/4 and 1/2.
First, cross from the 4 to the 1. That gives you 4 x 1 = 4. Then cross from the 2 to the 3. That gives you 2 x 3 = 6.
Now compare the results. Since 6 is greater than 4, the fraction linked to the 6 is larger. That means 3/4 is greater than 1/2.
This is a strong first example because the fractions are familiar. Many students already know that three-fourths is more than one-half, so the answer feels reasonable. That matters. When students see a shortcut produce a result they already trust, they are more willing to use it again.
Example 2: Comparing 3/20 and 5/12
The second example is more useful for real homework because the fractions are less obvious: 3/20 and 5/12.
You cross from 20 to 5, which gives you 20 x 5 = 100. Then you cross from 12 to 3, which gives you 12 x 3 = 36.
Now compare 100 and 36. Since 100 is greater than 36, the fraction connected to the 100 is greater. Therefore, 5/12 is greater than 3/20.
This example helps because students usually cannot tell the answer by sight. The denominators are different, the fractions are not benchmark fractions like one-half or one-fourth, and mental estimation may feel shaky. The criss-cross method gives you a direct path through that uncertainty.
It also shows why the shortcut matters. If you rewrote both fractions with a common denominator, you would still arrive at numerators that lead to the same comparison. The method is shorter because it focuses only on the part you need.
When the denominators do not match, compare the cross products, not the original numerators.
Example 3: Checking for equivalent fractions
The final example shows that the method also works for equivalent fractions. In the lesson, the products are 15 x 2 = 30 and 5 x 6 = 30.
Because the two products are equal, the two fractions are equal as well. Written in fraction form, that comparison is 6/15 = 2/5.
This is an important teaching point. Students often think a comparison problem must end with one fraction being larger. But equality is also a valid outcome. When the products match, you have evidence that both fractions describe the same amount.
That makes the criss-cross method useful for more than simple ordering. You can also use it to check whether two fractions are equivalent without reducing both fractions first.
For parents and teachers, that is helpful because it turns one strategy into a multipurpose tool. A student can use the same visual pattern, the same two multiplications, and the same final comparison. The only thing that changes is the symbol in the answer: >, <, or =.
When this method helps most
This method is best when you need to compare two fractions quickly. It is especially helpful in homework situations where a student knows that common denominators matter, but does not yet move through that process with confidence.
You may still want other strategies in some cases. For example, benchmark fractions, number lines, or simplification can build deeper number sense. Still, the criss-cross method has a clear place because it is efficient and consistent. When a student freezes on a comparison problem, a dependable procedure can keep the work moving.
If you’re teaching this method, encourage the student to draw the arrows every time at first. The written arrows reduce mix-ups. After enough practice, many students stop needing them, but the visual structure is useful in the early stage.
If you want more support beyond this lesson, you can explore my tutoring services at MyTutoringBee. I’m Beth, and I created MyTutoringBee to help parents support children with math homework, especially when school methods feel unfamiliar. My teaching background includes a B.S. in Elementary Education from the University of Central Florida, and my tutoring work has grown from part-time support into my full-time career.
The main idea to keep in mind
When fraction comparison feels messy, the criss-cross method gives you a clean structure. You multiply diagonally, compare the two products, and match the larger product to the larger fraction.
It is short, it is easy to remember, and it still rests on sound math. Once you understand that you are comparing hidden numerators with a shared denominator, the shortcut stops feeling like a trick and starts feeling like clear reasoning.
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