When students first encounter the times tables, they often wonder if there is a shortcut to mastering multiplication facts without memorizing every single answer. The truth is that multiplying by 6 is like multiplying by 3 because six is exactly double three, which means every product in the six times table is simply twice the corresponding product in the three times table. This relationship transforms a seemingly difficult multiplication task into a manageable mental math strategy, allowing learners to build confidence and speed. By understanding how multiplying by 6 connects to multiplying by 3, students can reduce math anxiety, improve calculation fluency, and develop a deeper number sense that serves them well beyond elementary arithmetic.
Understanding the Connection Between Multiplying by 6 and Multiplying by 3
At its core, the relationship between these two multiplication facts is based on a simple numerical truth: 6 equals 3 times 2. But because of this, any number multiplied by 6 can be broken down into two smaller, more familiar steps. Because of that, instead of trying to recall what 9 times 6 equals directly, a learner can first calculate 9 times 3 and then double the answer. This approach relies on the associative property of multiplication, which allows numbers to be grouped differently without changing the final result.
Here's one way to look at it: consider the equation 5 × 6. If a student knows that 5 × 3 equals 15, they only need to double 15 to reach 30. The same logic applies to 8 × 6. Consider this: since 8 × 3 equals 24, doubling 24 produces 48. This pattern holds true across the entire multiplication chart, making it one of the most reliable strategies for mastering the six times table Simple as that..
The Simple Math Trick: Double the Result of Multiplying by 3
The most practical way to apply this concept is through a three-step mental math trick. Rather than treating multiplication by 6 as an isolated fact to memorize, students can treat it as a variation of multiplication by 3.
Here is how the trick works:
- Step 1: Identify the number you want to multiply by 6.
- Step 2: Multiply that number by 3 instead.
- Step 3: Double the result from Step 2.
Take 7 × 6 as an example. First, multiply 7 by 3 to get 21. Then, double 21 to arrive at 4
2 to arrive at 42. This means 7 × 6 = 42.
The strategy works equally well with larger numbers. For 12 × 6, multiply 12 by 3 to get 36, then double 36 to reach 72. Even with single-digit facts like 4 × 6, the method holds: 4 × 3 is 12, and doubling 12 gives 24.
Why the Trick Works
Mathematically, multiplying by 6 is the same as multiplying by 3 and then by 2, because 6 = 3 × 2. Using the associative property of multiplication, (n × 3) × 2 always equals n × 6. This means students are not learning an isolated set of new facts; they are applying a rule they already understand to a new context Most people skip this — try not to..
Practice Problems
Try these using the double-after-three method:
- 6 × 6: 6 × 3 = 18; double 18 = 36
- 9 × 6: 9 × 3 = 27; double 27 = 54
- 11 × 6: 11 × 3 = 33; double 33 = 66
Encourage learners to say the steps out loud at first: “Three times the number, then double it.” With repetition, the process becomes automatic, and the six times table feels less like a wall of
Beyond the immediate convenience of the “double‑after‑three” shortcut, the connection between multiplying by 6 and multiplying by 3 cultivates a deeper numerical intuition that ripples throughout a student’s entire mathematical journey.
Linking to other tables – Once learners recognize that 6 = 3 × 2, they can apply the same reasoning to other even numbers. Take this case: multiplying by 8 can be viewed as multiplying by 4 and then doubling, while multiplying by 10 is simply adding a zero. This pattern‑recognition mindset makes it easier to see multiplication as a network of relationships rather than a list of unrelated facts.
Strengthening mental flexibility – The trick forces students to hold two operations in mind simultaneously: a basic multiplication (by 3) and a simple scaling (doubling). Practicing this dual‑step process sharpens working‑memory capacity and encourages flexible thinking, skills that are essential when tackling multi‑step word problems or when manipulating algebraic expressions Surprisingly effective..
Supporting division and fractions – Understanding that 6 is “3 times 2” also clarifies division. If a pupil knows that 18 ÷ 6 = 3, they can instantly infer that 18 ÷ 3 = 6, reinforcing the inverse relationship between multiplication and division. In fraction work, the same principle helps simplify ratios: recognizing that 6/12 reduces to 1/2 because the numerator is twice the denominator.
Building confidence through mastery – Because the strategy works for every number, students experience rapid success across the entire six‑times table. This early win creates a positive feedback loop: confidence in using a reliable method encourages them to attempt more challenging calculations, which in turn reinforces their overall belief in their mathematical abilities And that's really what it comes down to..
Integrating the trick into everyday life – The mental‑math approach is not confined to the classroom. When shopping, a child can estimate the cost of six items by first finding the price of three and then doubling it. When cooking, they can adjust a recipe that serves three people to serve six by simply doubling the ingredient amounts. These real‑world applications demonstrate that the connection is not merely an academic exercise but a practical tool for everyday problem solving.
Conclusion
The relationship between multiplying by 6 and multiplying by 3 is more than a convenient shortcut; it is a gateway to a richer understanding of how numbers interact. Here's the thing — by recognizing that 6 = 3 × 2, learners can break complex multiplications into simpler, more familiar steps, apply the same logic across the entire multiplication chart, and develop a flexible, confident approach to mathematics. Embracing this connection equips students with a versatile mental strategy that supports not only the six‑times table but also division, fractions, algebraic reasoning, and everyday quantitative tasks. In mastering this simple yet powerful link, learners lay a solid foundation for future mathematical success No workaround needed..
