The multiplication of 35 and 33, broken down and added, results in a larger value than the single two-digit number 38, showcasing the impact of multiplication properties on numerical values.
When comparing the expressions 38 and 35 × 33 using the properties of multiplication, it's essential to understand the impact of each factor and observe any patterns that emerge.
Let's break down the expressions:
38: This is a two-digit number.
35 × 33: The multiplication involves two factors. Breaking down the factors:
35: Decompose this into 30 + 5.
33: Decompose this into 30 + 3.
Now, multiply each part:
(30 + 5) × (30 + 3) = 30 × 30 + 30 × 3 + 5 × 30 + 5 × 3
Observe the multiplication properties:
The product of two multiples of 10 (30 × 30) results in a number ending in two zeros.
Multiplying 30 by a single-digit number (30 × 3 or 5 × 30) yields a number with one zero at the end.
The product of two single-digit numbers (5 × 3) results in a two-digit number.
Now, add these results together.
Observation:
When comparing 38 and 35 × 33, we notice that the product 35 × 33 is larger than 38. This aligns with the understanding that multiplying two multi-digit numbers tends to yield a larger result than a single two-digit number.