Problem 250 - Prealgebra

Question

In the following exercises, multiply. $$1\cdot 34$$

Step-by-Step Solution

Answer

34

Step 1: Understand the problem

The task requires multiplying the numbers 1 and 34.

Step 2: Apply the multiplication property

Recall the property of multiplication: multiplying any number by 1 gives the same number. Therefore, we have 1 multiplied by 34.

Step 3: Calculate the product

Using the multiplication property, calculate: \( 1 \times 34 \).

Step 4: Write the result

The product of \( 1 \times 34 \) is 34.

Key Concepts

Multiplication Property

In mathematics, the multiplication property is an essential concept. It states that when you multiply any number by another, you get a product. This is true for all numbers, whether they are whole, fractions, or decimals. For example, if you multiply 2 by 3, you get 6.
Mental math can help a lot with multiplication. A neat trick is breaking down one of the numbers. For instance, multiplying 34 by 2, you can think of it as multiplying 30 by 2 and then 4 by 2, and adding them up. It can make big numbers less intimidating.
Understanding the multiplication property helps in solving various problems and makes complex calculations easier.

Identity Property of Multiplication

The identity property of multiplication is a simple yet powerful concept. It tells us that any number multiplied by 1 stays the same. In other words, 1 is the 'identity' for multiplication because it doesn't change the number.
For example, in the exercise where we have to multiply 1 by 34, we use this property. Multiplying 1 by 34 simply gives us back 34. Another way to think of it is that 1 acts like a mirror, reflecting the number it's multiplied by.
This property is particularly handy when solving equations, as it simplifies calculations and keeps the integrity of numbers intact.

Single-Digit Multiplication

Single-digit multiplication involves multiplying numbers between 1 and 9. It's one of the first skills students learn in math. Despite being basic, it's the foundation for more advanced arithmetic.
For example, in the given exercise, we multiply 1 (a single digit) by 34 (a two-digit number). However, multiplying by 1 is still straightforward due to the identity property.
Memorizing multiplication tables for single digits helps with quick calculations. For instance, knowing that 3 times 4 is 12 or 6 times 7 is 42 makes solving larger problems faster. Practicing these tables can enhance your math fluency and confidence.