Problem 291 - Prealgebra

Question

In the following exercises, translate and simplify. fifty-one times sixty-seven

Step-by-Step Solution

Answer

51 * 67 = 3417.

Step 1: Identify the Numbers

Identify the numbers given in the problem: fifty-one and sixty-seven. These numbers are 51 and 67 respectively.

Step 2: Translate into an Expression

Translate the phrase 'fifty-one times sixty-seven' into a mathematical expression: 51 * 67.

Step 3: Perform the Multiplication

Multiply the numbers 51 and 67 together. Using long multiplication: | | 5 | 1 || x | 6 | 7 ||_________|First, 7 * 1 = 7.7 * 5 = 35 so write down 35.Next, 6 * 1 = 6, write 6 with a zero in units place, i.e., write down 60.6 * 5 = 30, write 30 with a zero in tens place, i.e., write down 300.Finally, add up the results: 3500 + 350 + 60 + 7 = 3417.

Key Concepts

Basic Arithmetic

Basic arithmetic is the foundation of all mathematics. It includes operations like addition, subtraction, multiplication, and division.

In this exercise, we focus on multiplication. Multiplication is one of the key operations and involves combining equal groups.

For example, when we multiply 51 by 67, we are basically combining 51 groups of 67. This operation can be visualized as repeated addition, but it is more efficient to use the multiplication operation directly.

Long Multiplication

Long multiplication is a method used to multiply larger numbers. It involves breaking the operation down into simpler steps.

Let’s illustrate this with our example of multiplying 51 by 67. First, break down each number into its tens and units place:

For 51: Tens place - 50, Units place - 1

For 67: Tens place - 60, Units place - 7

Now, we perform the multiplication step by step:

• 7 * 1 = 7
• 7 * 50 = 350
• 60 * 1 = 60
• 60 * 50 = 3000

Add up the results: 3500 + 350 + 60 + 7 = 3417. This is the final product.

Mathematical Expressions

Mathematical expressions are a way to represent operations using numbers and symbols.

In our exercise, the phrase 'fifty-one times sixty-seven' can be translated into the mathematical expression 51 * 67. This expression tells us to multiply 51 by 67.

Understanding how to translate words into mathematical expressions is crucial for solving word problems effectively.

By breaking down the phrase into familiar numbers and operations, we can solve the problem more easily.

Number Translation

Number translation involves converting words or phrases into numerical form.

In the exercise, we start with the words 'fifty-one' and 'sixty-seven.' We need to recognize that these phrases represent the numbers 51 and 67, respectively.

Once we know the numerical form, we can proceed to translate the entire phrase 'fifty-one times sixty-seven' into the multiplication expression 51 * 67.

This step is important as it allows us to move from a verbal description to a mathematical operation, making it easier to perform calculations.