Problem 267 In the following exercises, mult... [FREE SOLUTION]

91影视

Prealgebra

Lynn Marecek, MaryAnne Anthony-Smith

$Math Studyset 91影视 Explanations$ Math

2016 Edition

Chapter 1: Problem 267

In the following exercises, multiply. $$27 \times 85$$

Short Answer

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Step by step solution

Write Down the Numbers

Write the numbers you want to multiply, aligning them by place value: \[ \begin{array}{r} 27 \ \times 85 \ \end{array} \]

Multiply by the Units Digit

Multiply 27 by the units digit of the second number (5): \[ 27 \times 5 = 135 \] Write 135 below the line.

Multiply by the Tens Digit

Multiply 27 by the tens digit of the second number (8). Remember, 8 actually represents 80: \[ 27 \times 80 = 2160 \] Write 2160 below 135, shifted one place to the left.

Add the Partial Products

Add the numbers obtained in steps 2 and 3: \[ \begin{array}{r} 135 \ + 2160 \ \end{array} \] The sum is 2295.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

place value

Place value is a fundamental concept in mathematics. It helps us understand the value of each digit in a number. Each digit's value depends on its position, or 'place,' in the number. For example, in the number 85:

The digit 5 is in the units place and represents 5 ones
The digit 8 is in the tens place and represents 80 (8 tens)

By aligning numbers by their place values, we ensure that we are correctly multiplying digits of the same rank. So, always align numbers this way before performing any multiplication.

partial products

Partial products are the results of multiplying each digit of one number by each digit of another number, separately. To solve this type of multiplication problem, break it down into simpler and smaller multiplications:

First, multiply by the units digit
Then, multiply by the tens digit

For example, in the problem 27 脳 85, multiply 27 by 5 (units digit) to get 135.
Then, multiply 27 by 80 (tens digit, remembering that 8 corresponds to 80) to get 2160. These values (135 and 2160) are called partial products.
By combining these partial products, you get the final result.

units digit

The units digit is the rightmost digit of a number. It forms the basis for the first step of multiplication when solving problems using partial products.
In our problem, we first look at the units digit of the second number, which is 5 in 85. Multiplying the whole number 27 by 5 gives 135.
This is our first partial product. Remember, focusing on the units digit simplifies the problem, allowing for accurate multiplication before tackling the tens digit or higher values.

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91影视

In the following exercises, multiply. $$27 \times 85$$

Short Answer

Step by step solution

Write Down the Numbers

Multiply by the Units Digit

Multiply by the Tens Digit

Add the Partial Products

Key Concepts

place value

partial products

units digit

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