/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 61 Simplify. $$ 4.2 \times 5.7+... [FREE SOLUTION] | 91影视

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Chapter 4: Problem 61

Simplify. $$ 4.2 \times 5.7+0.7 \div 3.5 $$

Short Answer

Expert verified
24.14

Step by step solution

01

Multiply 4.2 and 5.7

Calculate the product of 4.2 and 5.7. Using standard multiplication, we get: \(4.2 \times 5.7 = 23.94\)
02

Divide 0.7 by 3.5

Calculate the quotient of 0.7 divided by 3.5. Using standard division, we get: \(0.7 \div 3.5 = 0.2\)
03

Add the results

Add the results from Step 1 and Step 2. \(23.94 + 0.2 = 24.14\)

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Key Concepts

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

Multiplication
Multiplication is one of the basic arithmetic operations. It involves finding the total of one number added repeatedly a certain number of times. For example, calculating the product of 4.2 and 5.7 means we are essentially summing up 4.2, 5.7 times. Using the standard multiplication method for decimals, you can align the numbers vertically and multiply as if there were no decimal points. Finally, you'll place the decimal in the product by counting the total number of decimal places in the factors being multiplied. This is why when multiplying 4.2 and 5.7, we get 23.94, carefully retaining two decimal places in our final answer.
Division
Division is another essential arithmetic operation. It involves splitting a number into equal parts. When we divide 0.7 by 3.5, we are determining how many times 3.5 can fit into 0.7. Using standard division, we perform this as if handling whole numbers and adjust for decimal places by moving the decimal point in both the dividend and the divisor. When we calculate, we align the decimal points correctly, leading us to the result: 0.2. It's crucial to ensure that your decimal placements are accurate to get the correct quotient.
Addition
Addition is the process of calculating the total of two or more numbers. It's foundational for many other mathematical concepts. In our scenario, after multiplying 4.2 and 5.7 to get 23.94, and dividing 0.7 by 3.5 to get 0.2, the next step is to add these two results. This means combining 23.94 and 0.2 through standard addition. We align the decimal points to ensure accuracy: 23.94 + 0.2 = 24.14. This final result demonstrates how simple operations can be used together to solve more complex mathematical problems systematically.

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