(a) 8362.64+768.3-190.57 (b) 593.38+604.7+7742.29 (c) 2235.925 ×4 (d) 9931.04-990.67 (e) 17880.7

(a) 8362.64+768.3-190.57 (b) 593.38+604.7+7742.29 (c)...

Key Concepts

Division of Decimals

Division involving decimals often requires adjusting the divisor to become a whole number by multiplying both the dividend and the divisor by the same power of ten. This adjustment simplifies the division process while preserving the relationship between the numbers, ensuring the accuracy of the quotient.

Subtraction of Decimals

Subtraction with decimals similarly requires aligning the decimal points to ensure that digits of the same place value are properly subtracted from each other. This alignment minimizes errors and ensures that the difference reflects accurate values, especially in contexts where precision is paramount.

Multiplication of Decimals

When multiplying decimals, the key idea is to perform the multiplication ignoring the decimal points initially and then placing the decimal in the final answer by counting the total number of decimal places in the factors. This method ensures the final answer maintains correct scale and precision.

Decimal Operations

This concept involves performing arithmetic operations—addition, subtraction, multiplication, and division—with decimal numbers. It highlights the importance of correctly handling place values and the decimal point, ensuring accuracy in the result when working with non-integer values.

Addition of Decimals

Addition with decimals requires aligning the decimal points so that each digit is added in its correct place value. Proper alignment ensures that the sums of the tenths, hundredths, and other decimal places are accurately computed, which is crucial when dealing with money, measurements, or other precise quantities.

Transcript

00:01 We're going to simplify each of the following expressions and round to two decimal places as needed.

00:07 So before we even start these, let's remember that our order of operations is pemdas, parentheses, exponents, multiplication, and division, and then addition and subtraction.

00:19 We need to follow the order of operations as we work.

00:22 In this first problem, i have an exponent.

00:25 So i'm going to do 5 .31 times 8 .47 minus 1 .01 to the second power, gives us 1 .0201.

00:37 5 .31 times 8 .47 gives us 44 .9757 minus 1 .409757 minus 1 .0201 is 43 .956.

00:59 Rounded to two decimal places, we get 43 .96.

01:04 Over here on the second one, we do have parentheses, so we're going to go ahead.

01:07 Do those first, 8 .34 plus 2 .27 gives us 10 .61 divided by 9 .41 gives us 1 .13 when routed to the two decimal places.

01:25 This third one, i don't have any parentheses.

01:28 I don't have any exponents.

01:29 There's a multiplication or division.

01:31 It's just straight up addition and subtraction so we can work at left to right.

01:35 9 .53 minus 3 .21 minus 4 .02 and we get 2 .3.

01:44 Over here we have 2 .41 times 0 .09 minus 1 .67 times 0 .03.

01:51 There's no parentheses or exponent, so we're going to jump right to the multiplication.

01:55 2 .41 times 0 .09 .29 .0 .269 minus 1 .169 minus 1 .666 .1 minus 1 .666 .1.

02:02 7 times 0 .03, 0 .0501.

02:08 0 .2169 minus 0 .0501 gives us 0 .168, which is 0 .17 when rounded to two decimal places.

02:21 Next we have 45 .76 minus 2 .55 plus 15 .3.

02:26 We do have parentheses, so we're gonna go ahead and do those first...

Please give Ace some feedback