The document provides step-by-step instructions for multiplying decimals. It shows the multiplication of 2.3 x 1.5 worked out over multiple steps: 1) multiply the ones, 2) add a placeholder zero, 3) multiply the tens, 4) add the products, and 5) determine the number of decimal places in the answer based on the number in the factors. The final answer is 3.45.
The document provides step-by-step instructions for multiplying decimals by whole numbers. It demonstrates multiplying 0.12 x 5, 9.74 x 8, and 219 x 7.2. For each problem, it lists the steps of multiplying the numbers, placing placeholders, adding products, and including the correct number of decimal places in the final answer.
The document provides step-by-step instructions for multiplying decimals. It shows the multiplication of 2.3 x 1.5 worked out over multiple steps: 1) multiply the ones, 2) add a placeholder zero, 3) multiply the tens, 4) add the products, and 5) determine the number of decimal places in the answer based on the number in the factors. The final answer is 3.45.
6-2 Multiplying Decimals by Whole NumbersRudy Alfonso
The document describes the step-by-step process for multiplying decimals by whole numbers. It shows examples of 0.12 x 5 and 9.74 x 8. The steps include: using guidelines to keep work neat, multiplying the ones and regrouping if necessary, counting the number of decimal places in the factors, and including the proper number of decimal places in the final answer.
4-7 Multiplying by One-Digit and Two-Digit NumbersRudy Alfonso
The document shows the step-by-step work for multiplying 28 x 12. It breaks 12 into 10 and 2. It then multiplies 28 by 10 to get 280, and 28 by 2 to get 56. Finally, it adds 280 + 56 to get the total of 336.
5-11 Relating Multiplication and DivisionRudy Alfonso
To find n, I would use the inverse operation of the rule.
Since the rule is to multiply by 6, I would divide 156 by 6 to isolate n.
Doing so gives n = 26.
The document discusses converting between customary units of length, including inches, feet, and yards. It provides examples of converting specific lengths such as 18 inches to feet and inches or 48 inches to yards and feet. It also reviews the relationships between customary units, such as there being 12 inches in 1 foot, 36 inches in 1 yard, and 3 feet in 1 yard. The document then provides practice problems and step-by-step work for converting between units and adding lengths expressed in feet and inches.
This document outlines spelling words and activities for 9 weeks of instruction. Each week contains 10 spelling words and the same spelling activities are assigned: dictionary meanings, word building, syllables, alphabetical order, and writing sentences using the words. The activities focus on understanding and practicing the spelling, meaning, and use of the weekly words.
The document summarizes the common uses of commas in English writing in 3-4 sentences each. It covers using commas to separate elements of a series, separate independent clauses joined by a conjunction, set off introductory elements, separate coordinate adjectives, set off contrasting or turning elements, set off states, countries, years, titles, parenthetical elements, quoted language, and interjections. The concluding slide advises not overusing commas and reviewing the rules of comma usage to improve writing skills.
The document provides step-by-step instructions for multiplying decimals by whole numbers. It demonstrates multiplying 0.12 x 5, 9.74 x 8, and 219 x 7.2. For each problem, it lists the steps of multiplying the numbers, placing placeholders, adding products, and including the correct number of decimal places in the final answer.
The document provides step-by-step instructions for multiplying decimals. It shows the multiplication of 2.3 x 1.5 worked out over multiple steps: 1) multiply the ones, 2) add a placeholder zero, 3) multiply the tens, 4) add the products, and 5) determine the number of decimal places in the answer based on the number in the factors. The final answer is 3.45.
6-2 Multiplying Decimals by Whole NumbersRudy Alfonso
The document describes the step-by-step process for multiplying decimals by whole numbers. It shows examples of 0.12 x 5 and 9.74 x 8. The steps include: using guidelines to keep work neat, multiplying the ones and regrouping if necessary, counting the number of decimal places in the factors, and including the proper number of decimal places in the final answer.
4-7 Multiplying by One-Digit and Two-Digit NumbersRudy Alfonso
The document shows the step-by-step work for multiplying 28 x 12. It breaks 12 into 10 and 2. It then multiplies 28 by 10 to get 280, and 28 by 2 to get 56. Finally, it adds 280 + 56 to get the total of 336.
5-11 Relating Multiplication and DivisionRudy Alfonso
To find n, I would use the inverse operation of the rule.
Since the rule is to multiply by 6, I would divide 156 by 6 to isolate n.
Doing so gives n = 26.
The document discusses converting between customary units of length, including inches, feet, and yards. It provides examples of converting specific lengths such as 18 inches to feet and inches or 48 inches to yards and feet. It also reviews the relationships between customary units, such as there being 12 inches in 1 foot, 36 inches in 1 yard, and 3 feet in 1 yard. The document then provides practice problems and step-by-step work for converting between units and adding lengths expressed in feet and inches.
This document outlines spelling words and activities for 9 weeks of instruction. Each week contains 10 spelling words and the same spelling activities are assigned: dictionary meanings, word building, syllables, alphabetical order, and writing sentences using the words. The activities focus on understanding and practicing the spelling, meaning, and use of the weekly words.
The document summarizes the common uses of commas in English writing in 3-4 sentences each. It covers using commas to separate elements of a series, separate independent clauses joined by a conjunction, set off introductory elements, separate coordinate adjectives, set off contrasting or turning elements, set off states, countries, years, titles, parenthetical elements, quoted language, and interjections. The concluding slide advises not overusing commas and reviewing the rules of comma usage to improve writing skills.
The document provides information about converting between customary units of measurement for capacity and weight. It defines the relationships between various units of capacity, including that 8 fluid ounces equals 1 cup, 2 cups equals 1 pint, 2 pints equals 1 quart, and 4 quarts equals 1 gallon. It also defines the relationships for units of weight, including that 16 ounces equals 1 pound and 2000 pounds equals 1 ton. It then provides examples of converting between gallons and quarts, and between pounds and tons.
The document provides step-by-step instructions for multiplying decimal numbers. It shows worked examples of 0.16 x 0.08, 7.2 x 0.009, and 0.07 x 0.8. For each problem, it lists the steps as: 1) set up the multiplication problem neatly, 2) multiply the numbers as whole numbers, 3) count the total number of decimal places in the factors, and 4) write the answer with the correct number of decimal places.
The document defines equivalent fractions as fractions that name the same amount. It then provides examples of equivalent fractions by showing how different fractions can represent the same portion of a whole through operations like multiplying or dividing the numerator and denominator by the same number. The key rule discussed is that to make fractions equivalent, the same operation must be applied to both the numerator and denominator.
The document defines fractions and their relationship to decimals. It explains that a fraction such as 3/10 represents the division problem 3 ÷ 10. Through examples of fractions like 3/10, 6/8, and 9/12, it shows how to calculate the decimal equivalent by dividing the numerator by the denominator. This provides the essential information that fractions represent division problems and can be converted to decimals.
The document provides instructions for dividing decimals by decimals using long division. It explains the steps as: Divide (DAD), Multiply (MOM), Subtract (SISTER), Bring Down (BROTHER), Repeat or Remainder (ROVER). An example problem walks through dividing 16.4288 by 16 using these steps: 1) 16 goes into 42 twice with 10 remaining, 2) bring down the 8, 3) 16 goes into 108 six times with a remainder of 8. The document also explains how to convert decimals to whole numbers by multiplying by powers of 10.
There are two main kinds of writing: summary writing and narrative writing. Summary writing focuses on conveying key information and ideas from a source in a condensed form, using an objective tone. It includes an introduction with a topic sentence, body paragraphs with explanations and key details, and a conclusion that restates the main topic. Narrative writing tells a story through characters, setting, plot, conflict, and a resolution. It draws the reader in with a beginning that sets up characters and events, a middle with a developing plot and conflict, and an end that brings resolution.
The document provides step-by-step instructions for multiplying two multi-digit numbers. It begins by showing the multiplication problem 287 x 104 written out. It then outlines the steps to solve the problem, which include multiplying the ones place, tens place, and hundreds place and carrying or regrouping the digits as needed. Working through each place value results in the solution of 30,048.
The document provides step-by-step instructions for multiplying two multi-digit numbers. It begins by showing the multiplication problem 287 x 104 written out. It then outlines the steps to solve the problem, which include multiplying the ones place, tens place, and hundreds place and carrying or regrouping the digits as needed. Working through each place value results in the solution of 30,048.
This document provides step-by-step instructions for multiplying 365 by 112. It begins by stating the problem and includes guidelines for keeping work neat. It then lists the steps as multiplying by the ones place, placing a zero as a placeholder, multiplying by the tens place, and placing two zeroes as placeholders before showing the final answer.
This document provides step-by-step instructions for multiplying 365 by 112. It begins by stating the problem and includes guidelines for keeping work neat. It then lists the steps as multiplying by the ones place, placing a zero as a placeholder, multiplying by the tens place, and placing two zeroes as placeholders before arriving at the final solution.
The document shows the step-by-step work for multiplying 28 x 12. It breaks 12 into 10 and 2. It then multiplies 28 by 10 to get 280, and 28 by 2 to get 56. Finally, it adds 280 + 56 to get the total of 336.
The document provides step-by-step instructions for multiplying multi-digit numbers. It shows worked examples of 28 x 12 and 354 x 23. For each problem, it breaks the multiplication into steps: 1) multiply the ones, 2) add a placeholder zero, 3) multiply the tens, 4) add the partial products. The goal is to demonstrate the standard algorithm for multiplying multi-digit numbers in a clear and organized manner.
4-7 Multiplying by One-Digit and Two-Digit NumbersRudy Alfonso
The document shows the step-by-step work for multiplying 28 x 12. It breaks 12 into 10 and 2. It then multiplies 28 by 10 to get 280, and 28 by 2 to get 56. Finally, it adds 280 + 56 to get the total of 336.
The document is a lecture on inverse trigonometric functions from a Calculus I class at New York University. It defines inverse trigonometric functions as the inverses of restricted trigonometric functions, gives their domains and ranges, and discusses their derivatives. The document also provides examples of evaluating inverse trigonometric functions.
Implicit differentiation allows us to find slopes of lines tangent to curves that are not graphs of functions. Almost all of the time (yes, that is a mathematical term!) we can assume the curve comprises the graph of a function and differentiate using the chain rule.
This document summarizes a calculus lecture on linear approximations. It provides examples of using the tangent line to approximate the sine function at different points. Specifically, it estimates sin(61°) by taking linear approximations about 0 and about 60°. The linear approximation about 0 is x, giving a value of 1.06465. The linear approximation about 60° uses the fact that the sine is √3/2 and the derivative is √3/2 at π/3, giving a better approximation than using 0.
This document contains lecture notes on related rates from a Calculus I class at New York University. It begins with announcements about assignments and no class on a holiday. It then outlines the objectives of learning to use derivatives to understand rates of change and model word problems. Examples are provided, including an oil slick problem worked out in detail. Strategies for solving related rates problems are discussed. Further examples on people walking and electrical resistors are presented.
Lesson 14: Derivatives of Logarithmic and Exponential FunctionsMel Anthony Pepito
The document discusses conventions for defining exponential functions with exponents other than positive integers, such as negative exponents, fractional exponents, and exponents of zero. It defines exponential functions with these exponent types in a way that maintains important properties like ax+y = ax * ay. The goal is to extend the definition of exponential functions beyond positive integer exponents in a principled way.
This document contains lecture notes on exponential growth and decay from a Calculus I class at New York University. It begins with announcements about an upcoming review session, office hours, and midterm exam. It then outlines the topics to be covered, including the differential equation y=ky, modeling population growth, radioactive decay including carbon-14 dating, Newton's law of cooling, and continuously compounded interest. Examples are provided of solving various differential equations representing exponential growth or decay. The document explains that many real-world situations exhibit exponential behavior due to proportional growth rates.
This document is from a Calculus I class lecture on L'Hopital's rule given at New York University. It begins with announcements and objectives for the lecture. It then provides examples of limits that are indeterminate forms to motivate L'Hopital's rule. The document explains the rule and when it can be used to evaluate limits. It also introduces the mathematician L'Hopital and applies the rule to examples introduced earlier.
The document provides an overview of curve sketching in calculus including objectives, rationale, theorems for determining monotonicity and concavity, and a checklist for graphing functions. It then gives examples of graphing cubic and quartic functions step-by-step, demonstrating how to analyze critical points, inflection points, and asymptotic behavior to create the curve. The examples illustrate applying differentiation rules to determine monotonicity from the derivative sign chart and concavity from the second derivative test.
This document is a section from a Calculus I course at New York University covering maximum and minimum values. It begins with announcements about exams and assignments. The objectives are to understand the Extreme Value Theorem and Fermat's Theorem, and use the Closed Interval Method to find extreme values. The document then covers the definitions of extreme points/values and the statements of the Extreme Value Theorem and Fermat's Theorem. It provides examples to illustrate the necessity of the hypotheses in the theorems. The focus is on using calculus concepts like continuity and differentiability to determine maximum and minimum values of functions on closed intervals.
The document provides information about converting between customary units of measurement for capacity and weight. It defines the relationships between various units of capacity, including that 8 fluid ounces equals 1 cup, 2 cups equals 1 pint, 2 pints equals 1 quart, and 4 quarts equals 1 gallon. It also defines the relationships for units of weight, including that 16 ounces equals 1 pound and 2000 pounds equals 1 ton. It then provides examples of converting between gallons and quarts, and between pounds and tons.
The document provides step-by-step instructions for multiplying decimal numbers. It shows worked examples of 0.16 x 0.08, 7.2 x 0.009, and 0.07 x 0.8. For each problem, it lists the steps as: 1) set up the multiplication problem neatly, 2) multiply the numbers as whole numbers, 3) count the total number of decimal places in the factors, and 4) write the answer with the correct number of decimal places.
The document defines equivalent fractions as fractions that name the same amount. It then provides examples of equivalent fractions by showing how different fractions can represent the same portion of a whole through operations like multiplying or dividing the numerator and denominator by the same number. The key rule discussed is that to make fractions equivalent, the same operation must be applied to both the numerator and denominator.
The document defines fractions and their relationship to decimals. It explains that a fraction such as 3/10 represents the division problem 3 ÷ 10. Through examples of fractions like 3/10, 6/8, and 9/12, it shows how to calculate the decimal equivalent by dividing the numerator by the denominator. This provides the essential information that fractions represent division problems and can be converted to decimals.
The document provides instructions for dividing decimals by decimals using long division. It explains the steps as: Divide (DAD), Multiply (MOM), Subtract (SISTER), Bring Down (BROTHER), Repeat or Remainder (ROVER). An example problem walks through dividing 16.4288 by 16 using these steps: 1) 16 goes into 42 twice with 10 remaining, 2) bring down the 8, 3) 16 goes into 108 six times with a remainder of 8. The document also explains how to convert decimals to whole numbers by multiplying by powers of 10.
There are two main kinds of writing: summary writing and narrative writing. Summary writing focuses on conveying key information and ideas from a source in a condensed form, using an objective tone. It includes an introduction with a topic sentence, body paragraphs with explanations and key details, and a conclusion that restates the main topic. Narrative writing tells a story through characters, setting, plot, conflict, and a resolution. It draws the reader in with a beginning that sets up characters and events, a middle with a developing plot and conflict, and an end that brings resolution.
The document provides step-by-step instructions for multiplying two multi-digit numbers. It begins by showing the multiplication problem 287 x 104 written out. It then outlines the steps to solve the problem, which include multiplying the ones place, tens place, and hundreds place and carrying or regrouping the digits as needed. Working through each place value results in the solution of 30,048.
The document provides step-by-step instructions for multiplying two multi-digit numbers. It begins by showing the multiplication problem 287 x 104 written out. It then outlines the steps to solve the problem, which include multiplying the ones place, tens place, and hundreds place and carrying or regrouping the digits as needed. Working through each place value results in the solution of 30,048.
This document provides step-by-step instructions for multiplying 365 by 112. It begins by stating the problem and includes guidelines for keeping work neat. It then lists the steps as multiplying by the ones place, placing a zero as a placeholder, multiplying by the tens place, and placing two zeroes as placeholders before showing the final answer.
This document provides step-by-step instructions for multiplying 365 by 112. It begins by stating the problem and includes guidelines for keeping work neat. It then lists the steps as multiplying by the ones place, placing a zero as a placeholder, multiplying by the tens place, and placing two zeroes as placeholders before arriving at the final solution.
The document shows the step-by-step work for multiplying 28 x 12. It breaks 12 into 10 and 2. It then multiplies 28 by 10 to get 280, and 28 by 2 to get 56. Finally, it adds 280 + 56 to get the total of 336.
The document provides step-by-step instructions for multiplying multi-digit numbers. It shows worked examples of 28 x 12 and 354 x 23. For each problem, it breaks the multiplication into steps: 1) multiply the ones, 2) add a placeholder zero, 3) multiply the tens, 4) add the partial products. The goal is to demonstrate the standard algorithm for multiplying multi-digit numbers in a clear and organized manner.
4-7 Multiplying by One-Digit and Two-Digit NumbersRudy Alfonso
The document shows the step-by-step work for multiplying 28 x 12. It breaks 12 into 10 and 2. It then multiplies 28 by 10 to get 280, and 28 by 2 to get 56. Finally, it adds 280 + 56 to get the total of 336.
The document is a lecture on inverse trigonometric functions from a Calculus I class at New York University. It defines inverse trigonometric functions as the inverses of restricted trigonometric functions, gives their domains and ranges, and discusses their derivatives. The document also provides examples of evaluating inverse trigonometric functions.
Implicit differentiation allows us to find slopes of lines tangent to curves that are not graphs of functions. Almost all of the time (yes, that is a mathematical term!) we can assume the curve comprises the graph of a function and differentiate using the chain rule.
This document summarizes a calculus lecture on linear approximations. It provides examples of using the tangent line to approximate the sine function at different points. Specifically, it estimates sin(61°) by taking linear approximations about 0 and about 60°. The linear approximation about 0 is x, giving a value of 1.06465. The linear approximation about 60° uses the fact that the sine is √3/2 and the derivative is √3/2 at π/3, giving a better approximation than using 0.
This document contains lecture notes on related rates from a Calculus I class at New York University. It begins with announcements about assignments and no class on a holiday. It then outlines the objectives of learning to use derivatives to understand rates of change and model word problems. Examples are provided, including an oil slick problem worked out in detail. Strategies for solving related rates problems are discussed. Further examples on people walking and electrical resistors are presented.
Lesson 14: Derivatives of Logarithmic and Exponential FunctionsMel Anthony Pepito
The document discusses conventions for defining exponential functions with exponents other than positive integers, such as negative exponents, fractional exponents, and exponents of zero. It defines exponential functions with these exponent types in a way that maintains important properties like ax+y = ax * ay. The goal is to extend the definition of exponential functions beyond positive integer exponents in a principled way.
This document contains lecture notes on exponential growth and decay from a Calculus I class at New York University. It begins with announcements about an upcoming review session, office hours, and midterm exam. It then outlines the topics to be covered, including the differential equation y=ky, modeling population growth, radioactive decay including carbon-14 dating, Newton's law of cooling, and continuously compounded interest. Examples are provided of solving various differential equations representing exponential growth or decay. The document explains that many real-world situations exhibit exponential behavior due to proportional growth rates.
This document is from a Calculus I class lecture on L'Hopital's rule given at New York University. It begins with announcements and objectives for the lecture. It then provides examples of limits that are indeterminate forms to motivate L'Hopital's rule. The document explains the rule and when it can be used to evaluate limits. It also introduces the mathematician L'Hopital and applies the rule to examples introduced earlier.
The document provides an overview of curve sketching in calculus including objectives, rationale, theorems for determining monotonicity and concavity, and a checklist for graphing functions. It then gives examples of graphing cubic and quartic functions step-by-step, demonstrating how to analyze critical points, inflection points, and asymptotic behavior to create the curve. The examples illustrate applying differentiation rules to determine monotonicity from the derivative sign chart and concavity from the second derivative test.
This document is a section from a Calculus I course at New York University covering maximum and minimum values. It begins with announcements about exams and assignments. The objectives are to understand the Extreme Value Theorem and Fermat's Theorem, and use the Closed Interval Method to find extreme values. The document then covers the definitions of extreme points/values and the statements of the Extreme Value Theorem and Fermat's Theorem. It provides examples to illustrate the necessity of the hypotheses in the theorems. The focus is on using calculus concepts like continuity and differentiability to determine maximum and minimum values of functions on closed intervals.
This document is the notes from a Calculus I class at New York University covering Section 4.2 on the Mean Value Theorem. The notes include objectives, an outline, explanations of Rolle's Theorem and the Mean Value Theorem, examples of using the theorems, and a food for thought question. The key points are that Rolle's Theorem states that if a function is continuous on an interval and differentiable inside the interval, and the function values at the endpoints are equal, then there exists a point in the interior where the derivative is 0. The Mean Value Theorem similarly states that if a function is continuous on an interval and differentiable inside, there exists a point where the average rate of change equals the instantaneous rate of
This document discusses the definite integral and its properties. It begins by stating the objectives of computing definite integrals using Riemann sums and limits, estimating integrals using approximations like the midpoint rule, and reasoning about integrals using their properties. The outline then reviews the integral as a limit of Riemann sums and how to estimate integrals. It also discusses properties of the integral and comparison properties. Finally, it restates the theorem that if a function is continuous, the limit of Riemann sums is the same regardless of the choice of sample points.
The document summarizes the steps to solve optimization problems using calculus. It begins with an example of finding the rectangle with maximum area given a fixed perimeter. It works through the solution, identifying the objective function, variables, constraints, and using calculus techniques like taking the derivative to find critical points. The document then outlines Polya's 4-step method for problem solving and provides guidance on setting up optimization problems by understanding the problem, introducing notation, drawing diagrams, and eliminating variables using given constraints. It emphasizes using the Closed Interval Method, evaluating the function at endpoints and critical points to determine maximums and minimums.
The document is about calculating areas and distances using calculus. It discusses approximating areas of curved regions by dividing them into rectangles and letting the number of rectangles approach infinity. It provides examples of calculating areas of basic shapes like rectangles, parallelograms, and triangles. It then discusses Archimedes' work approximating the area under a parabola by inscribing sequences of triangles. The objectives are to compute areas using limits of approximating rectangles and to compute distances as limits of approximating time intervals.
This document is from a Calculus I class at New York University and covers antiderivatives. It begins with announcements about an upcoming quiz. The objectives are to find antiderivatives of simple functions, remember that a function whose derivative is zero must be constant, and solve rectilinear motion problems. It then outlines finding antiderivatives through tabulation, graphically, and with rectilinear motion examples. The document provides examples of finding antiderivatives of power functions by using the power rule in reverse.
- The document is about evaluating definite integrals and contains sections on: evaluating definite integrals using the evaluation theorem, writing antiderivatives as indefinite integrals, interpreting definite integrals as net change over an interval, and examples of computing definite integrals.
- It discusses properties of definite integrals such as additivity and comparison properties, and provides examples of definite integrals that can be evaluated using known area formulas or by direct computation of antiderivatives.
Here are the key points about g given f:
- g represents the area under the curve of f over successive intervals of the x-axis
- As x increases over an interval, g will increase if f is positive over that interval and decrease if f is negative
- The concavity (convexity or concavity) of g will match the concavity of f over each interval
In summary, the area function g, as defined by the integral of f, will have properties that correspond directly to the sign and concavity of f over successive intervals of integration.
This document provides information about a Calculus I course taught by Professor Matthew Leingang at the Courant Institute of Mathematical Sciences at NYU. The course will include weekly lectures, recitations, homework assignments, quizzes, a midterm exam, and a final exam. Grades will be determined based on exam, homework, and quiz scores. The required textbook is available in hardcover, looseleaf, or online formats through the campus bookstore or WebAssign. Students are encouraged to contact the professor or TAs with any questions.
The document is a section from a Calculus I course at NYU from June 22, 2010. It discusses using the substitution method to evaluate indefinite integrals. Specifically, it provides an example of using the substitution u=x^2+3 to evaluate the integral of (x^2+3)^3 4x dx. The solution transforms the integral into an integral of u^3 du and evaluates it to be 1/4 u^4 + C.
This document outlines information about a Calculus I course taught by Professor Matthew Leingang at the Courant Institute of Mathematical Sciences. It provides details on the course staff, contact information for the professor, an overview of assessments including homework, quizzes, a midterm and final exam. Grading breakdown is also included, as well as information on purchasing the required textbook and accessing the course on Blackboard. The document aims to provide students with essential logistical information to succeed in the Calculus I course.
This document contains lecture notes from a Calculus I class at New York University on September 14, 2010. The notes cover announcements, guidelines for written homework, a rubric for grading homework, examples of good and bad homework, and objectives for the concept of limits. The bulk of the document discusses the heuristic definition of a limit using an error-tolerance game approach, provides examples to illustrate the game, and outlines the path to a precise definition of a limit.
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previous work.
STEP FOUR:
Add the products.
Regroup if necessary.
20. Find 2.3 x 1.5
STEP ONE:
STEP ZERO: Multiply by
Use guidelines
to keep work
2.3 the ones. Regroup
if necessary.
x 1.5
neat.
STEP THREE:
Multiply by the 1 15 STEP TWO:
+23 0
Place a zero in the
tens. Regroup
ones place.
if necessary.
(PLACEHOLDER)
Scratch out
STEP FOUR:
Add the products.
Regroup if necessary.
34 5 previous work.
22. Find 2.3 x 1.5
STEP FIVE:
Count the number of
decimal places.
2.3
x 1.5
1 15
+23 0
34 5
23. Find 2.3 x 1.5
STEP FIVE:
Count the number of
decimal places.
2.3
x 1.5
1 decimal place
1 decimal place
1 15
+23 0
34 5
24. Find 2.3 x 1.5
STEP FIVE:
Count the number of
decimal places.
2.3
x 1.5
1 decimal place
1 decimal place
1 15
STEP SIX:
Make sure the
number of decimals
+23 0
places is included in
your answer.
34 5
25. Find 2.3 x 1.5
STEP FIVE:
Count the number of
decimal places.
2.3
x 1.5
1 decimal place
1 decimal place
1 15
STEP SIX:
Make sure the
number of decimals
+23 0
places is included in
your answer.
3.4 5
36. Find 0.76 x 0.9
0.76
x 0.9
684
STEP TWO:
Count the number of
decimal places.
37. Find 0.76 x 0.9
0.76
x 0.9
2 decimal place
1 decimal place
684
STEP TWO:
Count the number of
decimal places.
38. Find 0.76 x 0.9
0.76
x 0.9
2 decimal place
1 decimal place
684
STEP TWO:
Count the number of
decimal places.
STEP THREE:
Make sure the
number of decimals
places is included in
your answer.
39. Find 0.76 x 0.9
0.76
x 0.9
2 decimal place
1 decimal place
0.6 8 4
STEP TWO:
Count the number of
decimal places.
STEP THREE:
Make sure the
number of decimals
places is included in
your answer.