Algorithm - Algebra 1, Math Dictionary

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Problem Problem Solving

Algorithm
Definition of Algorithm

An Algorithm is a list of well-defined instructions or a step-by-step procedure to solve a problem.

More about Algorithm

The process of algorithm is also used in computer programs to perform a specific task in a specific order.

Example of Algorithm

To add the numbers 150 and 457, split the numbers first and then add hundreds, tens and ones.
150 = 100 + 50, 457 = 400 + 50 + 7
150 + 457 = (100 + 400) + (50 + 50) + 7 = 500 + 100 + 7 = 607.

Solved Example on Algorithm

Identify the algorithm that would help you to find the sum 71 + 56 + 69.
Choices:
A. 7 + 5 + 6 = 18; 1 + 6 + 9 = 16; 18 + 16 = 34
B. 70 + 50 + 70 = 190; 1 + 6 - 1 = 6; 190 + 6 = 196
C. 70 + 50 + 90 = 200; 1 + 6 + 9 = 10; 200 + 10 = 210
D. 7 + 5 + 6 = 9; 1 + 6 + 9 = 8; 9 + 8 = 17
Correct Answer: B
Solution:
Step 1: 71 = 70 + 1 [Write in the expanded form.]
Step 2: 56 = 50 + 6 [Write in the expanded form.]
Step 3: 69 = 70 - 1 [Write in the expanded form.]
Step 4: To find 71 + 56 + 69, add the tens and the ones separately.
Step 5: Adding the tens we get: 70 + 50 + 70 = 190.
Step 6: Adding the ones we get: 1 + 6 - 1 = 6. [Subtract 1 from 6 and then add.]
Step 7: So, 71 + 56 + 69 = sum of tens + sum of ones = 190 + 6 = 196.
Step 8: So, the algorithm that helps us to find the sum of 71 + 56 + 69 is 70 + 50 + 70 = 190; 1 + 6 - 1 = 6; 190 + 6 = 196.

Related Terms for Algorithm

Problem
Problem Solving

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Browse for solved examples below on this Math Dictionary term:

SC BM Curriculum > Grade 4 > Number and Operations > III.B.2: Demonstrate fluency in the use of a multiplication algorithm and explain the steps involved.

SC BM Curriculum > Grade 5 > Number and Operations > III.B.2: Demonstrate fluency in the use of a division algorithm and explain the steps involved.

Michigan Assessment Curriculum - 2006 > Grade 4 > Number Sense and Computations > N.FL.04.10-Multiply fluently any whole number by a one-digit number and a three-digit number by a two-digit number; for a two-digit by one-digit multiplication use distributive property to develop meaning for the algorithm.

Massachusetts Assessment Curriculum - 2006 > Grade 4 > Number and Numerical Operations > 4.N.15-Demonstrate in the classroom an understanding of and the ability to use the conventional algorithm for division of up to a three-digit whole number with a single-digit divisor.

South Carolina Assessment Curriculum - 2006 > Grade 4 > Numbers Sense and Operations > III.B.2-Demonstrate fluency in the use of a multiplication algorithm and explain the steps involved.

South Carolina Assessment Curriculum - 2006 > Grade 5 > Numbers Sense and Operations > III.B.2-Demonstrate fluency in the use of a division algorithm and explain the steps involved.

Indiana Assessment Curriculum - 2006 > Grade 4 > Number Operations > 4.2.10-Use a standard algorithm to add and subtract decimals.

Indiana Assessment Curriculum - 2006 > Grade 4 > Number Operations > 4.2.5-Use a standard algorithm to multiply numbers up to 100 by numbers up to 10, using relevant properties of the number system.

Indiana Assessment Curriculum - 2006 > Grade 4 > Number Operations > 4.2.6-Use a standard algorithm to divide numbers up to 100 by numbers up to 10 without remainders, using relevant properties of the number system.

West Virginia Assessment Curriculum - 2006 > Grade 5 > Number and Numerical Operations > MA.5.1.9-Model multiplication and division of fractions to solve the algorithm.

UT Assessment Curriculum - 2006 > Grade > Students will acquire number sense and perform operations with whole numbers and simple fractions. > I.3.b-Model and illustrate meanings of the operations of addition, subtraction, multiplication, and division and describe how they relate: Model multiplication of a one-digit factor by a one-digit factor using various methods and connect the representation to an algorithm.

UT Assessment Curriculum - 2006 > Grade 3 > Students will acquire number sense and perform operations with whole numbers and simple fractions. > I.3.b-Model and illustrate meanings of the operations of addition, subtraction, multiplication, and division and describe how they relate: Model multiplication of a one-digit factor by a one-digit factor using various methods and connect the representation to an algorithm.

UT Assessment Curriculum - 2006 > Grade 4 > Students will acquire number sense and perform operations with whole numbers, simple fractions, and decimals. > I.3.a-Model and illustrate meanings of the four operations and describe how they relate: Use models to represent multiplication of a one-or two-digit factor by a two-digit factor using a variety of methods and connect the representation to an algorithm.

UT Assessment Curriculum - 2006 > Grade 4 > Students will acquire number sense and perform operations with whole numbers, simple fractions, and decimals. > I.3.d-Model and illustrate meanings of the four operations and describe how they relate: Represent division of a two-digit dividend by a one-digit divisor, including whole number remainders, using various methods and connect the representation to an algorithm.

South Carolina Assessment Curriculum - 2007 > Grade > Standard 3-2: The student will demonstrate through the mathematical processes an understanding of the representation of whole numbers and fractional parts; the addition and subtraction of whole numbers; accurate, efficient, and generalizable methods of mu > 3-2.3-Apply an algorithm to add and subtract whole numbers fluently.

South Carolina Assessment Curriculum - 2007 > Grade 3 > Standard 3-2: The student will demonstrate through the mathematical processes an understanding of the representation of whole numbers and fractional parts; the addition and subtraction of whole numbers; accurate, efficient, and generalizable methods of mu > 3-2.3-Apply an algorithm to add and subtract whole numbers fluently.

South Carolina Assessment Curriculum - 2007 > Grade 4 > Standard 4-2: The student will demonstrate through the mathematical processes an understanding of decimal notation as an extension of the place-value system; the relationship between fractions and decimals; the multiplication of whole numbers; and accurat > 4-2.3-Apply an algorithm to multiply whole numbers fluently.

South Carolina Assessment Curriculum - 2007 > Grade 5 > Standard 5-2: The student will demonstrate through the mathematical processes an understanding of the place value system; the division of whole numbers; the addition and subtraction of decimals; the relationships among whole numbers, fractions, and decima > 5-2.2-Apply an algorithm to divide whole numbers fluently.

South Carolina Assessment Curriculum - 2007 > Grade 5 > Standard 5-2: The student will demonstrate through the mathematical processes an understanding of the place value system; the division of whole numbers; the addition and subtraction of decimals; the relationships among whole numbers, fractions, and decima > 5-2.5-Apply an algorithm to add and subtract decimals through thousandths.

South Carolina Assessment Curriculum - 2007 > Benchmark - Algebra II > Standard 6-2: The student will demonstrate through the mathematical processes an understanding of the concepts of whole-number percentages, integers, and ratio and rate; the addition and subtraction of fractions; accurate, efficient, and generalizable met > 6-2.4-Apply an algorithm to add and subtract fractions.

South Carolina Assessment Curriculum - 2007 > Grade 6 > Standard 6-2: The student will demonstrate through the mathematical processes an understanding of the concepts of whole-number percentages, integers, and ratio and rate; the addition and subtraction of fractions; accurate, efficient, and generalizable met > 6-2.4-Apply an algorithm to add and subtract fractions.

South Carolina Assessment Curriculum - 2007 > Grade 7 > Standard 7-2: The student will demonstrate through the mathematical processes an understanding of the representation of rational numbers, percentages, and square roots of perfect squares; the application of ratios, rates, and proportions to solve problems > 7-2.9-Apply an algorithm to multiply and divide fractions and decimals.

South Carolina Assessment Curriculum - 2007 > Grade 8 > Standard 8-2: The student will demonstrate through the mathematical processes an understanding of operations with integers, the effects of multiplying and dividing with rational numbers, the comparative magnitude of rational and irrational numbers, the ap > 8-2.1-Apply an algorithm to add, subtract, multiply, and divide integers.

CBSE Common Curriculum - 2007 > Pre-Calculus > Polynomials > Division Algorithm for Polynomials

CBSE Common Curriculum - 2007 > Pre-Calculus > Real Numbers > Euclid′s Division Algorithm

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