Lesson Plans SET A for Grades 9-10-Lesson 5 Level 9-10 NumberTheory

Lesson 5 Level 9-10 NumberTheory - HW

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This document is a set of math practice problems from a Level 9-10 Number Theory lesson, designed for students preparing for the Math Kangaroo competition. It contains a mix of problems that test various number theory concepts, followed by their solutions.<br /><br />The first problem asks to solve an equation involving certain unknown digits represented by letters, where one of the components is a two-digit number. The solution provided identifies these digits as 2 and 3.<br /><br />The second problem involves finding the possible values of a number given its greatest common divisor (GCD) with 144 is 24 and its least common multiple (LCM) with 144 is less than 1500. The possible values are 24, 120, and 168.<br /><br />The third problem requires calculating how many positive divisors of 43,875 are multiples of 5. The given answer is 24 divisors.<br /><br />The fourth problem is two-fold: <br />(a) determining how many digits appear after the decimal point in the expansion of 1/237, which is 37 digits; <br />(b) finding the total number of digits in the decimal expansion of 237, which is 12 digits.<br /><br />The fifth problem involves finding all the positive integer pairs (x, y) that satisfy a given equation. The solutions provided are the pairs (x, y) as (4, 5) and (10, 20).<br /><br />These problems and answers are intended to reinforce understanding of number theory principles, helping students apply theoretical knowledge to practical problem-solving scenarios. Understanding these problems often requires familiarity with divisors, prime factorization, and other foundational mathematical concepts.

Keywords

Number Theory

Math Kangaroo

practice problems

equation solving

greatest common divisor

least common multiple

positive divisors

decimal expansion

integer pairs

prime factorization