Chapter 2 Estimation and Number Theory

  • Chapter 2

    Chapter Objectives:

    * When two factors are multiplied, the product is a multiple of both numbers.

    * Knowing factors and multiples of numbers can help in estimating products and quantities.


    Vocabulary:

    Estimate - An estimate is a calculated guess that is close to the exact number. An estimate of the sum of 214 and 545 is 700.

    Reasonable - An estimate that is close to the actual answer. Ex: If we know 683 X 4 is equal to 2,732, then we can also estimate to see if our answer can be reasonable. For example, we know that 683 is close to 700, and 700 X 4 is equal to 2,800. So, 2,732 is close to 2,800 and the answer is reasonable.

    Front-end estimation - Front-end estimation uses the leading digits in numbers to make an estimate. The front-end estimation of 324 is 300, and the front-end estimation of 9,782 is 9000.

    Rounding - To give an approximate value. A number can be rounded to the nearest ten or hundred by looking at the digit to the right of the tens or hundreds place. If it is less than 5, round down. If it is 5 or more, round up.

    Product - The product is the answer to a multiplication problem. Ex: 924 X 40 = 36,960. The product of 924 and 40 is 36,960.

    Quotient - The quotient is the answer to a division problem. Ex: 8,160 ÷ 6 = 1,360. The quotient of 8,160 divided by 6 is 1,360.

    Factor - A number can be divided exactly by its factor. Ex: 12 can be divided exactly by 2. So, 2 is a factor of 12. The factors of 12 are 1, 2, 3, 4, 6 and 12.

    Common factor - A common factor is a number shared by two or more numbers. Ex: The factors of 9: 1, 3, and 9. The factors of 12: 1, 2, 3, 4, 6 and 12. So, the common factors of 9 and 12 are 1 and 3.

    Greatest common factor - The greatest common factor is the largest factor shared by two or more numbers. Ex: The factors of 12: 1, 2, 3, 4, 6 and 12. The factors of 16: 1, 2, 4, 8 and 16. The common factors are 1, 2 and 4. The GREATEST COMMON FACTOR of 12 and 16 is 4.

    Prime number - A prime number has exactly two factors; 1 and itself. Ex: 7 is a prime number; its factors are only 1 and 7.