Learningexpress - Ged Test Mathematical Reasoning Flash Review

RULES OF NUMBERS What is a rational number ? ................................ Which of the following are not rational numbers? A. B. C. / D. ................................ ................................

What does it mean if k is a multiple of m ? A rational number is any number that can be expressed as a quotient or fraction of two integers. A rational number can be written as p / q , where p and q are integers and the denominator q does not equal zero. All integers are rational numbers as q can equal 1.
................................ A. is rational. , the square root of a negative, is imaginary and irrational. C. / is rational. D. 0.875 is rational. E. cannot be written as a fraction so it is irrational. ................................ ................................

A number k is a multiple of m if k can be written as m times another number. So if k = mn for any integer n , then k is a multiple of n . Ex: 20 is a multiple of 5 because 4 5 = 20. What are the first five multiples of 8? ................................ What is the l east common multiple (LCM) of two numbers or expressions? What is the LCM of 6 and 8? Note: The least common multiple of 6 and 8 is written as LCM (6, 8). ................................

What is the least common multiple of 12 and 20? The first five multiples of 8 are: 1 = 2 = 3 = 4 = 5 = ................................ The l east common multiple is the lowest multiple that both numbers have in common. LCM (6, 8) = 24 since 24 is the smallest number that is a multiple of both 6 and 8. ................................ Write out lists of multiples for each number, and the lowest number that is a multiple of both is the least common multiple: 12: 12, 24, 36, 48, , 72 20: 20, 40, , 80 So LCM (12, 20) = What does it mean if v is a factor of w ? What are the factors of 12? ................................ ................................ ................................

What is the greatest common factor of 98 and 35? If there is an integer k such that v k = w , then v is a factor of w . Ex: 3 and 4 are factors of 12 since 3 4 = 12. The complete list of factors of 12 is: 1, 2, 3, 4, 6, and 12 . ................................ In order to find the greatest common factor of two numbers, write them both out as the product of all of their factors and then identify the factors they have in common. If they just have one factor in common, then that is the GCF.

If they have two or more factors in common, then multiply those numbers together, and that product will be the GCF: 70 = 35 2 = 105 = 35 3 = 7 and 5 are the factors that 70 and 105 have in common, so multiply them together to get 35 as the GCF. ................................ Write 98 and 35 out as a product of all of their factors: 98 = 49 2 = 35 = The only factor they have in common is 7, so GCF (98, 35) = . What is the greatest common factor of the expressions 40 v f and 17 v f ? ................................ Sues favorite number is the greatest common factor of 16 and 24. Mikes favorite number is the least common multiple of 12 and 16.

What is the positive difference of Sues and Mikes favorite numbers? ................................ What are consecutive numbers , consecutive even numbers , and consecutive odd numbers ? Write 40 v f and 17 v f out as a product of all of their factors: v f = 5 v v f v f = 17 v v f f v , v , and f are the factors that these expressions have in common, so multiply them together to get v f as the GCF. ................................ The greatest common factor of 16 and 24 is the largest integer that divides evenly into both 16 and 24. The GCF of 16 and 24 is 8. The least common multiple of 12 and 16 is the smallest number that both 12 and 16 are multiples of, which is 48.

Subtract them to find the difference of . ................................ Consecutive numbers follow each other in order, without any gap or space between them: 17, 18, 19... Consecutive even numbers skip the odd integers between them: 22, 24, 26... Similarly, consecutive odd integers skip the even integers between them: 21, 23, 25... The product of two consecutive integers is 182.

If the smaller integer is x , write an equation modeling this situation. ................................ What is important to keep in mind when ordering negative numbers on a number line? ................................ For the following number, identify the name of which place value each of the digits are in (f or example, units, tenths, thousandths, etc .): 91,234.5678 If the first integer is x , then the second consecutive integer is x + 1. Their product is x ( x + 1) = x + x = 182 . ................................

The negative numbers sit to the left of zero on a number line. The larger a negative number is, the farther to the left of 0 it lies. For example, 5 is a smaller number than 2, and it is farther to the left on the number line than 2. ................................ 91,234.5678 9 = ten-thousands 1 = thousands 2 = hundreds 3 = tens 4 = units (sometimes called the ones place) 5 = tenths 6 = hundredths 7 = thousandths 8 = ten-thousandths Write out the following three numbers in words: A. 3.068 C. 3.0608 ................................ 3.0608 ................................

Order the following numbers from least to greatest: 1.22, 1.40, 1.15, 1.67, 1.53 ................................ What is important to keep in mind when ordering decimals on a number line like 0.1 and 0.09? A. 3.68 = three and sixty-eight hundredths B. 3.068 = three and sixty-eight thousandths C. 3.0608 = three and six-hundred-eight ten-thousandths ................................ Recall that with negative numbers, the larger the negative number is, the smaller its value: 1.67, 1.53, 1.40, 1.22, 1.15 ................................

The place value that a decimal holds is more important than the value of the number. For example, 0.1 is bigger than 0.09 because 0.1 = 0.10, which is equivalent to ten hundredths (which is like a dime), whereas 0.09 is only equivalent to nine hundredths (which is like 9 cents). Although 0.1 might look smaller than 0.09, 0.1 is actually the larger number. It has a number in the tenths position, while 0.09 only has a number in the hundredths position. How should decimals be rewritten so that they can be compared? For example, what is the best way to compare 0.2, 0.009, and 0.08? ................................ Put the following list of decimals in order of least to greatest: 0.083, 0.109, 0.2, 0.0600 ................................

Which point best represents 1 / on the number line below?
In order to compare decimals, add zeros after the last number to the right of the decimal until all of the decimals have the same number of digits to the right of the decimal point. Then, ignore the decimal point and compare the values of the numbers: 0.2 = 0.200 0.08 = 0.080 0.009 = 0.009 Since 200 is the largest number, 0.2 is the largest. 80 is larger than 9, so 0.08 is the middle number, and 0.009 is the smallest. ................................ 0.0600, 0.0830, 0.1090, 0.2000 ................................ / is smaller than / , so 1 / will be closer to 1 than 2, so Q is the correct answer. / is smaller than / , so 1 / will be closer to 1 than 2, so Q is the correct answer.