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Transcript
The Rational Numbers Honors Math – Grade 7 Problem of the Day 1 4 A small submarine descended to a depth of mi and then 3 ascended mi. These changes can be written as signed 2 8 (positive or negative) numbers. Let’s recall some words for positive and negative numbers. POSITIVE NEGATIVE Let’s write these signed numbers. 1 descended 2 mi 4 1 2 mi 4 Read: negative 2 and ¼. 3 ascended mi 8 3 mi 8 Read: positive three eighths or three eighths. A Rational Number is a number that can be written in a fractional form, , where a and b are integers and b 0. b Here are some examples of rational numbers. Rational Number Form All integers are rational numbers. Natural Numbers VOCAB ALERT N 1,2,3,4,... Integers – the set of whole numbers and their opposites Whole Numbers I ...,3,2,1,0,1,2,3,... W 0,1,2,3,4,... 0.5 1.3 1 2 Set of numbers that can be -4 2 expressed as the quotient of Rational Numbers 5 7 8 Integers -98 two integers. Set of whole numbers and their opposites. Whole Numbers 0 Set of natural numbers and 0 Natural or Counting Numbers 1, 2, 3, 4, … Set of numbers starting with 1 and counting up by ones. 3 5 7 4 9 Identify the set(s) of numbers to which each belongs. 7 -10 0 4 4 5 121 150 2 9 Rational Numbers can be represented in different forms. To write a mixed number as an improper fraction… 1. Multiply the denominator by the whole number part (integer). 2. Add the product to the numerator. 3. The denominator stays the same! + 63 4 67 7 9 9 x a Write in the form . b 4 3 11 a Write in the form . b 13 a Write in the form . b 2 15 3 A Rational Number in the form, decimal. a , b can be written as a To write a fraction as a decimal, follow one of these three methods… Inspection Equivalent Fractions Division If the fraction, has a denominator of 10, 100, 1000, etc…, say the fraction and write the decimal. If the fraction can be renamed as an equivalent fraction with a denominator of 10, 100 or 1000, rename the fraction and use inspection. If the previous methods do not work, divide the numerator by the denominator. Can be used all the time. 7 0.07 100 Seven hundredths 14 0.56 25 100 3 8 Fifty-six hundredths 251 1000 17 20 8 3 5 11 Write as a decimal. 6 4 25 If the quotient has a remainder of zero, the result is a terminating decimal. Write as a decimal. 9 10 If the quotient has a remainder of zero, the result is a terminating decimal. Write as a decimal. 5 6 If the quotient has a digit or a group of digits that repeat without end, the result is a repeating decimal. To show that one or more digits repeat in a decimal, use an ellipsis or an overbar.