Reteaching. Comparing and Ordering Integers

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Ralf Bruce
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1 - Comparing and Ordering Integers The numbers and - are opposites. The numbers 7 and -7 are opposites. Integers are the set of positive whole numbers, their opposites, and zero negative zero positive You can use the number line to compare integers. - is less than 0. 7 is greater than Compare using R, S, or Find the opposite of each number Find each sum. Numbers to the left are less. is farther left than Order the numbers from least to greatest.. -4,, -, 0,. 6, -, -, 4, -6 4., -, 4, -4, -7, 0.,, -7, -6,, - Numbers to the right are greater. 7 is farther to the right than. Course Lesson -

2 - Adding and Subtracting Integers Use these rules to add and subtract integers. Adding Integers Same Sign Different Signs The sum of two positive integers is positive. Example: = The sum of two negative integers is negative. Example: -9 + (-) = - Find each sum. Subtracting Integers. 8 + (-) (-) (-7) (-) (-) Complete Change to addition: - + = 4. - Change to addition: + = (-0) Change to addition: -6 + = Find each difference. To subtract integers, add the opposite. Then following the rules for adding integers. Example: 6 ( ) = 6 + = 9 First find the absolute values of each number. Then subtract the lesser absolute value from the greater. The sum has the sign of the integer with the greater absolute value. Example: = (-7) (-6) (-). - - (-) (-7) (-0) Course Lesson -

3 - Multiplying and Dividing Integers To multiply integers: If the signs are alike, the product is positive. To divide integers: If the signs are alike, the quotient is positive.? = 6 6 = -? - = = If the signs are different, the product is If the signs are different, the quotient negative. is negative.? - = = - -? = -6-6 = - Study these four examples. Write positive or negative to complete each statement When both integers are positive, the product is.. When one integer is positive and one is negative, the product is.. When both integers are negative, the product is. = 7 = 7 = 7 = 7 4. When both integers are positive, the quotient is.. When both integers are negative, the quotient is. 6. When one integer is positive and one is negative, the quotient is. Tell whether each product or quotient will be positive or negative. 7. 4? ? ? ? -7. 0? ? Course Lesson -

4 Fractions and Decimals..4 0 To change a fraction to a decimal, divide the numerator by the denominator. 0.6 Think: 0.6 q Write each fraction as a decimal Write each decimal as a mixed number or fraction in simplest form. To change a decimal to a fraction: Read the decimal to find the denominator. Write the decimal digits over 0, 00, or, is 6 hundredths S 6 00 Use the GCF to write the fraction in simplest form. The GCF of 6 and 00 is =. 0.7 =.. =. 0. = 4..7 =..8 = = = = Order from least to greatest. 9..6,, 0..0,,.00., ,.4 Course Lesson -4

5 - Rational Numbers A rational number is a number that can be written as a quotient of two integers, where the divisor is not zero. A negative rational number can be written in three different ways. Comparing Negative Rational Numbers Compare and 4. Method Use a number line. Graph both points on a number line and see which is farther to the left. Since is farther to the left, 4. Method Use the lowest common denominator Since 8,, then, 4. Compare. Use R, S, or Order from least to greatest. 7., 0., 0., , 0., 0., 0 9. You and your brother invested an equal amount of money in a college savings plan. In the last quarter your investment was worth 6 of its original value. Your brother s investment was worth.8 of its original value. Whose investment is worth more? Course Lesson -

6 -6 Adding and Subtracting Rational Numbers Use these rules to add and subtract rational numbers. Adding and Subtracting Integers Find each sum. Subtracting Rational Numbers (.) Find each difference. Same Sign The sum of two positive rational numbers is positive. Example: Example: The sum of two negative rational numbers is negative. Example:.4 (.74) 9.6 Example: 4 a4 4 b 6 To subtract rational numbers, add the opposite. Then following the rules for adding rational numbers. Example: 9. (.4) = Example: 4 a 0 b 4 a 0 b 6 0 Different Signs First find the absolute values of each addend. Then subtract the lesser absolute value from the greater. The sum has the sign of the addend with the greater absolute value. Example: Example: a7 b (.6) a b Course Lesson -6

7 -7 Multiplying Rational Numbers Remember these rules when multiplying rational numbers.. When both factors are positive, the product is positive. Multiply: a ba 8 b a8 ba 8 b When both factors are negative, the product is positive. Multiply: ( 4.)(.44) When both factors have different signs, the product is negative. Multiply: Find each product. Write the product in simplest form ? 4.. (.07)( 4.9) 6.? 7 8? a 0 b 7. 9.( 0.6) (.7) a ba 4 b Course Lesson -7

8 -8 Dividing Rational Numbers Divide: 8... Divide: Rewrite the problem with a whole number divisor.. )8. T. Rewrite mixed numbers as improper fractions as needed Place the decimal point in the quotient.. Divide. Then check...)8.. Find each quotient. Simplify your answers. c c Move place each.. ) Multiply to check.. Multiply by the reciprocal of the divisor.. Multiply numerators. Multiply denominators. 4. Simplify a b ? 7 4 4? 4? ( 7) Course Lesson -8

3 cups ¾ ½ ¼ 2 cups ¾ ½ ¼. 1 cup ¾ ½ ¼. 1 cup. 1 cup ¾ ½ ¼ ¾ ½ ¼. 1 cup. 1 cup ¾ ½ ¼ ¾ ½ ¼

3 cups ¾ ½ ¼ 2 cups ¾ ½ ¼. 1 cup ¾ ½ ¼. 1 cup. 1 cup ¾ ½ ¼ ¾ ½ ¼. 1 cup. 1 cup ¾ ½ ¼ ¾ ½ ¼ cups cups cup Fractions are a form of division. When I ask what is / I am asking How big will each part be if I break into equal parts? The answer is. This a fraction. A fraction is part of a whole. The