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Math 7 Challenge, Unit 1: Rational Numbers, Study Guide Name: _______________________________ Period: __________ Target 1: I can identify and classify numbers within the subsets of the real number system. Natural Numbers (Counting Numbers): 1, 2, 3, … Whole Numbers: 0, 1, 2, 3, … Integers: All whole numbers AND their opposites Rational Numbers: All integers and all of the numbers in between (fractions and decimals.) 1) The number (-2) is NOT in which subset(s)? a. Natural Numbers b. Whole Numbers c. Integers d. Rational Numbers 2) All Whole Numbers are also: a. Natural Numbers b. Integers c. Rational Numbers d. All of the above 3) All Integers are also: a. Natural Numbers b. Whole Numbers c. Rational Numbers d. All of the above 2 Math 7 Challenge, Unit 1: Rational Numbers, Study Guide Target 2: I can convert a fraction to a decimal to determine whether it is a terminating or repeating decimal using long division. 5 8 𝟖 Divide the numerator by the denominator. Divide the numerator by the denominator. 𝟏𝟓 0.625 8 ) 5.000 -48 20 -16 40 -40 0 The remainder is zero and there are not any parts of the original numerator to bring down. So, this decimal terminates. 3 4) Without a calculator, find the decimal equivalent for 8. 15 5) Does the fraction 24 convert to a terminating or repeating decimal? How do you know? Target 3: I can approximate the value of an irrational number and locate it on a number line. Approximate the square root of the following. If using a decimal approximation, estimate to the nearest tenth. If using a fractional approximation, simplify the fraction. 6) √114 8) Place the following numbers in their appropriate location on the number line. √2.25 −√7 − 1.7 7) √7 Math 7 Challenge, Unit 1: Rational Numbers, Study Guide Name: _______________________________ Period: __________ Target 4: I can convert a decimal to a fraction. Find the fraction equivalent for each decimal. Simplify. 9) 0.48 10) ̅̅̅̅ −0. 45 Target 5: I understand the absolute value of a rational number as its distance from 0 in the number line. 11) |−4| = 12) |4| = 13) |𝑥| = 7 14) |−4| − |9| = Target 6: I can add and subtract integers. 8) −3 + 4 10) −3 − 4 9) −3 + − 4 12) −3 − (−4) 10) 3 + 4 Adding Integers with the Same Sign: 1) Add the absolute values 2) Keep the sign the same 13) 3 − 4 Adding Integers with Different Signs: 1) Find the difference of the absolute values. 2) Use the sign of the integer with the larger absolute value. Subtracting Integers: 1) To subtract an integer, add the opposite. 4 Math 7 Challenge, Unit 1: Rational Numbers, Study Guide Target 7: I can multiply and divide integers. If the signs of the integers are the same, then the product (or quotient) is positive. If the signs of the integers are different, then the product (or quotient) is negative. 14) −3 × 4 = 15) 3 × (−4) = 16) −3 × (−4) = 17) −15 ÷ 3 = 18) 15 ÷ (−3) = 19) −15 ÷ (−3) = Target 8: I can add and subtract signed fractions and decimals (rational numbers). 20) 1 2 + (− 1 4 ) 21) −2.35 − (−1) Target 9: I can multiply and divide signed fractions and decimals (rational numbers). 2 4 22) −3 × 5 24) −3 ÷ 4 2 4 23) 1.5 × (− 15) 25) −0.6 ÷ (−0.3) Math 7 Challenge, Unit 1: Rational Numbers, Study Guide Name: _______________________________ Period: __________ Target 10: I can solve real-world problems using rational numbers including fractions, decimals and integers. 26) It was −3° in Columbia, MO when Shari got on a plane for Florida. There was a temperature increase of 60° when she got off of the plane in Miami, Florida. a. Write this as a number sentence. b. What was the temperature in Miami? 27) Five friends went to play golf. Jon shot a −2, Kaleb shot a 3, Carey shot a 4. What was the mean score for the four players? 28) Find the mean of these five daily temperatures: −4°, −6°, 2°, −5°, 3°. Show your work.