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SEVENTH GRADE “YOU SHOULD KNOW” Study Guide and Practice The Four Basic Operations: 1) Addition **the SUM is the answer to an addition problem** When adding whole numbers, be sure to line up the place values. 9545 + 8982 18,527 When adding decimal numbers, be sure to line up the decimal points and bring the decimal straight down into your answer. 4,785 + 9 + 2.307 4,785 9 + 2 .307 4,796.307 2) Subtraction **the DIFFERENCE is the answer to a subtraction problem** 5,312 **Be sure to line up place value and borrow if need be** − 2,579 2,733 When subtracting decimal numbers, you must line up the decimal points, add zeros to match place value, subtract, and bring decimal point straight down. 18.2 - 6.008 = 18.200 - 6.008 12.192 3) Multiplication **the PRODUCT is the answer to a multiplication problem** Multiply the top number by each place value of the bottom number starting with the ones place. Remember to put a zero or indent when multiplying by the next place value. When multiplying with decimal numbers, the decimal points are irrelevant until the very end. Multiply the numbers like normal and count the number of digits that are behind the decimal point in each number. This is how many places you move the decimal point in the product beginning at the end of the number. .2 × 6.03 = 1.206 ***MENTAL MATH – when multiplying by 10 or 100 or 1000, keep the original number and place 1, 2, or 3 zero at the end of the product. 36 × 10 = 360 36 × 100 = 3600 Add on one 0. Add on two 0’s 36 × 1000 = 36,000 Add on three 0’s 7.32 × 10 = 73.2 Move the decimal point one place right. 4) Division **the QUOTIENT is the answer to a division problem** **the DIVIDEND is the number that is inside the division box** **the DIVISOR is the number that is outside the division box** ** If there is a remainder, we no longer use the “R.” All remainders must be expressed as a decimal or fraction.** When dividing with decimals: if there is a decimal point in the divisor, you must move that decimal to the end of the number and then move the decimal point the same number of places in the dividend. Divide like normal and move the decimal point straight up in your quotient. ***MENTAL MATH: when dividing by 10 or 100 or 1000, move the decimal in to the left. 256 ÷ 10 = 25.6 256 ÷ 100 = 2.56 256 ÷ 1000 = .256 move the decimal 1 place move the decimal in 2 places move the decimal point in 3 places Practice: On your Own 1) 697 + 341 = 7) 56.3 – 8.987 = 2) 1, 234 + 876 = 8) 5.1 × 3.7 = 3) 34.987 + 5.9 = 9) 12 × 56 = 10) 1.21 × .05 = 4) 87.3 + 4.234 + 9 = 11) 804 ÷ 3 = 5) 93.32 – 9.3 = 6) 127 – 99 = 12) 1245 ÷ 27 = 13) 56.2 ÷ .02 = PLACE VALUE: COMPARING AND ORDERING: SYMBOLS: < less than > greater than = equal ***When we compare and order whole numbers and/or decimal numbers, we compare place value to place value*** 14,987 > 14, 912 the 8 is greater than the 1 in the tens place 5,123.6 < 5,124 the 3 is less than the 4 in the ones place 9.00876 < 9.09 the 0 is less than the 9 in the hundredths place 5.6 = 5.600 the zeros at the end of a decimal number do not affect the number Writing Numbers 1) Standard Numerical Form – written as a number ex: ninety-four thousand, sixty-two 94,062 2) Written word form – take a number and write it using words, dashes, and commas ex: 153.097 one hundred fifty-three and ninetyseven thousandths 3) Expanded Form – separate the number into the sum of each place value ex: 91,045.2 90,000 + 1000 + 40 + 5 + .2 Estimating and Rounding Estimate – a close guess (round before performing the operation) 923 + 490 + 313 ≈ 900 + 500 + 300 ≈ 1700 Rounding - look to the number to the right of the given place value - 5 and above, round up - Less than 5, round down 78,987 round to the thousand : 79,000 34,244 round to the hundred: 34,200 125.245 round to the hundredths : 125.25 67,998 round to the hundred : 68,000 Practice: On your Own!! 1) Identify the place value of the 9 in each of the following number: 1) 45,921 ___________________ 2) 8.987 ____________________ 3) 62.009 ___________________ 4) 9,000,000 ________________ 2) Compare using < , >, or = 5) 9.87 8.976 6) 41.9776 41.862 7) 56.213 5.613 8) 9.003 9.0030 3) Round 45,234 to the tens ________________ 4) Round 38,762.355 to the hundredths ____________ 5) Estimate the sum of 346 + 2345 + 467 = ______________ 6) Write 943.96 in written and expanded form. Written ___________________________________ Expanded __________________________________ Divisibility Rules: Divisible – can be divided by We know that a number is divisible by: 2: when the ones digit is even (346) 3: when the sum of the digits is divisible by 3 (123) 4: when the last two digits is divisible by 4 (336) 5: when the ones digit is a 5 or 0 (900) 6: when the number is divisible by 2 and 3 (246) 8: when the last three digits are divisible by 8 (4720) 9: when the sum of the digits is divisible by 9 (279) 10: when the ones digit is a 0 (450) Prime: a number that has only two factors; one and itself examples: 2, 3, 5, 7, 11, 13… Factor: numbers that can divide evenly into a larger number. (without a remainder) **smallest (and only even) prime number = 2 Composite: a number that has more than 2 factors examples: 4, 6, 8, 9, 10… ***ONE and ZERO are neither prime nor composite!! Prime Factorization: the breakdown of a composite number into the product of all of its prime factors. Example: Practice: On your Own Use the divisibility rules to determine which numbers the following are divisible by: 1) 456 ___________________________________ 2) 200 ___________________________________ 3) 135____________________________________ 4) 117____________________________________ Tell whether the following numbers are prime, composite, or neither: 5) 16 __________ 6) 81 _________ 7) 97 __________ 8) 1 __________ 9) 91 ___________ 10) 30 __________ Determine the Prime Factorization of each number: 11) 72 12) 156 GREATEST COMMON FACTOR (GCF): the largest factor that two or more numbers have in common LEAST COMMON MULTIPLE (LCM):the smallest multiple that two or more numbers have in common MULTIPLE – the product of a number with any whole number Practice: On your Own Determine the GREATEST COMMON FACTOR of each set of numbers: 1) 30, 48 2) 100, 25 Determine the LEAST COMMON MULTIPLE of each set of numbers: 3) 30, 45 4) 50, 75 Exponents: The Exponent of a number shows how many times that number is to be used in a multiplication problem. The Exponent is written as a small number to the right and above the base number. Squared – a number to the second power Cubed – a number to the third power Square Roots: The square root of a number is a value that, when multiplied by itself, gives the number. Practice: On your Own Evaluate: 1) 43 = 2) 24 = 3) 32 + 42 = 4) 102 – 82 = 5) 144 = 6) 900 = 7) 225 = 8) 196 = 9) 53 - 64 = 10) 23 × 100 =