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7th grade STAAR Review Skills to remember Fractions, Decimals, and Percents 3 Fraction to decimal: Decimal to percent: .875 = 87.5% move the decimal two places to the right Percent to decimal: 67% = .67 move the decimal two places to the left. The decimal is at the end of a number if it is not there. 25 1 Decimal to fraction: .25 = = put the number over a 10, 100 or 1,000 100 4 depending on the place value of the last digit. Reduce 10 = .3 Divide (top dog in the house) Ordering Fractions, Decimals, and Percents Put the following numbers in order from least to greatest: Try it before you look at the answer! .3, 87.5%, .67, - ¼ Steps: Change them all to fractions, decimals, or percent’s. Decimals and percent’s are the easiest. .3 = 30% .67 = 67% -¼ = - .25= - 25% 87.5% stays the same Answer: -25%, 30%, 67%, 87.5% Negatives come first because they are the smallest numbers. Decimals (adding, subtracting, multiplication, and division) Addition/Subtraction of decimals 1. Line up decimal points (add zero’s if needed) 2. Add/subtract 3. Bring decimal down 4.5 +8.9 13.4 8.9 - 4.5 4.4 Multiplication of decimals 1. Longer number on top. 2. Multiply as if the decimal isn’t there. 3. The number of digits behind the decimal in the problem, is how many should be in the answer. Ex. 2.1 X .6 1.26 Move the decimal twice from the right. Your answer should have two digits behind the decimal because there are 2 digits behind the decimals in the problem. Division of decimals 1. If there is a decimal on the outside of the , move it so that it is behind the number, then move it that many times in the inside also 2. Bring the decimal inside the house to the top. 3. Long divide as normal. Ex. 28.4 ÷ 2 = 14.2 Ex. 18.4 ÷ 2.4 = 7.66666 Try them and see if you get the same answers! Fractions (adding, subtracting, multiplying, and dividing) Adding/subtracting 1. Need a common denominator 2. Add or subtract the numerators only 1 2 7 9 8 3 1 9 7 9 2 18 Ex. + = Ex. - = Try them and see if you get the same answers! Multiplying 1. Multiply straight across the top and bottom 2. Reduce 1 2 2 9 3 27 Ex. . X = Division 1. Keep, change, flip 2. Keep the first number, change division to multiplication, flip the second fraction 3. Multiply straight across and reduce Ex. 1 9 ÷ 2 3 = 1 9 X 3 2 = 3 18 Integers – Remember the song!! Addition Same sign, add and keep Different signs subtract Keep the sign of the higher number Then it will be exact Ex. - 8 + - 8 = -16 (same signs) Ex. 18 + - 5 = 13 ( different signs) Subtraction Change the minus to a plus Change the sign of the next Then all you do is add them up As if it were a plus Ex. 18 – (-5) = 18 + 5= 23 (same signs, add) Ex. - 6 –(3) = -6 + - 3 = - 9 ( same signs, add) Ex. 7 – 8 = 7+ -8 = -1 (different signs, subtract) Multiplication/division Same signs, always positive Different signs, negative Ex. 18/-2 = -9 Ex. -18/-2 = 9 Ex 2 X -3 = -6 Ex. -2 X -3 = 6 Solving for X 1. X + 3 = 7 -3 -3 X=4 4. 𝑋 = 10 5 X = 50 2. X - 9 = 62 +9 + 9 X = 71 3. 2x= 10 Divide by 2 X=5 (multiply each side by 5 ) You are trying to get the variable by itself by doing the opposite operation. 2x + 9 = 21 Subtract 9 from both sides and then divide by 2. Always perform subtraction and addition first. Then multiply and divide to solve for X. 2x + 9 = 21 -9 -9 2x = 12 2 2 X= 6 Unit Rate- The price per one item If three loaves of bread cost $7.71, what is the cost of two loaves of bread? First, find the cost of 1 loaf of bread by dividing the cost ($7.71) by how much you have. This will give you the price of one (2.57). Once you know the price of one, you can multiply by two and figure out the price for two loaves of bread. Two loaves would cost $5.14. You can also set up a proportion like this: 3 𝑙𝑜𝑎𝑣𝑒𝑠 $7.71 = 2 𝑙𝑜𝑎𝑣𝑒𝑠 $𝑋 Cross multiply and divide by the last number to solve for X. Exponents: 42 = 4 X 4 which is 16 2³ = 2 X 2 X 2 which is 8 Square roots √25 = 5 because 5 X 5 equals 25. √32 = 5.7 because it is going to be in between 5 and 6. √25 = 5 Order of Operations Parenthesis Exponents Multiplication Division Addition Subtraction Geometry Translations= slide √36 = 6 Reflection = flip (normally across the x or y axis) Dilation= to make larger or smaller Finding Scale Factor: New Old Using Scale Factor: Multiply the sides by the scale factor Scale factor= how many times bigger or smaller a shape is in comparison to another. 3 7.5 4 The scale factor going from the smaller triangle to the larger triangle is 2.5. If you multiply the sides of the smaller triangle by 2.5, you will get the lengths of the larger triangle. Try it! Finding missing sides with similar figures: 5 15 7 X Set up a proportion and solve for X. 5 = 7 15 𝑥 X = 21 OR Figure out the scale factor and multiply to find the missing side. Scale factor is 3 because if you multiply the sides of the smaller trapezoid by 3, then you get the lengths of the larger trapezoid. Probability Theoretical probability – favorable outcomes Possible outcomes Experimental probability - number of times event occurs Number of trials Independent probability- the outcome doesn’t affect one another, you replace the items 1. Probability of rolling a 2 on a dice, and spinning a red on a spinner that has 4 sections (red, blue, green and yellow) 1 1 1 1 1 X = dice spinner 6 4 24 6 4 2. Probability that you will pull out a yellow and then a blue marble if there are 5 blue and 3 yellow. You replace after each draw 3 8 5 15 3 8 64 8 X = yellow 5 blue 8 Dependent probability – the outcome does affect the other, you DO NOT replace the items in the bag 1. Probability that you will pull out a yellow and then a blue if there are 5 blue and 3 yellow. You do not replace the marble after each draw. 3 8 5 15 3 5 7 56 8 7 X = yellow blue Percent proportions Part Whole = 𝑋 100% Cross multiply and divide by the last number to solve! Ex. A government agency has a car pool of 120 vehicles. Every week about 15% of the vehicles are pulled out of service for repair and inspection. How many vehicles per week is this? Try it! The answer is 18. Ex. The department of transportation inspected 200 rural bridges last year. Of that amount, 6 were determined to be unsafe. What percent of bridges were considered safe? The answer is 3%. Try it! Percent of change 𝐴𝑚𝑜𝑢𝑛𝑡 𝑜𝑓 𝑐ℎ𝑎𝑛𝑔𝑒 𝑏𝑒𝑡𝑤𝑒𝑒𝑛 𝑜𝑟𝑖𝑔𝑖𝑛𝑎𝑙 𝑎𝑛𝑑 𝑛𝑒𝑤 𝑂𝑟𝑖𝑔𝑖𝑛𝑎𝑙 𝑋 = 100% Cross multiply and divide by the last number to solve! Ex. A picture originally priced at 300 sold for 400. The answer is 33.3333% Try and solve it yourself! Proportional Relationships. Let, n, represent the position of a number in the following arithmetic sequence. 4, 9, 14, 19, 24... Which expression can be used to find any term in the sequence? A n2 B 5n - 1 C 4n + 9 D 9n + 4 N is the position of the number in the sequence. So 1st position, 2nd position and so on. When you are deciding which rule goes with the sequence of numbers, you need to plug in 1, 2, 3, and so on into the letter N. The answer is B. Measurement Perimeter- Add all the sides to find the perimeter! This will not be on the formula chart. Rectangle is on the formula chart… Circumference - is the perimeter of a circle. Formula - 2 𝜋 𝑟 𝑜𝑟 𝑑 𝜋 Area- the space inside of a 2-D shape measured in square feet) The formulas are on your math chart. Remember on the area of a circle (𝐴 = 𝜋𝑟 2 ), you must square the radius first!!!!!! Square means to multiply the number by itself for example Radius- is from the middle of the circle to any point on the outside Diameter- a straight line passing through the center of the circle. Area of a triangle A= (1/2)bh **(1/2) means to divide by 2 Volume Volume- the space inside of a 3-D object. REMEMBER: B MEANS AREA OF THE BASE Prism/pyramid- Pyramid comes to one point, prism does not. Also, remember :(1/3) MEANS TO DIVIDE BY 3 AND (4/3) MEANS TO multiply BY 4 AND DIVIDE BY 3. Prism Pyramid: Measures of Central Tendency and Variablility Mean: the average. Add up all the numbers and divide by how many there are. Median: the middle number. Put the numbers in order and cross them off until you get to the middle. If there are two, add them up and divide by two. Mode: most often Range- subtract the highest from the lowest (Measure of Variablility) TYPES OF GRAPHS STEM AND LEAF LINE PLOT BAR GRAPH LINE GRAPH CIRCLE OR PIE GRAPH – GREAT FOR SHOWING PERCENTAGES!! To find percent of graph used, look at data and write it as a fraction and then convert to a percent. For example $43 million from chocolate sales. Total sales $105 million. 43/105 = .409 = 40.9% round to 41% VENN DIAGRAM – COMPARE DATA How many people liked pizza? How many people liked tacos only? How many people like all three?? How many people didn’t like any of the choices?