Download Grade 7 MidYearаа StudentMade Practice Work

Grade 7 Mid­Year Student­Made Practice Work GCF & LCM What are factors, and how to find them What are multiples, and how to find them What is a Prime Number How to find Greatest Common Factor (GCF) How to find Lowest Common factor (LCM) When to use GCF and LCM in a word problem 1­ What is the LCM of 18 and 30? A) 90 C) 56 B) 180 D) 75 2­ What is the GCF of 22 and 48? A)13 C)6 B)11 D)2 3­ What is the LCM of 12, 2 and 1? A) 26 B) 2 C) 12 D) 6 4­ Find the LCM for these numbers. 12, 24, 6 5­​
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Which one is calculating the LCM and which one is calculating the GCF? A) 8­ 1,2,4,8 12­ 1,2,3,4,6,12 B) 3: 3,6,9,15,18,21,24,27 6: 6,12,18,24,30,36 Answers: 1) A, 2) D, 3) C Order of Operations Solving an equation using BEDMAS Properly showing your work for a BEDMAS equation What does BEDMAS stand for? 1­ Brackets 2­ Exponents 3­ Division 4­ Multiplication 5­ Addition 6­ Subtraction 1) 8 + (4x3) ÷ 2 = 2 ​
2) 5 + (4x2)​
­ 32/4 = 3) ​
5+8x (50 ÷ 5) 2 ÷ 5 = a) 201 b) 456 c) 165 d) 548 (​
18 × 50 ) x (50 ÷ 2) × 100 + 8 ÷ 2 (3+4)­(5+­2) +­5= What comes first in BEDMAS in this order? Circle the letter a: Addition b: Multiplication c: Division d: Exponents Answer: EXPONENTS (12 +6) ÷ 2 × 4 = ? What is an exponent, how do they work What is a square root, how to do one on my calculator EXPONENTS QUESTION 1 72 = 42 = 65 = QUESTION 2 53 = 3
8 = 6 5 = Rates, Ratios and Proportions What is a ratio Reducing and expanding ratios (using a common factor and divide or multiply for the purpose of getting an equivalent ratio) RATIO A ratio says how much of 1 thing compares to another. 10 apples to 3 oranges 10: 3 What is the ratio of x’s and o’s? XX 000 A) 3:2 B)2:5 C)2:3 answer: C What is the ratio of $ to # ? $$$$## A) 2:4 B) 4:2 C) 4:6 D) 6:4 answer: B Ron had 17 Pencils and 14 Erasers. What's the ratio of the Erasers and Pencils? Answer: 14 : 17 What's the ratio of :) and :( :) :) :( :) Answer: 3 : 1 What is the ratio of circles to triangles? a) 11:12 b) 12:11 c) 13:11 d) 11:13 Answer: d Scale Factor A term you can multiply or divide by each term in a ratio by to get the equivalent. EXAMPLE: 30 girls and boys have planned a party. There a ratio of 3 girls to 7 boys. how many boys are their? answer: 12 boys x 3 90 % 7 = 12 X = 30 7 whatever you do to the bottom you must do at the top so 30 x 3 = 90 % 7 = 12 How to solve a problem using rates (such as km/h, or $/week) Solving a word problem using ratios Finding the ratio in a problem Gabe worked 42 hours, Gabe got $84. How much does Gabe get per hour? A) 2/hr B) 10/hr C) 4/hr Recognizing the pattern in a proportional relationship Understanding if a relationship is proportional, or not Understanding and recognizing the pattern in a proportional relationship Two ratios are in a proportional relationship if they are equivalent. This means that the 2 ratios represent the same basic proportions. In other words, that no matter if we bake 2 cakes or 20 cakes, they will all taste the same because we used the right proportions of ingredients. Questions: 1: According to Greg, perfect cherry pies have a ratio of​
240​
cherries to​
3​
pies. How many cherries does Greg need to make​
9​
perfect cherry pies? 2: A ratio equivalent to 3 : 7 is: (a) 3 : 9 (b) 6 : 10 ​
(c) 9 : 21 ​
(d) 18 : 49 3: The ratio 35 : 84 in simplest form is: (a) 5 : 7 (b) 7 : 12​
(c) 5 : 12 ​
(d) none of these Answer key Question 1: ​
step 1: cross multiply ​
240 x 9 = 2,160. ​
step 2:​
2,160÷3=​
720 question 2: step 1:​
7 x 3 = 9 ​
step 2:​
7 x 3 = 21 question 3: step 1: Four students ran for the position of school president. Use the following results to figure out who won. 1. Jenna received 22% of the votes 2. Jordan received 1/4 of the vote. 3. Kelsey received 6 out of every 20 votes 4. Nathan received 23/100 of the votes. Fractions Expanding fractions (multiply both numbers by a common factor to obtain an equivalent ratio) Reducing fractions (divide both numbers by a common factor to obtain an equivalent ratio) Finding equivalent fractions Comparing fractions by finding a common denominator, converting to decimal or percent Finding part of a number, when given a fraction Adding fractions Subtracting fractions Definition: Before you can add or subtract fractions with different denominator, you must first find equivalent fractions with the same denominator. Find the smallest multiple (LCM) of both numbers. Rewrite the fractions as equivalent fractions fractions with the LMC as the denominator. 3
5
8
EX: 15 + 13 = 15
+ 15
= 15
Questions: 1) 46 ­ 16 = 1
2) 13 + 12
= Multiplying fractions Dividing fractions Multiple choice question 1. ¾ / 1/2 = a: ⅜ b: 5/4 c: 3/2 2. One ­twelfth Of 24 students In the classroom wear glasses. How many wear glasses? a: 12 b: 2 c: 6 3. Order the following multiplications from least to greatest. a: 38 x 23 = b: 35 ÷ 45 = c: 25 x 65 = _______________ 4: solve 4 ) ÷ 20 =________________ ( 15 x 27 ÷ 10
7
Answer key Dividing fractions: definition: Dividing a friction is multiplying by its reciprocal. The reciprocal of a fraction is the numerator and the denominator switched around. ● The first fraction stays the same. ● Change the division sign to multiplication ● Flip the least fraction ● Multiply the top number and the bottom number ● Simply if needed 1. C ¾ / ½ = ? ¾ x 2/1 = 6/4= 3/2 Multiplying fractions. ● If you have a whole number put it over one ●
●
●
Multiply the top number and the bottom number Simply if needed dont do this. If you have a phone number but over one 2. b 1/12 x 24 = ? 1/12 x 24/1= 24/12 = 2 3.​
a: 8 3 x 23 = 246 = 14 3
b: 35 ÷ 45 = 35 x 54 = 11
20 = 4 c: 25 x 65 = 251 x 65 = 150
5 = 30 answer: 14 , 34 , 30 Converting an improper fraction to a mixed number Converting a mixed number to an improper fraction Converting a percent to a fraction, or decimal Converting a fraction to a percent Percent Converting a decimal to a percent Finding the percent of a number Finding a number when given the percent Converting decimal to percentage: 1.First way: to convert a decimal to percentage is done by multiplying the decimal value by 100. Ex: 93×100=93% .08×100=8% .67×100=67% 2.Second way: the short way to convert from a decimal to percentage is by adding the percentage sign and moving the decimal 2 places to the right. Ex: .08=8.% 0.00008=.008 Finding the percentage of a number: 1.First way: turn the percent into a decimal and multiply it by the number. Ex: 30% of 90 would be .30×90=27 2.Second way: or you can cross multiply and divide. Multiply 30×90 and your answer divided by 100. Finding a number when given the percent 1. Convert the percentage to a decimal 2. Divide. Ex:24 is 96% of what number? Divide 24 by 0.96 which will give the result as 25. A grade 7 student had a Big test, he got 54 questions correct, and 16 questions incorrect what is the student’s score in percent? Finding the price of an item after a discount Finding the price of an item after tax Finding the price of an item after a discount AND tax Tax and Discount Tax:​
First, you would take the total price and subtract the pre­​
tax item​
price from it. Then you would divide the whole thing by the pre­​
tax item​
price. And you'll ​
find​
that your sales ​
tax​
is… So if you paid $3,780 for an ​
item ​
that was $3,500, then you bought that ​
item​
in a region with an 8% sales ​
tax​
rate Discount:Procedure: The rate is usually given as a percent. To ​
find​
the ​
discount​
, multiply the rate by the original price. To ​
find​
the sale original price.price, subtract the ​
discount​
from. Tax+Discount:The rate is usually given as a ​
percent​
. To ​
find​
the ​
discount​
, multiply the rate by the original price. To ​
find​
the sale price, subtract the ​
discount​
from original price. Data Analysis What is the mean, how do you find it? What is the mode, how do you find it? What is the median, how do you find it? What is the range, how do you find it? Mean: Is the average to find the average you have to add up all of the numbers and then divide them by how many numbers there are. Mode: Is the number that is repeated the most after you have put all the numbers in order. Range: After putting all the numbers in order smallest to biggest you subtract the biggest number from the smallest. Median: Is the middle number in a ​
SORTED ​
list of numbers. 16, 10, 9, 14, 33 SORTED: 9, 10, 14, 16, 33 MEDIAN­ 14 Choose the right answer for the question below a) Mode: 1,3,6,7,9,10,10 [ ]6 [ ]3 [ ]10 [ ] 9 b) Range: 6,9,10,15,20,39 [ ]7 [ ]19 [ ]24. [ ]20 a) What is the range for the data set below 6,3,9,7,10: show your work! b) What is the median: 4,10,11,16,16,29 Show your work below! 3. Find the mean: 3,4,6,10,15,21,28 What is the mean of 10,56,23,68,86,9,39?. Use only the number before the decimal. a) 42 b) 51 c) 39 d) 41 e) 43 Answer: d) What is the median of 5,8,2,9,6,0,1? a) 9 b) 5 c) 0 d) 2 Answer: b) What is the range of 12,34,31,42? Answer:30 What is the mode of 7,9,4,8,22,7,5,7,12? Answer:7 Find out the mode of 1,8,0,6,4,8.Then add the range of 3,5,6,8,9,6,4,,5 Answer:14 1 ) What Is the mean of 27,42,4,2,7 ? Put the number in order smallest to largest 2,4,7,27,42 and add all of them 2+4+7+27+42= 82 now divide the number you get by the numbers in the question .82/5= 16,4 is your answer. 2) Lance when to the shop and get 5 pen , 7 pencil, 3 pencil case and a 1 school bag . What is his range of his object ? Put the number in order smallest to largest 1,3,5,7 take the smallest and largest and subtract 1​
7=6 your answer is 6. 3) What is the mode of 36,28,17,7,1,9,15,7,15 ? Look for the number or numbers that pops up the most 36,28,17,7,1,9,15, 15,7 in this case it is 15 and 7 is your answer. 4) What the median of 3,6,5,2,17,12,35 a)2 b)6 c) 7 Put the number in order smallest to largest and find your middle number. Your answer is 6 or B. 5) What the mode of 62,5,26,26,6,62 a)5 and 6 b) 26 and 5 c) 62 and 26 Look for the number or numbers that pops up the most 62,5,26 26,6,62 In this case it is 62 Finding a missing value when given the mean Finding a missing value when given the range Finding the missing value when given the mean You can still use the method for determining mean, work backwards. We add up all the values, then we divide by the number of values. Finding the missing value when given the range You arrange the numbers from least to greatest. Subtract the least number from the greatest number. When the missing number is the least number thats subtracted, its the answer. Ex: 2, 3, 10, 10, 15 15­2=13 Answer 2 or 8 8 Ex: 5, 11, 11, 14, 15 ,16 16­5=11 v = Ex: 2, 2, 7, 10 10­2=8 s= Ex:13, 13, 13, 16, 17, 17 17­13=4 p= Ex: 11, 13, 14, 16, 19, 20 20­11=9 x= How do you read/find information on a bar graph How do you read/find information on a line graph How do you read/find information on a circle graph (pie chart) How to read/find bar graphs To find the amount of something count the lines on the y axis and to know what the things your measuring is you read the x axis. How to read/find a line graph To find the amount of something you read the numbers on the y axis and to find what your measuring look at the x axis. How to read a circle graph(pie chart) Pepperoni: 50% Cheese: 25% Sausage: 15% Supreme: 10% To read a pie graph you have to read the legend for example in this case it's pizza flavours so you see the colour on the side so then to find out what percent it is look on the chart and it should tell you. Bar graph questions How many people prefer comedy movies to drama: ________________________ How many people like action movies: ___________________________ Which movie type has the most likes: __________________________ Integers Positive numbers: The further away from zero the number is, the bigger it is. Example: 1 < 10 and 1000 > 27 Negative numbers: The further away from zero the number is, the smaller it is. Example: ­1 > ­10 and ­ 1000 < ­27 Question: Which of the following integers is the greatest? ­100, ­20, ­5, ­7, ­8, ­1 Answer: ­1 Adding Rule #1 – If the signs are the same, pretend the signs aren’t there. Add the numbers and then put the correct sign of in front of your answer. Example: 1 + 2 = 3 ­1 + ­2= ­3 Rule #2 – If the signs are different 1. Pretend the signs aren’t there. 2. Subtract the smaller from the larger one 3. Put the sign of the one with the larger absolute value in front of your answer. Example: ­9 + 5 = (­9 is has a larger absolute value) 9 ­ 5 = 4 Answer: ­4 (you take the ­ from the 9 because it was the bigger number) Questions: ­6 + 7 = 5 + ­9 = ­9 + 9 = Subtracting Rule #1: If both the numbers are positive, subtract normally. 3 ­ 1 = 2 Rule #2: If they are different signs, you add the opposite. 2 – (­7) is the same as 2 + (+7) 2 + 7 = 9! ­1 ­ (2) ­1 + ­2= ­3 Question: 3 ­ 7 = ­4 ­ ­5= ­5 ­ 2= What is (­2) – (­3): a) 5 b) 1 c) ­5 d) ­1 Find the lowest integer : A) ­7 , ​
­10 ,​
15 , 25 , ­1 , 0 , ­2 , Answer : ​
­10 B) ­2 , ­1 , 0 , 1 , 3 ,​
​
­4 , ​
5 , Answer :​
­4 Find each answer : a) ­8 + 5 =​
­3 ​
(​
­3​
,­5,­6,­1,­2) b) ­5 + 9 =​
4 ​
(­5,­9,​
4​
,6,7) Circle the lowest integer:​
­2, 5, ­9, 8, 0, 23 Know the place values (Ex: ones, tens, tenths hundredths) How to round to the nearest ____________ Does 5 round up or down:​
_________ Round 1572 to the nearest 100:​
_________ What is 530 rounded to the nearest 10: