UNIT 1 LEARNING GUIDE NUMERACY

Math 7

2021-12-08 Page 1 of 24

Name:

UNIT 1 LEARNING GUIDE – NUMERACY

INSTRUCTIONS:

Using a pencil, complete the following questions as you work through the related lessons. Show ALL of your work as is explained in the lessons. Do your best and always ask questions if there is anything that you don’t understand.

1.1 PLACE VALUE: DECIMALS

1. Write the number 789.03 into the place value chart below.

2. Match the number to its correct standard word form.

____ 8.32 a. three hundredths

____ 3.44 b. twelve and sixty-three thousandths

____ 0.03 c. eight and thirty-two hundredths

____ 0.009 d. eight hundred sixty-four

____ 12.063 e. seventy and two hundred five thousandths

____ 0.807 f. nine thousandths

____ 864.0 g. eight hundred seven thousandths

____ 70.205 h. three and forty-four hundredths

Units Decimals

Hundreds Tens Ones . Tenths Hundredths Thousandths

Math 7

2021-12-08 Page 2 of 24

3. Write out the following numbers in standard word form. This is the same as how you would say the numbers out loud. Reminder: In place of the decimal, write the word "and".

Ex. 6.792 = sixandsevenhundredninety-twothousandths

a. 42.57 =

b. 89.04 =

c. 0.071 =

d. 0.6 =

e. 1.467 =

4. Write the following numbers in expanded form. Reminder: Start with the biggest number.

Ex. 36.582 = 30+6+0.5+0.08+0.002

a. 8.2 =

b. 9.764 =

c. 0.86 =

5. Write the following numbers in standard form. Reminder: You may have to add a 0 as a place holder in some cases.

Ex. 6 + 0.04 + 0.001 = 6.041

a. 3 + 0.2 + 0.07 + 0.009 =

b. 0.2 + 0.01 + 0.003 =

c. 50 + 8 + 0.09 + 0.006 =

Math 7

2021-12-08 Page 3 of 24

1.2 MULTIPLYING AND DIVIDING DECIMALS

1. Draw a decimal in the proper place in each answer. Reminder: Count the number of digits after the decimals in the question, then place the decimal in the answer so that there are the same number of digits after it.

Ex. 0.62 × 81 = 50.22

a. 0.59 × 64 = 3776

b. 731.8 × 0.34 = 248812

c. 0.467 × 1.2 = 05604

2. Multiply.

a. 0.71×56

b. 1.461× 4.1 c. 45.2× 0.1

3. Label the division below with the terms quotient, dividend, and divisor.

b.

a. 4 60.415.1

c.

Math 7

2021-12-08 Page 4 of 24

4. Draw a decimal in the proper place in each answer. Reminder: When dividing with a decimal, place the decimal of the quotient directly above the decimal in the dividend. You may need to add leading zeros in the quotient.

Ex.

a.

b.

c.

5. Divide. Reminder: When necessary, change the format of the question into long division before dividing.

Ex.

a. 89.4 ÷ 7 b.

c. 566.30 ÷23

4 49.4412.36

6 17.2742879

5 0.450559011

253 45 494.4617982

6 14.4 6 14.42.4

−1224

−240

194.48 ÷11

Math 7

2021-12-08 Page 5 of 24

6. Rewrite the division so that there is no decimal in the divisor. Place the decimal above the dividend. Do NOT solve. Reminder: Move the decimal to the right the same number of spaces in the divisor and the dividend. You may need to add zeros at the end of the dividend.

Ex.

a.

b.

c.

d.

e.

2.3 155.48.

23 1554.8

4.8 91.344

44.1 66.5469

1.2 2.478

0.31 9

0.004 3.75

Math 7

2021-12-08 Page 6 of 24

7. Divide. Reminder: When there is a remainder, add zeros to the dividend and continue dividing

until the quotient terminates or is repeating.

Ex.

b.

a.

c.

1.1 2.4 2.18

11 24.00002.1818

−2220

−1190−8820

−1190

8 12.1

0.3 6.88 0.4 15.7

Math 7

2021-12-08 Page 7 of 24

1.3 NUMBER STRATEGIES

1. Use the mental math strategy of rounding to add or subtract the following numbers. Write down how you would change the numbers in your head for each question.

Ex. 27 + 51 = 26+50 = 76

Ex. 18 + 36 = 20+34 = 54

a. 72+43 = =

b. 123+85 = =

c. 672+189 = ___________________ = _______

d. 378 + 210 = __________________ = _______

e. 65 – 23 = ____________________ = _______

f. 89 – 72 = ____________________ = _______

g. 58 – 24 = ____________________ = _______

2. List at least three specific tips from the Strategy for Solving Word Problems video that you will

use when you solve word problems.

3. Match the phrase with the correct math operation.

____ ÷ a. triple the ingredients

____ - b. 3 cm longer

____ ÷ 2 c. combined total of animals

____ ´ d. used to find the quotient

____ + 3 e. half the speed

____ ´ 3 f. operation used to find the product of the length and the height

____ + g. 3 fewer points than

____ ÷ 3 h. the difference in weight

____ - 3 i. split between 3 friends

Math 7

8

4. Show all of the problem-solving steps that you use to solve the following words problems.

a. Rowan ran 8 km on Saturday. Deeksha ran double that distance but needed to pause 4 times during her run. How far did Deeksha run?

b. Antonio pays $8.99 per month for a subscription to a music streaming service. The rate will be increasing by $1.50 per month in 2 months. What will the new subscription fee be?

c. Throughout the summer vacation, Cheyenne read 5 Big Nate books, all 3 books in the Divergent trilogy, the first 2 Harry Potter books as well as the book The Giver. How many books did she read in total during the summer?

d. Mr. Dalworth bought a pack of 72 fancy pencils to give to his students. There are 24 students in his class. If Mr. Dalworth splits the pencils evenly between all of the students, how many pencils will each student get?

Math 7

9

1.4 GREATEST COMMON FACTOR/LOWEST COMMON MULTIPLE

1. Circle all of the prime numbers. Reminder: Prime numbers only have 2 factors.

5 12 3 7 20 6 1

13 10 4 2 9 31 14

2. Circle all of the composite numbers. Reminder: Composite numbers have more than 2 factors.

15 2 16 17 29 27 8

10 0 9 6 11 3 20

3. Put a circle around the numbers that are neither prime nor composite.

4 1 10 12 0 9 16

4. Find all of the factors of each number.

Ex. 14 14 = 7 ´ 2 Factors: 1,2,7,14 14 = 14 ´ 1

a. 16 16 = ´ Factors:

16 = ´

16 = ´

Math 7

10

b. 36 36 = ´ Factors:

36 = ´

36 = ´

36 = ´

36 = ´

5. Find all of the prime factors of each number and then write the prime factorization for that number. Use a factor tree to determine your answer. Some numbers may be a prime number.

Prime Factorization: 2´3´3

a. 12

Prime Factorization:

b. 30


c. 70


d. 89


Ex.18 / \9 2/ \ 3 3

Math 7

11

6. Match the divisibility rule to the factor.

____ Divisible by 4 a. Number ends in 0 or 5

____ Divisible by 3 b. The last 2 digits of the number are divisible by 4

____ Divisible by 10 c. The sum of the digits of the number is divisible by 3

____ Divisible by 5 d. Number is divisible by both 2 and 3

____ Divisible by 2 e. Number ends in 0, 2, 4, 6, or 8 (ie. an even number)

____ Divisible by 6 f. Number ends in 0

7. Find the Greatest Common Factor of each of these pairs of numbers. Use the listing method for these questions

a. 10, 5 Factors of 10 ______________________________________________

Factors of 5 ______________________________________________

GCF _________________

b. 12, 8 Factors of 12 ______________________________________________

Factors of 8 ______________________________________________

GCF _________________

c. 15, 25 Factors of 15 ______________________________________________

Factors of 25 ______________________________________________

GCF _________________

d. 9, 12 Factors of 9 ______________________________________________

Factors of 12 ______________________________________________

GCF _________________

Math 7

12

8. Find the Greatest Common Factor of each of these pairs of numbers. Use the prime factorization method for these questions. Reminder: To find the prime factorization for a number, you need to create a factor tree. Show the factor tree for each number.

a. 12, 18

Prime Factorization of 12 ____________________________________________


Multiplication of common prime numbers _______________________________

GCF _________________

b. 112, 36



Multiplication of common prime numbers _______________________________

GCF _________________

Math 7

13

9. Find the Lowest Common Multiple for each set of numbers. Use the listing of multiples method.

a. 25, 15

Multiples of 25_________________________________________

Multiples of 35_________________________________________

LCM _________________

b. 16, 24

Multiples of 16_________________________________________

Multiples of 24_________________________________________

LCM _________________

c. 60, 40

Multiples of 60_________________________________________

Multiples of 40_________________________________________

LCM _________________

d. 12, 18

Multiples of 12_________________________________________

Multiples of 18_________________________________________

LCM _________________

Math 7

14

10. Find the Lowest Common Multiple for each set of numbers. Use the prime factorization method. Show the factor tree for each number. Reminder: When multiplying the factors of both numbers together, common factors of both numbers are only represented once. a. 52, 76

Prime Factorization of 52 _________________________________________


Multiplication of factors _________________________________________

LCM ________________

b. 81, 9



Multiplication of factors _________________________________________

LCM ________________

Math 7

15

1.5 INTEGERS

1. Name as many examples as you can of when integers (whole positive and negative numbers) are used in real life. ___________________________________________________________________________

___________________________________________________________________________

2. Order the integers from least to greatest.

Least Greatest

Ex. -3, 1, 7, -2, -7 -7 -3 -2 1 7 a. 0, -4, -1, 8, -8

b. 5, -6, 2, -3, -10

c. -12, -6, -19, 0, -3,

3. Rewrite these problems without the brackets. You do not need to solve the problem.

Ex. 3 + (+ 2) 3+2 a. 3 - (- 2)

b. 3 + (- 2)

c. 3 - (+ 2)

d. 5 - ( - 9)

e. (- 8) + (- 3)

f. 20 - (+43)

g. (-15) - (+10)

h. (- 650) + (+75)

4. Use a number line to solve these problems. Reminders: First rewrite the problem without the

brackets, then solve. Go left on the number line for subtraction. Go right on the number line for addition. Ex. 4 - (+5)

4-5

a. 6 + (- 3)

b. (-2) + (+7)

Math 7

16

c. 5 - (-2)

d. (-4) + (-1)

e. (-1) - (+6)

5. Solve. Reminder: First rewrite the problem without the brackets, then solve. Use a number line if you wish. a. 7 + (-3)

b. 4 - (-5)

c. (-7) - (+4)

d. 6 - (+7)

e. (-5) + (-4)

f. 8 + (+4)

6. Georgia and Paul went for a mountain bike ride on the West Side Trail. The graph below shows the elevation profile of the trail. Use the graph to answer the following questions.

Math 7

17

a. What is the elevation at the 8km mark of the trail? _____________________

b. At what km mark on the trail is the elevation -10 metres? _____________________

c. What is the maximum elevation of the trail? _____________________

d. What is the elevation of the lowest point of the trail? _____________________

e. What is the change in elevation between kilometre 6 and kilometre 12? Write an equation to solve the question.

f. What is the change in elevation between kilometre 16 and kilometre 24? Write an equation to solve the question.

7. Write out the following multiplications as repeated additions or subtractions, then solve.

Reminder: The first number of the multiplication is repeated the number of times of the second number. Ex. (−4) × (+2)

This means that we have the number -4 that will be added two times (+2).

Ex. (−5) × (−3) This means that we have the number -5 that will be subtracted three times (-3).

a. (+6) × (+4)

b. (−10) × (+3)

c. (−3) × (−4)

d. (+8) × (−2)

+(−4) + (−4)−4 − 4= − 8

−(−5) − (−5) − (−5)+5 + 5 + 5= +15

Math 7

18

8. Add a positive or a negative sign into the equation to make the multiplication true.

9. Multiply. Hint: Figure out if the answer will be a positive or a negative, then multiply the

numbers. a. (+5) × (−7)

b. (−30) × (−2)

c. (−9) × (+9)

d. (+8) × (+6)

e. (−4) × (−10)

f. (+11) × (−3)

Ex. (- 1) × (+ 3) = (- 6) d. ( 2) × (- 7) = (+ 14)

a. ( 4) × (- 8) = (- 32) e. (- 15) × ( 3) = (- 45)

b. (+ 5) × (+ 6) = ( 30) f. (+ 4) × (- 12) = ( 48)

c. (- 9) × (- 3) = ( 27) g. (- 25) × ( 3) = (+ 75)

Math 7

19

10. Divide. Reminder: The rules for dividing with integers are the same as for multiplying with integers: first, figure out if the answer will be a positive or a negative, then divide the numbers.

a. (+20) ÷ (−5)

b. (−12) ÷ (−2)

c. (+36) ÷ (+6)

d. (−75) ÷ (+3)

e. ├(+18┤) ÷ (−6)

f. (−56) ÷ (−7)

11. Match the word problem with the expression that describes the situation.

a. Lana withdrew $50 from her bank account every week for 4 weeks. How much did she withdraw in total? ____

b. Li ran a 50m sprint 4 times in a row. How far did he run in total? ____

c. Tanjeet had a fishing lure 50 feet below the surface of the lake and then he lowered the line by 4 more feet. How far below the surface is the fishing lure now? ____

d. Serenity spent a total of $50 on coffee over a period of 4 weeks. How much did she spend per week (she spent the same amount each week)? ____

i. (+50) × (+4)

ii. (−50) ÷ (+4)

iii. (−50) × (+4)

iv. (−50) + (−4)

Math 7

20

12. Without completing the multiplications and divisions, determine whether the answer will be positive or negative. Reminder: An even number of negatives will result in a positive answer; an odd number of negatives will result in a negative answer.

Ex. (+4)(−2)(−1) + a. (−3)(−5)(−2)

b. (+6)(−1)(+10)

c. (−3)(−3) ÷ (2)

d. (−2)(−2)(−3)(+1)

e. (−10) ÷ (+2)(+1)(−1)

f. (−5)(−1)(+2)(+2)(−1)

g. (+20) ÷ (−5) ÷ (−2) ÷ (+1)

13. First determine whether the result will be positive or negative, then calculate the answer.

a. (+4)(−3)(−1)

b. (−25) ÷ (−5)(−2)

c. (+8) ÷ (−2) ÷ (+2)

d. (100) ÷ (−2)(1)(−1)

e. (−5)(−1)(−2)(−2)(−1)

f. (+40) ÷ (+10)(−2) ÷ (−4)

Math 7

21

1.6 BEDMAS WITH INTEGERS & DECIMALS

1. Solve. Rewrite the problem after each step to determine what is left to calculate.

Ex. (−4)(+5) + (−6)

a. (−9) + 10 × 4

b. [8 + (−5)] × (−4)

c. (2)(−2) − 3

d. 4 ÷ [5 + (−7)]

e. [(−10) + 8] × (−7)

2. When solving problems that include a division line like this: !"($)("&)("'()"("&))

, what must you

do to the top and bottom parts of the problem?

3. Solve.

a. *+("',)("$)+-*

b. *+("&)())(&"))×(')

c. ("$)[*+("&)]'"("')

d. ("!)(1)+',×[("!)+)]

Math 7

22

4. Solve.

a. 8.8 ÷ 4 + (1.5 − 0.4)

b. (−2.5)(4) − (−3.75)

c. 4.3 + (−0.8) ÷ [1.3 + (−0.9)]

d. [4 + (−6.2)] ÷ (0.1 × 4)

Math 7

23

UNIT 1 – ANSWER KEY SECTION 1.1

1.

2. c, h, a, f, b, g, d, e 3. a. forty two and fifty seven hundredths b. eighty-nine and four hundredths c. seventy-one thousandths d. six tenths e. One and four hundred sixty-seven thousandths 4. a. 80 + 02. b. 90 + 0.7 + 0.06 + 0.00. c. 0.8 + 0.06 5. a. 3.279 b. 0.213. c. 58.096

SECTION 1.2

2.a. 39.76. b. 5.9901. c. 4.52

3. a. divisor. b. quotient. C. dividend

5. a. 12.77142. b. 17.68. c. 24.62173

SECTION 1.3

1. a. 115 b. 208 c. 861 d. 588 e. 42 f. 17 g. 34 3. d, h, e, f, b, a, c, i, g 4. a. $120 b. 31 cm c. 16 km d. $10.49 e. 19 songs f. 11 books g. 3 pencils h. 36 hours

SECTION 1.4

1. 5, 3, 7, 13, 2, 31 2. 15, 16, 27, 8, 10, 9, 6, 20 3. 1, 0 4. a. 1, 2, 4, 8, 16 b. 1,2,3,4,6,9,12,18,36 5. a. 2x2x3. b. 2x3x5. c.2x5x7. d. 89 is a prime number 6. b, c, f, a, e, d 7. She can make 10 groups.

Units Decimals

Hundreds Tens Ones . Tenths Hundredths Thousandths

7 8 9 0 3

Math 7

24

SECTION 1.5

1. Many possible answers. May include: temperatures, elevation, finances, sports, and health.

2. a. -8, -4, -1, 0, 8 b. -10, -6, -3, 2, 5 c. -19, -12, -6, -3, 0 3. a. 3 + 2 b. 3 – 2 c. 3 – 2 d. 5 + 9 e. -8 – 3 f. 20 – 43 g. -15 – 10 h. -650 + 75 4. a. 3 b. 5 c. 7 d. -5 e. -7 5. a. 4 b. 9 c. -11 d. -1 e. -9 f. 12 6. a. +5m b. 16km c. +35m d. -10m e. (-5) – (+15) = -20m f. (+35) – (-10) = +45m 7. a. +(+6)+(+6)+(+6)+(+6), +24 b. +(-10)+(-10)+(-10), -30 c. -(-3)-(-3)-(-3)-(-3), +12

d. -(+8)-(+8), -16 8. a. + b. + c. + d. - e. + f. - g. – 9. a. -35 b. +60 c. -81 d. +48 e. +40 f. -33 10. a. -4 b. +6 c. +6 d. -25 e. -3 f. +8 11. a. iii b. i c. iv d. ii 12. a. - b. - c. + d. - e. + f. - g. + 13. a. +12 b. -10 c. -2 d. +50 e. -20 f. +2

SECTION 1.6

1. a. 31 b. -12 c. -7 d. -2 e. 14

2. Treat the top and bottom as though they each are in brackets.

3. a. -2 b. 2/9 c. -4 d. 5

4. a. 3.3 b. -6.25 c. 2.3 d. -5.5

Documents

UNIT 1 LEARNING GUIDE NUMERACY