Grade 7 Math Review Name: _____________ Unit 3 – Fractions, Decimals and Percents

1. Fractions and Decimals (Section 3.1 and 3.2) (a) Fractions to Decimals using a calculator (b) Fractions to Decimals using “nice” denominators (c) Fractions in simplest form (d) Ordering Fractions on a number line

2. Decimals (Section 3.3, 3.4, 3.5 and 3.6) (a) Adding and Subtracting Decimals (b) Multiplying Decimals (c) Dividing Decimals (d) Order of Operations with Decimals

3. Percents (Section 3.7 and 3.8) (a) Relating Fractions, Decimals and Percents (b) Solving Percent Problems

1. Fractions and Decimals (Section 3.1 and 3.2) (a) Fractions to Decimals using a calculator Examples: Convert each fraction to a decimal and state whether it is terminal, repeating or neither. (a)

3 6

_____________

(b)

7 11

(c)

_____________

1 3

____________

(d)

4 12

____________

(b) Fractions to Decimals using “nice” denominators - when given a “nice” denominator Examples: Convert the following without using your calculator (a)

3 10

(b)

6 100

(c)

135 10

(d)

24 100

- when making a “nice” denominator Examples: Convert the following by multiplying or dividing the numbers in the fraction. Make sure you make either 10, 100 or 1000 in the denominator (a)

3 25

(b)

52 50

(c)

36 60

(c) Fractions in simplest form Examples: write fractions in the simplest form by using division. Remember, as long as you multiply or divide both the numerator and the denominator by the same number, you will create an equivalent fraction. (a)

3 6

(a)

7 21

(a)

6 9

(d) Comparing and Ordering Fractions Benchmarks - You can use scrap paper to draw fraction circles, convert the fractions to decimals or 1 use benchmarks to help you order the fractions. For example, you should realize that 8 is closer to zero whereas

7 8

is closer to 1.

Common Denominators - Find a common denominator for all of the fractions and change each fraction. Order them from least to greatest. Place Value - Change all fractions to decimals and order them from least to greatest. Examples: Place the following fractions and decimals on the number lines below. Use whatever method you prefer.

(a)

3 , 4

3

7

2 4 , 1 8,

15 12 , 5 5

0

(b)

2 , 4

3 4

1 ,

14 , 8

0

1

2

3

1

2

3

2 10 , 5 5

2. Decimals (Section 3.3, 3.4, 3.5 and 3.6) (a) Adding and Subtracting Decimals - Use mental math and show workings to calculate as well as estimation to check your answers. Examples: Estimate each sum or difference, then calculate.

(a)

3.1 + 8.2

(b)

7.32 - 1.45

(c)

3.5 + 4.26

(d)

3.63 - 2.5

(b) Multiplying Decimals - using the area model, mental math and word problems. Examples: Use the area model to find the product. Draw your model on the grid below and your answer underneath. (a) 2.2 x 1.5

Examples: Calculate the following products using mental math and show your workings. (a)

6.1 x 2.7

(b)

8.36 x 4.5

(c)

35.5 x 5

(d)

3.63 x 2.53

Examples: Complete the following word problems below by finding the product. (a) George has been sneaking Christmas chocolates but only takes a few bites out of one in every box. George’s mom is very upset and claims “George, there are four and six tenths chocolates left in each box of Christmas chocolates. We are supposed to have 15 Christmas chocolates in total and now we only have . . . . “ How many chocolates do George have left in total if he opened all three boxes that his mom bought for Christmas? (Hint: Multiply three boxes by four and six tenths chocolates in each box)

(b) Casey the cat hates snow. It snowed so much yesterday that he was afraid to go outdoors since he might get buried alive!! If it snowed four times during the day and snowed two and a half inches every time, should Casey go outside? (Casey is 6 inches tall).

(c) Dividing Decimals - using mental math and word problems.

Examples: Calculate the following quotients using mental math, long division and show your workings.

(a) 8.24 ÷ 4

(b) 9.50 ÷ 0.50

(a) 9.24 ÷ 0.3

Examples: Find the quotient for the word problems below.

(a) Sally had three and three tenths of a pizza left. She wanted to share this with two of her friends and eat some herself. How much of the pizza will each person get?

(b) Jerry is baking a pan of muffins. He uses seven and one fifth cups of flour for the entire recipe. If there are twelve muffins in a pan, how much flour will end up in each muffin?

(d) Order of Operations with Decimals - Remember BEDMAS Examples: Perform the following calculations by using the correct order of operations.

(a) 4 x 5.6 + (3.3 + 4.2)

(b) (7.1 x 2.6) + (6.3 - 4.2)

(c) 8.4 ÷ 2.1 x 3.2 + 5.1

(d) What is the total cost for a family with two parents and three children for theatre tickets if three children go and two parents go? Children’s tickets cost $8.50 and parents cost $14.80.

3. Percents (Section 3.7 and 3.8) (a) Relating Fractions, Decimals and Percents Examples: 1. Complete the table: Fraction (in lowest terms) 3 4

Decimal

Percent 0.12 46% 55% 1.35

2. Aaron got 93% on a test and Seth got

35 38

. Who did better?

(b) Solving Percent Problems (Discounts and Sales Tax) Examples: 1. Calculate (a) 10% of 30

(b) 20% of 75

(c) 35% of 144

2. The regular price of a t-shirt is $45. Find the sale price of the t-shirt before taxes if it is on sale for 25% off.

3. Calculate the total price you would pay if a TV costs $39.99 and the sales tax is 13%.

4. Calculate the total prices: (a) A DVD player costs $19.99 and is 20% off. The sales tax is 14%.

(b) A box of chocolates is on sale for $10.50. If the chocolates are on sale at 19% off and the sales tax is 12% what is the total cost you will pay?