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Math unit 3
Transcript of Math unit 3
and Percents 3.1 Fractions to Decimals To write a fraction to a decimal:
Change the fraction to an equivalent fraction with a denominator of 10, 100, or 1000. 1 4 = 25 100 x 25 x 25 = 0.25 Terminating decimal:
0.25. It has a definite number
of decimal places. Repeating decimal:
You draw a bar over the repeating digits. 3.2 Comparing and Ordering Fractions and Decimals You can Use bench marks on a number line Key Words:
Repeating Decimals 3.1 Fractions to Decimals 3.2 Comparing
Decimals 3.3 Adding
Decimals 3.4 Multiplying
Decimals 3.5 Dividing Decimals 3.6 Order of Operations with Decimals 3.7 Relating Fractions, Decimals, and Percents 3.8 Solving Percent Problems 3.3 Adding and Subtracting Decimals Add 5.763 + 3.94
Step One: Use Front- end estimation to estimate the sum: 5+3=8
Step Two: Add. Write each number with the same number of decimal place, using zeros as the place holders. Record the numbers without the decimal points. Subtraction: 5.763-3.94
Step One: Use front- end estimation to estimate the difference:
Step Two: Subtract. Write each number with the same number of decimal places, using zeros as place holders. Record the numbers without the decimal points. Easy Example 2 3 = 0.6 5 9 = 0.5 Medium Example For Each Fraction, Write an equivalent Fraction with denominator 10, 100, and 1000.
Then write the fraction as a decimal Hard Example Take It Further: , A) Write each fraction as a decimal.
Identify the decimals as repeating or terminating. 7 8 = i) 0.875; terminating A) B) Write the denominator of each fraction in part a as a product of prime factors. i) 2x2x2 C) What do you notice about the prime factors of the denominators or the terminating decimals?
The repeating decimals? When the prime factors of the denominator are 2 and 5 only, the corresponding decimal is terminating. When the denominator has any other prime factors, the fraction can be written as a repeating decimal. Easy Example Medium Example Hard Example Easy Example Melissa bought 4.83 kilograms of apples and 5.2 kilograms of oranges. How much fruit did she buy in all? Hard Example Terrence mixed 0.61 grams of salt into a pot of soup he was cooking. Before he served the soup, Terrence added 0.79 grams of salt. How much salt did Terrence put into the soup in all? A) Write each fraction as a decimal i) Example: ii) 3 4 = 0.75 iii) 4 5 = 0.8 iv) 5 6 = 0.83 v) 6 7 = 0.857 142 B) Identify each decimal as terminating or repeating i) repeating
v) repeating 3.4 Multiplying Decimals >Use the method for multiplying 2 whole numbers.
The area, in square kilometers, is 1.7x2.5.
Multiply: 17x25 Easy Example Assessment Focus: Medium Example Use a calculator when needed Hard Example Take It Further: Medium Example 3.5 Dividing Decimals Easy Example Medium Example Hard Example Assessment Focus 3.6
Order Of Operations Easy Example Medium example Hard Example 3.7 Relating Fractions, Decimals, and Percents 1 Easy Example Write each percent as a fraction and a decimal. Medium Example Hard Example: 3.8 Solving Percent Problems Easy Example Find the answer to the percent problems shown below: Answers:
A) about 12 pieces;assumptions may vary
B) No, he needs 14 pieces and he has material for 12
C) if Alex cannot use the 0.28-m piece left after he cut twelve 0.8-m pieces, he needs 1.6m of fabric. if he can use it, he only needs 1.32 m of fabric
D) yes; Alex would only need 0.7 m x 14= 9.8 m of fabric. Alex finds a remnant of landscaping fabric at a garden store.
The fabric is standard width, with length 9.88m. Alex needs fourteen 0.8 pieces for a garden patio
A) How many 0.8-m pieces can A
Alex cut from the remnant? What assumptions did you make?
B) Will Alex have all the fabric he needs? Why or why not?
C) If your answer to part b is no, how much more fabric does he need?
D) Alex redesigns his patio so that he needs fourteen 0.7-m pieces of fabric. Will the remnant be enough fabric? Explain. A) Answer: She bought 10.03 B) A) Lily walked 8 kilometers on Monday. Then she walked 5.5 km on Tuesday. How much farther did Christine walk on Monday than on Tuesday? Answer: 2.5 Km C) A) 0.61
+0.71 1.40 Answer: 1.40 grams of salt 0.8
-5.5 2.5 Add and subtract decimals in the equations below: B) A) B) 17 x 25 85 340 425 Using front- end estimation to place the decimal point, 1.7x2.5= 4.25.
The area of the park is 4.25 km square. 1.7x2.5
Think: 1x2 =2
So,1.7x2.5 is about 2.
Place the decimal point between the 4 and the 2. An area rug is rectangular.
Its dimensions are 3.4m by 2.7m.
Show different strategies you can use to find the area of the rug.
Which strategy is best? Justify your answer. Answer: 9.18m square The fuel consumption estimates of Josie's car are: City: 21.2km/L Highway: 23.3km/L The car's gas tank holds 40.2L of fuel A) How far could Josie drive on a full tank of gas on the highway before she runs out of fuel? B) How far could she drive on a fuel tank of gas in the city?
What assumptions did you make? Answers: A) 936.66 km B) 852.24 km A) Multiply i) 6.3 X 1.8 ii) 0.37x0.26 iii) 3.52x2.4 iv) 1.234x0.9 B) Look at the questions and products in part a. What patterns do you see in the numbers of decimal places in the question and the product? How could you use this pattern to place the decimal point in a product without estimating? C) Multiply: 2.6 x 3.5
Does the pattern from part b hold true? If the answer is no, explain why not. Answers:A) i) 11.34
iv) 1.1106 B) The number of decimal places in the product is the sum of the number of decimal places in the question. Evaluate
B) 8-3.6 2
C) 46.4-10.8 3
D) 85.6 x 0.4 x 7 C) 9.1; Yes, the rule applies, but the product must be written as 9.10. The calculator does not show the product this way. Product: The result when two or more numbers are multiplied. Quotient: The result when one number is divided by another. Sum: The result of adding two or more numbers. 5763 - 3940 1823 Since the estimate is 2, place the decimal point after the 1.
The difference is 1.823. You can use Base Ten Blocks to divide decimals, similar to the way you multiplied decimals. For example, to divide 3.6 divided by 0.8: Make a rectangle with an area of 3.6 and a width of 0.8. Divide. Give the exact answer, written as a decimal.
284.4 ÷ 6 = The area of a large rectangular flowerbed is 22.32m square. The width is 0.8m. What is the length? Answer: 27.9m A 0.4-kg bag of oranges costs
$1.34. A) estimate. About how much does 1kg of oranges cost?
B) What is the actual cost of 1kg of oranges? How do you know your answer is reasonable?
C) Suppose you spent $10 on oranges. What mass of oranges did you buy. Answers:
A) About $3
C) About 3kg Get to
Know Me Alice Elizabeth Turner was born in Richmond, Virginia. After receiving a full scholarship to study at the University of Richmond, she earned her B.A. degree in mathematics in 1936
June 18, 1915 - September 27, 2009 Alice Elizabeth Turner 3.4
– 1.2 2.2 C) D) 88. 4
+13 .9 102.3 5.3
=1.1 = 0.6
=0.4 D) A carpenter bought a piece of wood that was 0.5 metres long. Then he sawed 0.43 metres off the end. How long is the piece of wood now? Answer: It was 0.07 m long. 2 5 1 4 = 4 10 0.4 25 100 = 0.25 A) B) = Answers:
The denominator is the bottom number in a fraction.
It shows how many equal parts the item is divided into
If two fractions have the same denominator then they are easy to compare: B=brackets
S=subtract We use the same order of operations for decimals as for whole numbers here is the order of operation:
-do the operations in brackets first.
- then divide and multiply, in order from left to right.
-then add and subtract, in order, from left to right Answer:
D) 1498 Evaluate
A)1.35+(5 4.9 0.07)-2.7 2.1
B) 9.035 5.2-4.32 6.7 Answer:
B) 18.038 Gary mixed 0.7 grams of salt into a pot of soup he was cooking. Before he served the soup, Gary added 0.6 grams of salt. How much salt did Gary put into the soup in all? Answer: 1.3 grams of sugar. B) D) C) On a school trip, a class travels 9.99 kilometers by train and 1.99 kilometers by bus. How far did the class travel? Answer: They traveled 11.98km 9.99
+1.99 11.98 Megan bought two rolls of tape. The first roll had 50 meters of tape and the second roll had 10.12 meters of tape. How many meters of tape did Megan buy in all? Answer: 60.12 m 50
+10.12 60.12 Grace went jogging, and she ran 31 kg on Thursday and then 40.12 on Friday. How much running has she done in total this week? Answer: 71.12 kg 31
+40.12 71.12 We can use number lines to show how percents can relate
to fractions and decimals.
50% = 50 = 0.50 100 2 50 50 100 50 A) B) C) D) 2%= 9%= 28%= 95%= Write an equivalent fraction with
denominator of 100. 1 50 And 0.02 9 100 And 0.09 7 25 And 0.28 19 20 And 0.95 Percent means parts out of 100. A percent is 1 part out of 100. 1% is equal to
0.01. Proportions can be used to solve percent problems.
100 A) 100% of 38 =
Answer 38 The part is 38.
The whole is 38. C) B) 40% of 20 =
Answer 8 D) 75% of 32 =
Answer 24 20% of $5 =
Answer $1 The part is 1.
The whole is 5. The part is 24.
The whole is 32. The part is 8.
The whole is 20. Medium Example Find the sale price of each item: Hard Example The goods and services tax (GST) is currently %6 percent for each item below.
Find the GST, and the cost of the item with GST. A) C) B) D) Use equivalent fractions. order each set from least to greatest.
A) 3 1/2, 13/4, 31/8
B) 5/6, 2/3, 1 /12, 9/12
C) 1 2/5, 4/3, 3/2
A) 3 1/2, 13/4, 3 1/8; 3.5, 3.25, 3.125
B) 1 1/12, 5/6, 9/12, 2/3; 1.083, 0.83, 0.75, 0.6
C)3/2, 1 2/5, 4/3; 1.5, 1.4, 1.3 1) Ioana, Aidia, and Norman fot different asnwers for this problem: 12x (4.8 0.3) - 3.64 x 3.5
Ioana's answer was 39.12, Aidias answer was 179.27, and Normans answer was 659.26.
A) which student had the correct answer?
B) show how the other students got their answer.
B) Ioana: 12 x (4.8 0.3 - 3.64 x 3.5)= 39.12
Norman: (12 x 4.8 0.3- 3.64)x 3.5= 659.26 1 7 5 1 6 1 8 1 2 5 1 Least to Greatest: 1, 1.25,1.6, 7 , 1 4 4 5 Use place value.
Order each set of numbers from least to greatest. A) B) C) D) Coat: 55% off $90 Answer: $40.50 Shoes: 45% off $40
Answer:$22.00 Sweater: 30% off $50
Answer: $35.00 Jeans: 60% off $30
Answer: $30.00 A) B) C) Bicycle: $129.00 Answer: i) $7.74
ii)$136.74 DVD: $24.99
Answer: i) 1.50
ii) $26.49 Skateboard: $42.97
Answer: i) $2.58
ii) $45.55 Fred had 8 out of 10 on a
test. Janet had 82%
Who did better on the test? Answer: 82% is the
better mark. Melissa had 5 out of 10
on a quiz. Megan got 93%
Who had the better mark? Answer: 93% is the
better mark. Maria had 16 out of 20 on a
test. Jake got 74%
Who had the better mark? Answer: 77% is the
better mark. Anna had 90 out of 100 on
a test. Hallie had 89%
Who had the better mark? Answer: 90% is the
better mark. Out of the options below
who did better on the test? In each set identify the number that is not in the correct order4. show where it should go.
A) 29/5, 6 2/10, 6.25, 6 2/20
B) 1 1/16, 1 3/8, 3/2, 1.2, 3/4
A) 6 2/20 should be the second number in set A
B) 3/2 should be the first number in set B Tax is always 1. 25. The sale Price is the price the object is on sale for Write each percent as a fraction and then a decimal: A) C) B) D) 80%= 4
5 And 0.8 12%= 3
25 And 0.12 2%= 1
50 And 0.02 63
100 And 0.63 63%= Whats the area of the rug? Solution: You have to times 3.4
by 2.7 to get your answer.