Fractions, Decimals and Percents Unit 3 Topic 3.1 Fractions to Decimals
Numbers can be written as both a fraction and a decimal. For example, 4 can be written as and 4.0
A fraction tells us to divide, so means
Decimals with a definite number of decimal places are ______. In other words the numbers after the decimal will stop. For example, 0.1, 0.25, 0.47 are all terminating decimals.
Decimals that have an infinite number of decimal places are ______. In other words the number after the decimal keeps going on forever. We draw a bar over the digits that repeat. For example, , or 0.454 545 454 ...
Writing Decimals as Fractions
Fraction Decimal 0.05 0.193 0.07
**Remember that the number of 0’s in the denominator will help determine place value. A number with a denominator of 10, will be a decimal in the tenths. A number with a denominator of 100, will be a decimal in the hundredths. A number with a denominator of 1000, will be a decimal in the thousandths.
We need to recognize the patterns that will occur when working with decimals
1 Mount Pearl Intermediate Fractions, Decimals and Percents Unit 3 Ex 1.
Ex 2.
Ex 3.
For fractions with a denominator ______the digits in the numerator of the fraction are the repeating digits in the decimal. We can use this pattern to help us make predictions. To write as a fraction let 53 be the numerator and 99 be the denominator, so Similarly,
Example: Write each fraction as a decimal with denominator 10, 100 or 1000 and determine if they are repeating or terminating decimals.
(a)
(b)
c)
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d)
3.2 Comparing and Ordering Fractions and Decimals
When ordering fractions and decimals we need to use what is called benchmarks. These are rules that help us determine values that fractions are close too.
3 Mount Pearl Intermediate Fractions, Decimals and Percents Unit 3 For example, is close to 0 because the numerator is much ______than the denominator
is close to because the numerator is about ______the denominator.
is close to 1 because the numerator and denominator are ______in value.
Recall: Mixed Numbers
Write the following as mixed numbers
(a)
(b)
(c)
Example 1: Write the following numbers in order from least to greatest:
Write equivalent fractions with like denominators, then compare the numerators.
Change to a fraction in lowest terms (easy to compare).
4 Mount Pearl Intermediate Fractions, Decimals and Percents Unit 3 What is a common denominator we could use between all the terms?
Each fraction now has a denominator of _____, so compare the numerators:
We can verify this by placing the numbers on a number line
Example 2: Write a fraction between and
Solution: We will use our knowledge of equivalent fractions to help us. Remember, you cannot write decimals as the numerator (or denominator) of a fraction.
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Topic 3.3 Adding and Subtracting Decimals
When adding or subtracting decimals we will use estimation if we do not need an exact answer. We will also estimate to check if the answer is reasonable.
We will first examine adding of decimals using what is called front end estimation.
Example 1: Heather spends her evening training for an upcoming race. Her practice distances for Monday-Friday are listed in the table below. 6 Mount Pearl Intermediate Fractions, Decimals and Percents Unit 3
Day Distance (km) Monday 8.5 Tuesday 7.45 Wednesday 10.9 Thursday 9.15 Friday 8.85
(a) How far did heather run in the five days?
(b) How much farther did Heather run on Wednesday than she did on Tuesday?
(a) Solution A Solution B
(b) Solution A Solution B
Examples: Use front-end estimation to estimate each sum and difference
(a) (b) 7 Mount Pearl Intermediate Fractions, Decimals and Percents Unit 3
(c) (d)
Examples: Determine the exact values of the following sum or difference
(a) (b)
(c) (d)
Topic 3.4 Multiplying Decimals
Example 1: The park outside the school measures 1.6 by 2.3 km. What is the area of the park?
We will multiply as we would whole numbers. We then count the number of decimal places and that will represent the number of decimal places in our answer.
8 Mount Pearl Intermediate Fractions, Decimals and Percents Unit 3 Example 2: Multiply the following:
(a) (b)
(c) (d)
Topic 3.5 Dividing Decimals
First let’s look at how division and multiplication are related. 2 and 5 are the factors and 10 is the product. To check this problem we can use division.
10 is the ______or 10 is the ______2 is the ______5 is the ______5 is the ______2 is the ______
When we divide by decimal’s we use a strategy to help us.
9 Mount Pearl Intermediate Fractions, Decimals and Percents Unit 3 What we do is we change the divisor to a whole number by multiplying by 10,100, 1000. Remember though, if we change one number, we must change the other.
Examples:
(a)
We will make the divisor a whole number by multiplying it by 10. Remember to also multiply the dividend by 10 as well.
Now, we have We can use long division to solve:
(b)
(c)
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(d)
(e)
3.6 Order of Operations with decimals
When we have more than one operation we need to follow a particular order to determine the solution to the problem.
The order of operations:
Perform what is in ______
Perform ______and ______in the order it appears from left to right.
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Perform ______and ______in the order it appears from left to right.
Let’s attempt some examples: Note: Make sure to copy down any operations you do not use. Underline the operation you are performing. (a)
(b)
(c)
(d) 12 Mount Pearl Intermediate Fractions, Decimals and Percents Unit 3
(e)
Topic 3.7 Relating Fractions, Decimals and Percents
Name some places that use percent often:
We also should notice a relationship between fractions decimals and percents. Remember that percent means per hundred
13 Mount Pearl Intermediate Fractions, Decimals and Percents Unit 3 So
Changing from Percent to Decimal: ______
Changing from Percent to Fraction: ______
Changing from Decimal to Percent: ______
Fraction to Percent: ______
Example: Write each fraction as a percent and a decimal.
(a) (b)
Example: Write each percent as a fraction and a decimal. (a) (b)
14 Mount Pearl Intermediate Fractions, Decimals and Percents Unit 3 Example: What percent of the hundred chart is shaded? Write the percent as a fraction and a decimal.
Topic 3.8 Solving Percent Problems
When we are out shopping we need to always consider things such as tax, or discounts. We will learn ways to calculate these sorts of costs and other percent problems.
We must use our knowledge of changing percents to decimals to help us calculate different percent problems.
15 Mount Pearl Intermediate Fractions, Decimals and Percents Unit 3 Example: Calculate the following
(a) (b) (c)
Solutions:
Calculating Sales Tax
In Newfoundland and Labrador the sales tax is 13%. That means we need to add 13% of the cost to the original price when we get to the checkout.
For example, a shirt that says $14.99 is really $14.99 plus tax.
Example: Let us calculate the sales tax on the following items. (a) A hoodie for $24.50
16 Mount Pearl Intermediate Fractions, Decimals and Percents Unit 3 (b) A dress for $49.99 (c) A Baconator Meal for $6.99 and a Big Bacon Classic Meal for $5.49
Solution:
Percent Discount
We also must take into account price discount. For example, there are times when stores have 25% off, 30% off and so on. In these cases we need to subtract the amount of discount.
Example: The following items are 30% off the ticket price. (a) Team Canada Jersey $129.99
17 Mount Pearl Intermediate Fractions, Decimals and Percents Unit 3 (b) Ice Caps hat $29.79 Determine: (i) The amount of discount (ii) The new sales price
Solution:
Total Price
Since sales tax is added to the price of an item we need to use our knowledge of sales tax to find the total price.
Example: The price of a pair of sneakers at Sports Chek is $89.99 and a t- shirt is $29.99. What is the total of these two items including sales tax.
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Example: The price of a hoodie at American Eagle is $49.99 regular price. However the store has a 40% off everything sale, so you decided to buy two hoodies at that price. What is the total including sales tax for the two hoodies?
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