<p> Fractions, Decimals and Percents Unit 3 Topic 3.1 Fractions to Decimals</p><p>Numbers can be written as both a fraction and a decimal. For example, 4 can be written as and 4.0</p><p>A fraction tells us to divide, so means </p><p>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.</p><p>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 ...</p><p>Writing Decimals as Fractions</p><p>Fraction Decimal 0.05 0.193 0.07</p><p>**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.</p><p>We need to recognize the patterns that will occur when working with decimals</p><p>1 Mount Pearl Intermediate Fractions, Decimals and Percents Unit 3 Ex 1. </p><p>Ex 2.</p><p>Ex 3.</p><p>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, </p><p>Example: Write each fraction as a decimal with denominator 10, 100 or 1000 and determine if they are repeating or terminating decimals.</p><p>(a)</p><p>(b)</p><p> c)</p><p>2 Mount Pearl Intermediate Fractions, Decimals and Percents Unit 3</p><p> d)</p><p>3.2 Comparing and Ordering Fractions and Decimals</p><p>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.</p><p>3 Mount Pearl Intermediate Fractions, Decimals and Percents Unit 3 For example, is close to 0 because the numerator is much ______than the denominator</p><p> is close to because the numerator is about ______the denominator.</p><p> is close to 1 because the numerator and denominator are ______in value.</p><p>Recall: Mixed Numbers</p><p>Write the following as mixed numbers</p><p>(a)</p><p>(b)</p><p>(c)</p><p>Example 1: Write the following numbers in order from least to greatest: </p><p>Write equivalent fractions with like denominators, then compare the numerators.</p><p>Change to a fraction in lowest terms (easy to compare).</p><p>4 Mount Pearl Intermediate Fractions, Decimals and Percents Unit 3 What is a common denominator we could use between all the terms?</p><p>Each fraction now has a denominator of _____, so compare the numerators:</p><p>We can verify this by placing the numbers on a number line</p><p>Example 2: Write a fraction between and </p><p>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.</p><p>5 Mount Pearl Intermediate Fractions, Decimals and Percents Unit 3</p><p>Topic 3.3 Adding and Subtracting Decimals</p><p>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.</p><p>We will first examine adding of decimals using what is called front end estimation.</p><p>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</p><p>Day Distance (km) Monday 8.5 Tuesday 7.45 Wednesday 10.9 Thursday 9.15 Friday 8.85</p><p>(a) How far did heather run in the five days?</p><p>(b) How much farther did Heather run on Wednesday than she did on Tuesday?</p><p>(a) Solution A Solution B</p><p>(b) Solution A Solution B</p><p>Examples: Use front-end estimation to estimate each sum and difference</p><p>(a) (b) 7 Mount Pearl Intermediate Fractions, Decimals and Percents Unit 3</p><p>(c) (d)</p><p>Examples: Determine the exact values of the following sum or difference</p><p>(a) (b)</p><p>(c) (d)</p><p>Topic 3.4 Multiplying Decimals</p><p>Example 1: The park outside the school measures 1.6 by 2.3 km. What is the area of the park?</p><p>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.</p><p>8 Mount Pearl Intermediate Fractions, Decimals and Percents Unit 3 Example 2: Multiply the following:</p><p>(a) (b)</p><p>(c) (d)</p><p>Topic 3.5 Dividing Decimals</p><p>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.</p><p>10 is the ______or 10 is the ______2 is the ______5 is the ______5 is the ______2 is the ______</p><p>When we divide by decimal’s we use a strategy to help us.</p><p>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.</p><p>Examples:</p><p>(a)</p><p>We will make the divisor a whole number by multiplying it by 10. Remember to also multiply the dividend by 10 as well.</p><p>Now, we have We can use long division to solve:</p><p>(b)</p><p>(c)</p><p>10 Mount Pearl Intermediate Fractions, Decimals and Percents Unit 3</p><p>(d)</p><p>(e)</p><p>3.6 Order of Operations with decimals</p><p>When we have more than one operation we need to follow a particular order to determine the solution to the problem.</p><p>The order of operations:</p><p>Perform what is in ______</p><p>Perform ______and ______in the order it appears from left to right.</p><p>11 Mount Pearl Intermediate Fractions, Decimals and Percents Unit 3</p><p>Perform ______and ______in the order it appears from left to right.</p><p>Let’s attempt some examples: Note: Make sure to copy down any operations you do not use. Underline the operation you are performing. (a)</p><p>(b)</p><p>(c)</p><p>(d) 12 Mount Pearl Intermediate Fractions, Decimals and Percents Unit 3</p><p>(e)</p><p>Topic 3.7 Relating Fractions, Decimals and Percents</p><p>Name some places that use percent often:    </p><p>We also should notice a relationship between fractions decimals and percents. Remember that percent means per hundred </p><p>13 Mount Pearl Intermediate Fractions, Decimals and Percents Unit 3 So </p><p>Changing from Percent to Decimal: ______</p><p>Changing from Percent to Fraction: ______</p><p>Changing from Decimal to Percent: ______</p><p>Fraction to Percent: ______</p><p>Example: Write each fraction as a percent and a decimal.</p><p>(a) (b)</p><p>Example: Write each percent as a fraction and a decimal. (a) (b)</p><p>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.</p><p>Topic 3.8 Solving Percent Problems</p><p>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.</p><p>We must use our knowledge of changing percents to decimals to help us calculate different percent problems. </p><p>15 Mount Pearl Intermediate Fractions, Decimals and Percents Unit 3 Example: Calculate the following</p><p>(a) (b) (c)</p><p>Solutions: </p><p>Calculating Sales Tax</p><p>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. </p><p>For example, a shirt that says $14.99 is really $14.99 plus tax.</p><p>Example: Let us calculate the sales tax on the following items. (a) A hoodie for $24.50</p><p>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</p><p>Solution:</p><p>Percent Discount</p><p>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.</p><p>Example: The following items are 30% off the ticket price. (a) Team Canada Jersey $129.99</p><p>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</p><p>Solution: </p><p>Total Price</p><p>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.</p><p>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.</p><p>18 Mount Pearl Intermediate Fractions, Decimals and Percents Unit 3</p><p>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? </p><p>19 Mount Pearl Intermediate</p>