Question and Answers #2 Fractions

Questions and Answers Sheet 2 Fractions Question #1 What is 0.17 in fraction form, simplified? Answer: 17 100 Explanation: 0.17 × 100 = 17 So 0.17 = 17 100 This does not simplify further since 17 is ' and not a factor of 100 . Question #2 How do you change 9/16 into a percentage? Answer: Explanation: A percentage can be obtained from a fraction with a denominator with a power of 10, or from a decimal. 9 ÷ 16 = 0.5625 5625 ÷ 100 56.25 = = 56.25% 10000 ÷ 100 100 Question #3 What fraction is equivalent to 3/8? Answer: Multiply 3 8 by an equivalent fraction that equals 1 An equivalent fraction is equal to 1 such as 2 2 or 3 3 An equivalent fraction is the same as multiplying by 1 so the ratio does not change. This fraction would be equal to 𝑎 𝑎 Hence an example would be that Question #4 How to solve Answer: Explanation: 18 √3 ? = 1 where a is an integer. 2 2 3 6 8 16 ⋅ = to simplify 18 √3 Make use of the following √𝑎 × √𝑎 = 𝑎 as an example √100 × √100 = 10 × 10 = 100 what we have to do here is rationalise the denominator this means eliminating the radical from the denominator multiply the numerator/denominator by √3 ⇒ 18 √3 × √3 √3 = 6√3 Question #5 What is the fraction 1 5 as a percent? Answer: To the fraction 1 5 as a percent is 20% Explanation: Here's the step-by-step process. 1. 2. Start by changing the fraction to a decimal by diving the numerator by the denominator (1 divided by 5). That equals 0.2 Change the decimal to a percent by multiplying it by 100%, or moving the decimal two places. That gives you 20%. Another way of thinking about it is multiplying the numerator by 100%, hen dividing that by the denominator (100% divided by 5). This gives you 20%. Question #6 How do you simplify 12 20 ? Answer: Explanation: First you can notice that both numerator and denominator are even numbers, so the fraction can be reduced by 2: 12 6 = 20 10 In the result still both numbers are even, so you can repeat the reduction. 6 10 = 3 5 Now you get the fraction in which both numerator and denominator are ' numbers, so the result cannot be simplified any more. The result: 12 20 = 3 5 Question #7 How do you write 0.3 as a fraction? Answer: See below You can write 0.3 as a fraction in a couple of way. 30 = 0.30 100 3 = 0.30 10 Question #8 How do you write the fraction 2 3 as a decimal? Answer: Explanation: If we put in a calculator 2 3 and convert it into fraction it would dispaly 0.666... with infinite sixes. We could also write it as 0. 6 Question #9 How do you write 5 6 as a percent? Answer: Percent'' or ''%'' means ''out of 100'' or ''per 100'', Therefore x% can be written as 𝑥 100 Therefore we can write an equation as and solve for x: 𝑥 5 = 100 6 100 × 1 5 = 100 × 100 6 100 × 𝑥 500 = 100 6 𝑥 = 83.3 5 = 83.3% 6 Question #10 How do you convert 3 1/8 into a decimal and percent? Answer: Explanation: Divide the numerator by the denominator and add the whole number to convert a mixed fraction into a decimal. 1 = 0.125 + 3 = 3.125 8 3 1 8 as a decimal is 3.125 Multiply the mixed number converted into a decimal by 100 to convert the mixed number to a percentage. 3.125 × 100 = 312.50\% 3 1 8 is 3.125 as a decimal and 312.50% as a percentage. Question #11 How do you figure out this fraction? 1/2 + 1/4 = Answer: Explanation: 1 1 2 4 We are starting with + If both fractions had 4 as the denominator, we would be in good shape. We need a ''common denominator''. OK, one of the algebra rules is that if you multiply both top and bottom of a fraction by the same value, no change in 1 value happens. So let's take that and play with it. 2 If you multiply both top and bottom of the fraction by 2, it becomes 2⋅1 2⋅2 = 2 4 2 That algebra rule that I paraphrased says that no change in value happened when we did that. So now we have + 1 4 = 2+1 4 = 4 3 4 Question #12 How do you convert 7/15 into a decimal and percent? Answer: Explanation: 7 = 7 ÷ 15 15 So, 7 ÷ 15 = 0,46 7 15 in decimal form is 0,46 In percentages we just multiply it my 100: 0,46 ⋅ 100 = 46 so the answer 46% Question #13 How do you change 0.2 into a fraction? Answer: Explanation: When changing a decimal to a fraction, think of the decimal ''out of 1.'' In mathematical terms, ''out of'' generally suggests division. For example on this question, think of 0.2 as 0.2 out of 1, which would be shown as 0.2 1 To more easily simplify this, multiply both the top and bottom by 10: 0.2 10 ⋅ 1 10 You are able to do this because Then you get 2 10 10 10 is equal to 1 and multiplying by a number and 1 results in the same number. . Both 2 and 10 are divisible by 2: 2 2 = 1and 10 2 =5 So the final answer is 1 5 Question #14 For each of the sets below, determine whether {2} is an element of that set. a) b) c) d) e) f) {𝑥 ∈ 𝑅 | "{𝑥 𝑖𝑠 𝑎𝑛 𝑖𝑛𝑡𝑒𝑔𝑒𝑟 𝑔𝑟𝑒𝑎𝑡𝑒𝑟 𝑡ℎ𝑎𝑛 1}} {𝑥 ∈ 𝑅 | "{𝑥 𝑖𝑠 𝑡ℎ𝑒 𝑠𝑞𝑢𝑎𝑟𝑒 𝑜𝑓 𝑎𝑛 𝑖𝑛𝑡𝑒𝑔𝑒𝑟}} 2,2 2,2 2,2,2 𝑓 ) {{{2}}} Answer: (a) The set thus contains all elements greatr than 1. 2 is an integer greater than 1, thus 2 is an element of the set. (b) The set thus contains all squares of integers. 2 is not the square of an integer, thus 2 is NOT an element of the set. (c) The set contains the integer 2 and a subset {2} that contains the integer 2. 2 is the irst element mentioned in the set, thus 2 is an element of the set. (d) The set contains the subset {2} and the subset {{2}} (subset containing a subset). The set contains only subsets, while 2 is not subset an thus 2 is not an element of the set. (e) The set contains the subset {2} and the subset {2,{2}}. The set contains only subsets, while 2 is not a subset and thus 2 is not an element of the set. (f) The set contains the subset {{2}} (subset containing a subset). The set contains only subsets, while 2 is not a subset and thus 2 is not an element of the set. Question #15 Define Equivalent fractions. Answer: Step 1 Equivalent fractions- Fractions are said to be equivalent of they have different numerator and denominator but have the same values. Step 2 Examples of the equivalent fractions are: 1) 2) 1 2 1 3 , , 2 4 2 6 , , 3 6 3 9 (Fractions have the same value (Fractions have the same value 1 2 1 3 ) ) Question #16 What are the types of rational algebraic fractions? Answer: Step 1 There are two types of rational algebraic fractions namely proper algebraic fractions and improper algebraic fractions. A rational algebraic fraction 𝑓(𝑥) 𝑔(𝑥) consisting of the numerator with lower degree than the denominator is defined as proper algebraic fractions. Example: 𝑥2 𝑥 3 +1 Step 2 A rational algebraic fraction 𝑓(𝑥) 𝑔(𝑥) consisting of the numerator with higher degree than the denominator is defined as improper algebraic fractions. Example: 𝑥 2 +1 𝑥 Question #17 Fractions that represent the same quantity are called ? fractions. Answer: Equivalent fractions There are many ways to write a fraction of a whole. Fractions that represent the same number are called equivalent 1 2 4 fractions. This is basically the same thing as equal ratios. For example, , , and are all equivalent fractions. To 2 4 8 find out if two fractions are equivalent, use a calculator and divide. If the answer is the same, then they are equivalent. Answer: equivalent ( fill in the blank) Question #18 In your own words, explain how to multiply two fractions. Answer: Two fractions can be multiplied as follows: Step 1: Multiply the numerators of the factor fractions. Step 2: Multiply the denominators of the factor fractions. Step 3: Simplify the product if required. For, example: 2 6 × 3 7 Step 1: Step 2: Step 3: 12 3×7 12 21 4 7 Question #19 What mathematical concepts or principles did you apply in adding or subtracting the fractions? Answer: Step 1 Addition: Consider two fraction as 𝑎 𝑐 and 𝑏 𝑑 Here, the denominators in the fractions are same. So, add the numerators and write the common denominator. That is, 𝑎 𝑏 𝑐 𝑎+𝑐 𝑑 𝑏 + = Consider two fraction as 𝑎 𝑏 and 𝑐 𝑑 Here, the denominators in the fractions are not same. So, first find the common denominator and convert the terms to equivalent fractions with that denominator then add the numerators. That is, 𝑎 𝑏 𝑐 𝑎×𝑑 𝑑 𝑏𝑑 + = + 𝑐×𝑏 𝑏𝑑 = 𝑎𝑑+𝑏𝑐 𝑏𝑑 Step 2 Subtraction: Consider two fraction as 𝑎 𝑏 𝑐 and 𝑏 Here, the denominators in the fractions are same. So, subtract the numerators and write the common denominator. That is, 𝑎 𝑏 𝑐 𝑎−𝑐 𝑏 𝑏 − = Consider two fraction as 𝑎 𝑏 𝑐 and 𝑑 Here, the denominators in the fractions are not same. So, first find the common denominator and convert the terms to equivalent fractions with that denominator then subtract the numerators. That is, 𝑎 𝑏 𝑐 𝑎×𝑑 𝑑 𝑏𝑑 − = − 𝑐×𝑏 𝑏𝑑 = 𝑎𝑑−𝑏𝑐 𝑏𝑑 Question #20 Minju says that fractions that use bigger numbers are greater than fractions that use smaller numbers. Make up an example that would help her see that this is not always true. Answer: Step 1 Lets assume fractions with bigger numbers and check 1 2 3 7 Lets assume two fractions that has bigger numbers and To compare both fractions we make the denominators same multiply the first fraction by 7 and second fraction by 3 So the fractions becomes 9 21 and 6 21 Step 2 9 21 and 6 21 From these two fractions , we can say that 9 is greater than 6 So 9 12 is greater than 6 21 1 2 > 3 7 From this she can understand that , that fractions that use bigger numbers are greater than fractions that use smaller numbers are not always true.