Download Mastering Fraction and Decimal Operations and more Exams Law in PDF only on Docsity!
Civil service exam prep questions with correct
answers
Numerator CORRECT ANSWER The whole number that appears on the top of a fraction. ?/D Denominator CORRECT ANSWER The number that appears on the bottom of the fraction. N/? Proper fraction CORRECT ANSWER The numerator is smaller than the denominator. Ex. 1/ Improper fraction CORRECT ANSWER The numerator is larger than the denominator. Ex. 2/ Mixed numbers CORRECT ANSWER A mixed number consists of a whole number and a proper fraction. A improper fraction can be written into a mixed number.
How do you convert an improper fraction into a mixed number? CORRECT ANSWER 1. Divide the numerator by the denominator. The result will be a whole number, with or without a remainder.
- Write the whole number.
- If there is a remainder, write a fraction with the remainder in the numerator and the original denominator in the denominator. Ex. Convert 17/5 to a mixed number? 17/5=3 with a remainder of 2 17/5=3 2/ How do you convert a mixed number into a improper fraction? CORRECT ANSWER 1. Multiply the whole number in the mixed number by the denominator of the fraction.
- Add the result to the numerator of the fraction. Ex. Convert 5 1/6 to an improper fraction. 5x6= 30 30+1= 31 5 1/6= 31/ When should you convert mixed numbers into improper fractions? CORRECT ANSWER Whenever you are asked to multiply or divide mixed numbers
example of key words for subtraction. Jacob has 5 fewer than Leslie? CORRECT ANSWER Would be Leslie-5=Jacob Distance formula problems include key words such as? CORRECT ANSWER speed, plane, train, boat, car, walk, run, climb, and swim Distance Formula CORRECT ANSWER Rate x Time = Distance Key word in the distance formula provide 2 of the 3 elements CORRECT ANSWER rate, time, distance Plug those 2 elements into the formula and solve for the third Rate and time have to be measured into common units CORRECT ANSWER If the rate is measured in miles per hour, the time has to be measured in hours, not minutes or days 2 ways to solve word problems CORRECT ANSWER 1. Translate the problem into an algebraic equation and then solve for the missing information
- Work backwards by plugging in one of the answer choices A neat trick to see if a number is divisible by 3. CORRECT ANSWER Add all of its digits. If the sum of the digits is divisible by 3, the number itself is divisible by
Ex. Is 132 divisible by 3? 1+3+2=6 6/3=
Which means that 132 is divisible by 3. This method also works for 9. Raising fraction to higher terms CORRECT ANSWER It allows you to rewrite a fraction with a larger numerator and denominator When would you usually have to raise a fraction to higher terms CORRECT ANSWER you often have to raise one or more fractions to higher terms in order to add or subtract them How to add fractions that have common denominators CORRECT ANSWER simply just add the numerators and write the result over the denominator. Do not add the denominators Ex. 3/12+6/12= 9/ How to add mixed numbers CORRECT ANSWER add the whole numbers together, and then add the numerators together and place them over the denominators. Do not add the denominators. Ex. 3 3/12 + 6 3/12= 9 6/12 Reduced equals 9 1/ If the sum of the 2 fractions happen to be an improper fraction CORRECT ANSWER You must convert the improper fraction into a mixed number 4/7 + 6/7 = 10/7 so converted into a mixed number it would be 1 3/ when can you not add fraction? CORRECT ANSWER You cannot add fractions unless it has a common denominator
When will have to make extra steps while subtracting fractions CORRECT ANSWER If the fraction in the second mixed number is larger than the fraction in the first mixed number, you will have to borrow in order to rewrite the first number. Ex. 12 1/5 - 7 3/5= You can't subtract 3/5 from 1/5 because it would be a negative number. in the first fraction you'll need to borrow from the whole number to make it into an improper fraction. 11 6/5 - 7 3/5= 4 3/ Since the first fraction is now bigger you are able to subtract. Remember do not subtract the denominator. If the fraction that you're subtracting does not share common denominators CORRECT ANSWER Its like adding fractions you must find the common denominator Ex. 3/4 - 1/6 = The common denominator is 12: 3x3= 9 4x3= 12 = 9/ 1x2= 2 6x2= 12 = 2/ 9/12 - 2/12 = 7/
Remember do not subtract the denominators when they're common Multiplying fractions CORRECT ANSWER Multiplying fraction is much easier than adding or subtracting. all you have to do is multiply the numerators and the denominators. Ex. 2/3 x 5/7 = 2x5= 15 3x7= 21= 15/ If you can reduce go ahead and reduce 3/ How to multiply mixed numbers? CORRECT ANSWER 1. Change any mixed numbers to an improper fraction.
- Then multiply as normal. Ex. 4 2/3 x 5 1/2= 4 2/3= 14/ 5 1/2= 11/ 14/3 x 11/2= 154/6 = 25 2/ Ex. 8,400 fans attended a college football game 3/4 of the fans rooted for the home team. the rest rooted for the visiting team. How many fans rooted for the home team? CORRECT ANSWER To solve, multiply 8400 by 3/
How to divide mixed numbers CORRECT ANSWER Rewrite them as improper fractions Ex. 3 1/5 / 1 1/2? 3 1/5= 16/ 1 1/2= 3/ take the reciprocal of 3/2 which would be 2/ 16/5 x 2/3 = 32/15 = 2 2/ If the problem ask for an answer in the form of a mixed number, use the conversion technique to convert. 0.1 CORRECT ANSWER 1 tenth, 1/ 0.01 CORRECT ANSWER 1 hundredth, 1/ 0.001 CORRECT ANSWER 1 thousandth, 1/ 0.0001 CORRECT ANSWER 1 tenth thousandth, 1/ can zero be be added to the right of the decimal without it changing the value CORRECT ANSWER yes, .01 is the same value as .01000. this is helpful when adding, subtracting or dividing by decimals.
Mixed decimal CORRECT ANSWER A decimal with numbers on both sides of the decimal point Ex. 32. A decimal with numbers to the right of the decimal point only Is called CORRECT ANSWER A decimal not a mixed decimal how to write a fraction into a decimal CORRECT ANSWER divide the numerator by the denominator Ex. Write 3/4 as a decimal 3/4=. How to change a decimal into a fraction CORRECT ANSWER write the digits of the decimal as the numerator of a fraction and write the decimals name as the denominator of the fraction. reduce if possible. Ex. rewrite 0.018 as a fraction?
- write 18 as the numerator of the fraction 2 write the name of the fraction in the denominator. 0.018 is eighteen one- thousandth, so you should write 1,000 in the denominator of the fraction.
- Reduce. Both 18 and 1000 are divisible by 2, so 18/1000 can be reduced. 18/1000= 9/
with cash. you encounter percentages every day. Sales tax, interest, discounts, and tips, on meals are just a few of the percent calculations people make on a daily basis. Changing a percent to a fraction and vice versa CORRECT ANSWER A percent can easily be written as a fraction. Simply take the percent and put it in the numerator of the fraction. Then, write 100 in the denominator. Ex. Convert 75% to a fraction? 75/ How to write a fraction as a percent CORRECT ANSWER Multiply the fraction by 100/ Ex. Convert 1/4 to a percent? 1/4 x 100/1= 25 which means it converts to 25% another way to convert a fraction to a decimal CORRECT ANSWER Divide the numerator by the denominator, and then move the decimal point 2 places to the right in your quotient. 10% converted to a fraction? CORRECT ANSWER 1/ 20% converted to a fraction? CORRECT ANSWER 1/ 25% converted to a fraction? CORRECT ANSWER 1/
30% converted to a fraction? CORRECT ANSWER 3/ 33 1/3% converted to a fraction? CORRECT ANSWER 1/ 40% converted to a fraction? CORRECT ANSWER 2/ 50% converted to a fraction? CORRECT ANSWER 1/ 60% converted to a fraction? CORRECT ANSWER 3/ 66 2/3% converted to a fraction? CORRECT ANSWER 2/ 80% converted to a fraction? CORRECT ANSWER 4/ 100% converted to a fraction? CORRECT ANSWER 1/1 = 1 Changing a percent to a decimal CORRECT ANSWER Its the same way as converting a decimal to percent, but instead of moving the decimal point to the right 2 places you move the % sign to the left 2 places and change the sign to a decimal. Solving for % word problems generally take one of three forms CORRECT ANSWER 1. find the percent of a whole
- find what percent one number is of another number
- find the whole when the percent of a number is given
1200 = 30y Divide both sides by 30 1200/30 = 30y/ y = 40 Techniques for questions that ask about percent increase and percent decrease CORRECT ANSWER Remember that after you calculate the percent, you must add (increase) or subtract (decrease) in order to determine the final result. Ex. A merchant usually sells hats for $20. He decides to have a sale during which he decreases the price of the hats by 25%. What are the price of the hats during the sale? 25/100 x 20 25/100 x 20/ 500/ = 5 25% 0f $20 is $5. The merchant plans to decrease the price of the hat by 25%, so he plans to decrease the price by $5. That means the sale price of the hats will be $20 - $5, which equals $ The most common questions in reading comprehension. CORRECT ANSWER 1. Describe the main idea the passage
- Identify a specific fact or detail in the passage
- Draw an inference or conclusion based on the information in the passage
- Define a vocabulary word that appears in the passage
The main idea of a paragraph or passage? CORRECT ANSWER Is what the paragraph or passage is mostly about When can an answer to a main idea question not be the right one? CORRECT ANSWER When the answer choice only applies to one detail or a small portion of the paragraph or passage. Topic sentence CORRECT ANSWER The sentence that expresses the main idea. Sometimes the answer to a main idea question is stated clearly in the passage, frequently found in the first or last sentence. Other times that the main idea is not stated in the topic sentence CORRECT ANSWER it is usually implied by the overall content of the passage. In such circumstances you will need to deduce the main idea from the passage. The main idea of the passage describes CORRECT ANSWER the entire passage or paragraph. if it only describes one prat or one detail, it is not the correct answer. Just because an answer refers to an entire passage doesn't mean that it is correct CORRECT ANSWER Although such answers are usually correct, occasionally an incorrect answer will refer to the entire passage or paragraph. What makes an answer that describes a passage or paragraph incorrect in a main idea question CORRECT ANSWER It describes the content in the passage or paragraph inaccurately. Most often, it states a position stronger than the one the writer takes. Make sure that the answer to the main idea accurately describes? CORRECT ANSWER The content of the passage or paragraph
The passage suggest... Which of the following conclusions is best supported.. When answering an inference question CORRECT ANSWER Do not choose an answer that requires you to make a major assumption or to use outside knowledge. Look for answers that are fully supported by information in the passage. Questions that are designed to test vocabulary CORRECT ANSWER Are really trying to measure how well you can figure out the meaning of a unfamiliar word from its context Context refers to CORRECT ANSWER the words and ideas surrounding the vocabulary word If the context is clear enough in a vocabulary question CORRECT ANSWER you should be able to substitute a nonsense word for the one being sought and still be able to find the correct answer, because you will be able to determine meaning strictly from the sense of the sentence. The tested word itself may contain a context clue CORRECT ANSWER Look for familiar prefixes and suffixes. Look to see if the word shares a common root with some other word you know On vocabulary questions test your answer choice CORRECT ANSWER By rereading the sentence with the answer choice in the place of the vocabulary word. Eliminate answers that don't make sense.
Learn to skim passages for information CORRECT ANSWER You don't want to answer questions from memory you want to be able to return to the passage and find the part that addresses the subject in the question, and reread it before choosing your answer. Take advantage of the multiplication part of the exam and use the process of elimination CORRECT ANSWER In multiple choice test it gives you the correct answer buried in with incorrect answers. Use the process of elimination to eliminate answers you know are incorrect. This will give you better odds of getting the right answer. Skip question that you find to be difficult CORRECT ANSWER The test is timed and is graded on how many you get right. If you come across a question that you don't know circle it and move on to another. Once you get the ones you know come back to the circled question. Some times coming back will will free up the block and make it easier for you to answer it the second time. There are 2 types of vocabulary questions CORRECT ANSWER 1. Synonyms and antonyms; These questions provide a word and ask you to identify an answer that has the same or opposite meaning
- Complete the sentence; These questions provide a sentence with a crucial word missing and ask you to select the best option for the missing word 2 words are synonyms if CORRECT ANSWER The 2 words have the the same meaning or nearly the same meaning Antonyms are CORRECT ANSWER 2 words that have opposite meaning Synonym and antonym question ask CORRECT ANSWER They ask you to find the answer that has the same or opposite meaning as an underlined word in the question stem
