{"id":18587,"date":"2025-12-14T07:05:35","date_gmt":"2025-12-13T23:05:35","guid":{"rendered":"https:\/\/3d-universal.com\/en\/?p=18587"},"modified":"2025-12-13T12:36:42","modified_gmt":"2025-12-13T04:36:42","slug":"fractions-and-decimals-master-guide","status":"publish","type":"post","link":"https:\/\/3d-universal.com\/en\/blogs\/fractions-and-decimals-master-guide.html","title":{"rendered":"Fractions and Decimals Master Guide: Civil Service Exam Guide"},"content":{"rendered":"<p><!--more--><\/p>\n<h1>Fractions and Decimals Master Guide: Civil Service Exam Guide<\/h1>\n<p>Understanding fractions and decimals is a fundamental part of the Civil Service Exam (CSE). Many numerical ability questions require converting, comparing, or performing operations with fractions and decimals. This master guide provides clear explanations, step-by-step procedures, common errors to avoid, and exam-style examples to help you strengthen your confidence in this topic.<\/p>\n<h2>What Are Fractions?<\/h2>\n<p>Fractions represent parts of a whole. A fraction has two parts:<\/p>\n<ul>\n<li><strong>Numerator<\/strong> \u2013 the number of parts taken<\/li>\n<li><strong>Denominator<\/strong> \u2013 the total number of equal parts<\/li>\n<\/ul>\n<p>Example: 3\/5 means 3 parts out of 5 equal parts.<\/p>\n<p>Fractions are used to express quantities that are not whole numbers.<\/p>\n<h2>Types of Fractions<\/h2>\n<h2>Proper Fractions<\/h2>\n<p>The numerator is smaller than the denominator. Example: 4\/7<\/p>\n<h2>Improper Fractions<\/h2>\n<p>The numerator is greater than or equal to the denominator. Example: 9\/4<\/p>\n<h2>Mixed Numbers<\/h2>\n<p>A combination of a whole number and a proper fraction. Example: 2 1\/3<\/p>\n<h2>Like Fractions<\/h2>\n<p>Fractions with the same denominator. Example: 3\/8 and 5\/8<\/p>\n<h2>Unlike Fractions<\/h2>\n<p>Fractions with different denominators. Example: 2\/3 and 4\/5<\/p>\n<h2>Converting Improper Fractions and Mixed Numbers<\/h2>\n<h2>Improper Fraction to Mixed Number<\/h2>\n<p>Divide the numerator by the denominator.<\/p>\n<p>Example: 17\/5 = 3 2\/5<\/p>\n<h2>Mixed Number to Improper Fraction<\/h2>\n<p>Multiply the whole number by the denominator and add the numerator.<\/p>\n<p>Example: 4 3\/4 = (4 \u00d7 4 + 3) \/ 4 = 19\/4<\/p>\n<h2>Equivalent Fractions<\/h2>\n<p>Equivalent fractions express the same value.<\/p>\n<p>Example: 2\/3 = 4\/6 = 10\/15<\/p>\n<p>To create an equivalent fraction, multiply or divide both numerator and denominator by the same non-zero value.<\/p>\n<h2>Simplifying Fractions<\/h2>\n<p>To simplify a fraction, divide the numerator and denominator by their greatest common factor (GCF).<\/p>\n<p>Example: 18\/24 = (18 \u00f7 6) \/ (24 \u00f7 6) = 3\/4<\/p>\n<h2>Operations Involving Fractions<\/h2>\n<h2>Adding and Subtracting Fractions<\/h2>\n<h2>Like Fractions<\/h2>\n<p>For like fractions, add or subtract the numerators and keep the same denominator.<\/p>\n<p>Example: 3\/10 + 2\/10 = 5\/10 = 1\/2<\/p>\n<h2>Unlike Fractions<\/h2>\n<p>For unlike fractions, find the Least Common Denominator (LCD).<\/p>\n<p>Example: 2\/5 + 1\/4<\/p>\n<ul>\n<li>LCD of 5 and 4 is 20.<\/li>\n<li>2\/5 = 8\/20, 1\/4 = 5\/20.<\/li>\n<li>8\/20 + 5\/20 = 13\/20.<\/li>\n<\/ul>\n<h2>Multiplying Fractions<\/h2>\n<p>Multiply the numerators and then the denominators.<\/p>\n<p>Example: 3\/7 \u00d7 14\/5 = (3 \u00d7 14) \/ (7 \u00d7 5) = 42\/35 = 6\/5<\/p>\n<p>You can simplify early if possible by cross-cancelling common factors before multiplying.<\/p>\n<h2>Dividing Fractions<\/h2>\n<p>To divide by a fraction, multiply by its reciprocal.<\/p>\n<p>Example: 5\/6 \u00f7 2\/3 = 5\/6 \u00d7 3\/2 = 15\/12 = 5\/4<\/p>\n<h2>Converting Fractions to Decimals<\/h2>\n<p>To convert a fraction to a decimal, divide the numerator by the denominator.<\/p>\n<ul>\n<li>1\/2 = 0.5<\/li>\n<li>3\/4 = 0.75<\/li>\n<li>2\/3 = 0.666&#8230; (repeating)<\/li>\n<\/ul>\n<h2>Converting Decimals to Fractions<\/h2>\n<h2>Terminating Decimals<\/h2>\n<p>Count the decimal places and write the decimal as a fraction with a power of 10 as the denominator, then simplify.<\/p>\n<p>Example: 0.125 = 125\/1000 = 1\/8<\/p>\n<h2>Repeating Decimals<\/h2>\n<p>Use an algebraic method for repeating decimals.<\/p>\n<p>Example: let x = 0.333&#8230;<\/p>\n<ul>\n<li>10x = 3.333&#8230;<\/li>\n<li>10x \u2212 x = 3.333&#8230; \u2212 0.333&#8230;<\/li>\n<li>9x = 3<\/li>\n<li>x = 3\/9 = 1\/3<\/li>\n<\/ul>\n<h2>What Are Decimals?<\/h2>\n<p>Decimals are another way of expressing fractions whose denominators are powers of 10.<\/p>\n<p>Example: 0.8 = 8\/10<\/p>\n<h2>Place Values in Decimals<\/h2>\n<ul>\n<li>Tenths (0.1)<\/li>\n<li>Hundredths (0.01)<\/li>\n<li>Thousandths (0.001)<\/li>\n<\/ul>\n<p>Example: 0.527 has 5 tenths, 2 hundredths, and 7 thousandths.<\/p>\n<h2>Comparing Fractions and Decimals<\/h2>\n<h2>Method 1: Convert Fractions to Decimals<\/h2>\n<p>Convert the fractions to decimals and compare the values.<\/p>\n<p>Example: Which is bigger, 3\/5 or 0.55?<\/p>\n<ul>\n<li>3\/5 = 0.6<\/li>\n<li>0.6 &gt; 0.55, so 3\/5 is bigger.<\/li>\n<\/ul>\n<h2>Method 2: Convert Decimals to Fractions<\/h2>\n<p>Convert decimals to fractions and then compare, especially when an LCD is easy to find.<\/p>\n<h2>Ordering Fractions and Decimals<\/h2>\n<p>To order fractions and decimals, you can convert all of them to decimals or all of them to fractions.<\/p>\n<p>Example: Order 0.45, 1\/2, and 0.375 from least to greatest.<\/p>\n<ul>\n<li>1\/2 = 0.5<\/li>\n<li>So the order is: 0.375, 0.45, 0.5<\/li>\n<\/ul>\n<h2>Operations with Decimals<\/h2>\n<h2>Adding and Subtracting Decimals<\/h2>\n<p>Align the decimal points and then add or subtract as usual.<\/p>\n<p>Example:<\/p>\n<p>12.45 + 3.6 = 16.05<\/p>\n<h2>Multiplying Decimals<\/h2>\n<p>Ignore the decimal points and multiply as whole numbers, then count the total decimal places from both factors and place the decimal in the product accordingly.<\/p>\n<p>Example: 0.4 \u00d7 0.3<\/p>\n<ul>\n<li>4 \u00d7 3 = 12<\/li>\n<li>Total of two decimal places, so the answer is 0.12.<\/li>\n<\/ul>\n<h2>Dividing Decimals<\/h2>\n<p>Move the divisor\u2019s decimal point to the right until it becomes a whole number, and move the dividend\u2019s decimal point the same number of places. Then divide as with whole numbers.<\/p>\n<p>Example: 3.6 \u00f7 0.12<\/p>\n<ul>\n<li>Move decimal point two places: 3.6 \u2192 360, 0.12 \u2192 12<\/li>\n<li>360 \u00f7 12 = 30<\/li>\n<\/ul>\n<h2>Fractions and Decimals in Word Problems<\/h2>\n<p>Many Civil Service Exam questions require interpreting real-world scenarios with fractions and decimals.<\/p>\n<h2>Example 1: Work and Time<\/h2>\n<p>A worker completes 3\/4 of a task. The decimal form is 0.75.<\/p>\n<h2>Example 2: Discounts<\/h2>\n<p>A 25% discount can be represented as multiplying by 0.75 (because you pay 75% of the original price).<\/p>\n<h2>Example 3: Ratio and Proportion<\/h2>\n<p>Using fraction form is often easier for solving ratio and proportion equations, especially when numbers are already in fraction form.<\/p>\n<h2>Common Errors to Avoid<\/h2>\n<ul>\n<li>Forgetting to find a common denominator when adding or subtracting unlike fractions<\/li>\n<li>Misplacing decimal points during multiplication or division<\/li>\n<li>Not simplifying fractions to lowest terms<\/li>\n<li>Forgetting to convert denominators to powers of 10 when changing decimals to fractions<\/li>\n<li>Incorrect cross-multiplication when comparing fractions<\/li>\n<\/ul>\n<p>Being aware of these mistakes helps reduce errors on exam day.<\/p>\n<h2>Practice Questions with Solutions<\/h2>\n<p><strong>1. Convert 7\/8 to decimal.<\/strong><br \/>\n7 \u00f7 8 = 0.875<\/p>\n<p><strong>2. Add 3\/4 + 2\/5.<\/strong><br \/>\nLCD = 20. Convert: 3\/4 = 15\/20, 2\/5 = 8\/20. Sum = 23\/20 = 1.15<\/p>\n<p><strong>3. Multiply: 0.6 \u00d7 0.25<\/strong><br \/>\n6 \u00d7 25 = 150. There are three decimal places in total, so 0.150 = 0.15<\/p>\n<p><strong>4. Compare: 2\/3 and 0.67<\/strong><br \/>\n2\/3 \u2248 0.666&#8230;, so 0.67 is slightly larger.<\/p>\n<p><strong>5. Divide: 5\/6 \u00f7 1\/3<\/strong><br \/>\n5\/6 \u00d7 3\/1 = 15\/6 = 5\/2 = 2.5<\/p>\n<p><strong>6. Simplify: 42\/56<\/strong><br \/>\nGCF is 14, so 42\/56 = (42 \u00f7 14) \/ (56 \u00f7 14) = 3\/4<\/p>\n<p><strong>7. Convert 0.048 to a fraction.<\/strong><br \/>\n0.048 = 48\/1000 = 6\/125 after simplification.<\/p>\n<p><strong>8. Subtract: 3.75 \u2212 2.08<\/strong><br \/>\n3.75 \u2212 2.08 = 1.67<\/p>\n<p><strong>9. Order from least to greatest: 1\/4, 0.3, 0.28<\/strong><br \/>\n1\/4 = 0.25, so the order is: 0.25, 0.28, 0.3<\/p>\n<p><strong>10. A tank is 5\/6 full. What percent is this?<\/strong><br \/>\n5\/6 \u2248 0.833&#8230;, which is approximately 83.33%<\/p>\n<h2>Final Tips for the Civil Service Exam<\/h2>\n<ul>\n<li>Always simplify fractions when possible to reduce computation.<\/li>\n<li>Use approximation when comparing decimals to save time.<\/li>\n<li>Practice mental math to handle decimal operations quickly.<\/li>\n<li>Convert everything into the same form (all fractions or all decimals) before comparing values.<\/li>\n<li>When time is limited, choose the fastest conversion or computation method that you are comfortable with.<\/li>\n<\/ul>\n<p>Mastering fractions and decimals gives you a strong advantage in the numerical ability section. Regular practice will help build accuracy and speed, which are essential skills for passing the Civil Service Exam.<\/p>\n<h2>Problem Sets<\/h2>\n<p><strong>Instructions:<\/strong> Answer the following questions on fractions and decimals. Show your solutions on scratch paper if you are using this for practice. These problems are patterned after typical Civil Service Exam numerical ability questions.<\/p>\n<p><strong>Question 1.<\/strong> Write the fraction 3\/5 in words and explain its meaning in English.<\/p>\n<p><strong>Question 2.<\/strong> Simplify the following fractions to lowest terms:<\/p>\n<ul>\n<li>a) 18\/24<\/li>\n<li>b) 42\/56<\/li>\n<li>c) 30\/45<\/li>\n<\/ul>\n<p><strong>Question 3.<\/strong> Convert the following improper fractions to mixed numbers:<\/p>\n<ul>\n<li>a) 17\/5<\/li>\n<li>b) 29\/4<\/li>\n<li>c) 50\/9<\/li>\n<\/ul>\n<p><strong>Question 4.<\/strong> Convert the following mixed numbers to improper fractions:<\/p>\n<ul>\n<li>a) 3 2\/3<\/li>\n<li>b) 4 3\/4<\/li>\n<li>c) 7 1\/5<\/li>\n<\/ul>\n<p><strong>Question 5.<\/strong> Add or subtract the following fractions and give your answer in simplest form:<\/p>\n<ul>\n<li>a) 3\/10 + 2\/10<\/li>\n<li>b) 2\/5 + 1\/4<\/li>\n<li>c) 7\/8 \u2212 3\/8<\/li>\n<li>d) 5\/6 \u2212 1\/3<\/li>\n<\/ul>\n<p><strong>Question 6.<\/strong> Multiply the following fractions. Simplify your answers:<\/p>\n<ul>\n<li>a) 3\/7 \u00d7 14\/5<\/li>\n<li>b) 2\/3 \u00d7 9\/4<\/li>\n<li>c) 5\/8 \u00d7 4\/15<\/li>\n<\/ul>\n<p><strong>Question 7.<\/strong> Divide the following fractions. Write answers in simplest form:<\/p>\n<ul>\n<li>a) 5\/6 \u00f7 2\/3<\/li>\n<li>b) 7\/9 \u00f7 1\/3<\/li>\n<li>c) 4\/5 \u00f7 6\/7<\/li>\n<\/ul>\n<p><strong>Question 8.<\/strong> Convert the following fractions to decimals. Round to three decimal places if necessary:<\/p>\n<ul>\n<li>a) 1\/2<\/li>\n<li>b) 3\/4<\/li>\n<li>c) 2\/3<\/li>\n<li>d) 5\/8<\/li>\n<\/ul>\n<p><strong>Question 9.<\/strong> Convert the following decimals to fractions in simplest form:<\/p>\n<ul>\n<li>a) 0.4<\/li>\n<li>b) 0.125<\/li>\n<li>c) 0.75<\/li>\n<li>d) 0.048<\/li>\n<\/ul>\n<p><strong>Question 10.<\/strong> Compare the following pairs of numbers using &lt;, &gt;, or =:<\/p>\n<ul>\n<li>a) 3\/5 ___ 0.55<\/li>\n<li>b) 2\/3 ___ 0.67<\/li>\n<li>c) 1\/4 ___ 0.25<\/li>\n<li>d) 5\/6 ___ 0.8<\/li>\n<\/ul>\n<p><strong>Question 11.<\/strong> Arrange the following numbers in ascending (increasing) order:<\/p>\n<ul>\n<li>a) 0.45, 1\/2, 0.375<\/li>\n<li>b) 1\/4, 0.3, 0.28<\/li>\n<\/ul>\n<p><strong>Question 12.<\/strong> Perform the following operations with decimals:<\/p>\n<ul>\n<li>a) 12.45 + 3.6<\/li>\n<li>b) 15.08 \u2212 6.725<\/li>\n<li>c) 0.6 \u00d7 0.25<\/li>\n<li>d) 3.6 \u00f7 0.12<\/li>\n<\/ul>\n<p><strong>Question 13.<\/strong> A water tank is 3\/4 full. Express this as:<\/p>\n<ul>\n<li>a) a decimal<\/li>\n<li>b) a percentage<\/li>\n<\/ul>\n<p><strong>Question 14.<\/strong> A student scored 18 out of 25 items in a test.<\/p>\n<ul>\n<li style=\"list-style-type: none;\">\n<ul>\n<li>a) Express the score as a fraction in simplest form.<\/li>\n<li>b) Express the score as a decimal.<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p>&lt;li)c) Express the score as a percentage.<\/p>\n<p><strong>Question 15.<\/strong> A shirt originally costs 800 pesos and is sold at a 25% discount.<\/p>\n<ul>\n<li>a) What decimal represents the part you have to pay after the discount?<\/li>\n<li>b) How much is the discount in pesos?<\/li>\n<li>c) What is the final price of the shirt?<\/li>\n<\/ul>\n<p><strong>Question 16.<\/strong> A worker completes 5\/6 of a job in one day.<\/p>\n<ul>\n<li>a) Express 5\/6 as a decimal (rounded to three decimal places).<\/li>\n<li>b) Express 5\/6 as a percentage (rounded to the nearest tenth of a percent).<\/li>\n<\/ul>\n<p><strong>Question 17.<\/strong> A recipe requires 2 1\/2 cups of flour and 3\/4 cup of sugar.<\/p>\n<ul>\n<li>a) Express 2 1\/2 as an improper fraction.<\/li>\n<li>b) How many cups total are needed if you combine the flour and sugar? Write your answer as a mixed number.<\/li>\n<\/ul>\n<p><strong>Question 18.<\/strong> In a class, 3\/8 of the students are male and the rest are female.<\/p>\n<ul>\n<li>a) What fraction of the class is female?<\/li>\n<li>b) Express the fraction of female students as a decimal.<\/li>\n<li>c) Express the fraction of female students as a percentage.<\/li>\n<\/ul>\n<p><strong>Question 19.<\/strong> A jogger completes 0.75 of a 12-kilometer route.<\/p>\n<ul>\n<li>a) Express 0.75 as a fraction in simplest form.<\/li>\n<li>b) How many kilometers did the jogger complete?<\/li>\n<\/ul>\n<p><strong>Question 20.<\/strong> A container holds 1.25 liters of juice. Express 1.25 as:<\/p>\n<ul>\n<li>a) a fraction in simplest form<\/li>\n<li>b) a mixed number<\/li>\n<\/ul>\n<p><strong>Question 21.<\/strong> A certain quantity x is equal to 0.333&#8230; in decimal form, where 3 repeats infinitely.<\/p>\n<ul>\n<li>a) Express x as a fraction.<\/li>\n<li>b) Explain briefly why this fraction is equivalent to the repeating decimal.<\/li>\n<\/ul>\n<p><strong>Question 22.<\/strong> Without using a calculator, estimate the answer and then compute exactly:<\/p>\n<ul>\n<li>a) 7\/8 + 0.3<\/li>\n<li>b) 2\/3 \u2212 0.15<\/li>\n<\/ul>\n<p><strong>Question 23.<\/strong> A Civil Service Exam item states: \u201cA tank is 2\/5 full. After adding 0.35 of its capacity, it becomes completely full.\u201d Is this statement logically correct? Show your reasoning using fraction or decimal operations.<\/p>\n<p><strong>Question 24.<\/strong> A store marks up the price of an item by 1\/4 of its original price. The original price is 640 pesos.<\/p>\n<ul>\n<li>a) How much is the mark-up?<\/li>\n<li>b) What is the new selling price?<\/li>\n<li>c) Express the mark-up (1\/4) as a decimal and as a percentage.<\/li>\n<\/ul>\n<p><strong>Question 25.<\/strong> A fraction has a value of 0.2 when written as a decimal.<\/p>\n<ul>\n<li>a) Write this fraction in simplest form.<\/li>\n<li>b) Give another equivalent fraction with a denominator of 25.<\/li>\n<\/ul>\n<h2>Answer Key<\/h2>\n<p><strong>Question 1.<\/strong><br \/>\n3\/5 is read as \u201cthree fifths.\u201d It means 3 parts out of 5 equal parts of a whole.<\/p>\n<p><strong>Question 2.<\/strong><br \/>\na) 18\/24 = 3\/4<br \/>\nb) 42\/56 = 3\/4<br \/>\nc) 30\/45 = 2\/3<\/p>\n<p><strong>Question 3.<\/strong><br \/>\na) 17\/5 = 3 2\/5<br \/>\nb) 29\/4 = 7 1\/4<br \/>\nc) 50\/9 = 5 5\/9<\/p>\n<p><strong>Question 4.<\/strong><br \/>\na) 3 2\/3 = 11\/3<br \/>\nb) 4 3\/4 = 19\/4<br \/>\nc) 7 1\/5 = 36\/5<\/p>\n<p><strong>Question 5.<\/strong><br \/>\na) 3\/10 + 2\/10 = 5\/10 = 1\/2<br \/>\nb) 2\/5 + 1\/4 = 8\/20 + 5\/20 = 13\/20<br \/>\nc) 7\/8 \u2212 3\/8 = 4\/8 = 1\/2<br \/>\nd) 5\/6 \u2212 1\/3 = 5\/6 \u2212 2\/6 = 3\/6 = 1\/2<\/p>\n<p><strong>Question 6.<\/strong><br \/>\na) 3\/7 \u00d7 14\/5 = (3 \u00d7 14) \/ (7 \u00d7 5) = 42\/35 = 6\/5 = 1 1\/5<br \/>\nb) 2\/3 \u00d7 9\/4 = (2 \u00d7 9) \/ (3 \u00d7 4) = 18\/12 = 3\/2 = 1 1\/2<br \/>\nc) 5\/8 \u00d7 4\/15 = (5 \u00d7 4) \/ (8 \u00d7 15) = 20\/120 = 1\/6<\/p>\n<p><strong>Question 7.<\/strong><br \/>\na) 5\/6 \u00f7 2\/3 = 5\/6 \u00d7 3\/2 = 15\/12 = 5\/4 = 1 1\/4<br \/>\nb) 7\/9 \u00f7 1\/3 = 7\/9 \u00d7 3\/1 = 21\/9 = 7\/3 = 2 1\/3<br \/>\nc) 4\/5 \u00f7 6\/7 = 4\/5 \u00d7 7\/6 = 28\/30 = 14\/15<\/p>\n<p><strong>Question 8.<\/strong><br \/>\na) 1\/2 = 0.5<br \/>\nb) 3\/4 = 0.75<br \/>\nc) 2\/3 \u2248 0.667 (to three decimal places)<br \/>\nd) 5\/8 = 0.625<\/p>\n<p><strong>Question 9.<\/strong><br \/>\na) 0.4 = 4\/10 = 2\/5<br \/>\nb) 0.125 = 125\/1000 = 1\/8<br \/>\nc) 0.75 = 75\/100 = 3\/4<br \/>\nd) 0.048 = 48\/1000 = 6\/125<\/p>\n<p><strong>Question 10.<\/strong><br \/>\na) 3\/5 = 0.6 &gt; 0.55 \u2192 3\/5 &gt; 0.55<br \/>\nb) 2\/3 \u2248 0.667 &lt; 0.67 \u2192 2\/3 &lt; 0.67<br \/>\nc) 1\/4 = 0.25 = 0.25 \u2192 1\/4 = 0.25<br \/>\nd) 5\/6 \u2248 0.833 &gt; 0.8 \u2192 5\/6 &gt; 0.8<\/p>\n<p><strong>Question 11.<\/strong><br \/>\na) 0.375, 0.45, 1\/2<br \/>\nb) 1\/4, 0.28, 0.3<\/p>\n<p><strong>Question 12.<\/strong><br \/>\na) 12.45 + 3.6 = 16.05<br \/>\nb) 15.08 \u2212 6.725 = 8.355<br \/>\nc) 0.6 \u00d7 0.25 = 0.15<br \/>\nd) 3.6 \u00f7 0.12 = 30<\/p>\n<p><strong>Question 13.<\/strong><br \/>\na) 3\/4 as a decimal = 0.75<br \/>\nb) 3\/4 as a percentage = 75%<\/p>\n<p><strong>Question 14.<\/strong><br \/>\na) Fraction (simplest form): 18\/25<br \/>\nb) Decimal: 18 \u00f7 25 = 0.72<br \/>\nc) Percentage: 72%<\/p>\n<p><strong>Question 15.<\/strong><br \/>\nOriginal price = 800 pesos; discount = 25%.<br \/>\na) Decimal representing the part you pay = 0.75 (75% of the price).<br \/>\nb) Discount in pesos = 800 \u00d7 0.25 = 200 pesos<br \/>\nc) Final price = 800 \u2212 200 = 600 pesos<\/p>\n<p><strong>Question 16.<\/strong><br \/>\na) 5\/6 as a decimal \u2248 0.833 (to three decimal places)<br \/>\nb) 5\/6 as a percentage \u2248 83.3% (to the nearest tenth of a percent)<\/p>\n<p><strong>Question 17.<\/strong><br \/>\na) 2 1\/2 as an improper fraction = (2 \u00d7 2 + 1)\/2 = 5\/2<br \/>\nb) Total cups = 2 1\/2 + 3\/4 = 5\/2 + 3\/4 = 10\/4 + 3\/4 = 13\/4 = 3 1\/4 cups<\/p>\n<p><strong>Question 18.<\/strong><br \/>\nMale = 3\/8 of the class.<br \/>\na) Female fraction = 1 \u2212 3\/8 = 5\/8<br \/>\nb) Decimal: 5\/8 = 0.625<br \/>\nc) Percentage: 0.625 \u00d7 100 = 62.5%<\/p>\n<p><strong>Question 19.<\/strong><br \/>\nRoute = 12 km, jogger completes 0.75 of it.<br \/>\na) 0.75 as a fraction = 75\/100 = 3\/4<br \/>\nb) Distance completed = 0.75 \u00d7 12 = 9 km<\/p>\n<p><strong>Question 20.<\/strong><br \/>\na) 1.25 as a fraction = 125\/100 = 5\/4<br \/>\nb) As a mixed number = 1 1\/4<\/p>\n<p><strong>Question 21.<\/strong><br \/>\nx = 0.333&#8230; (3 repeats).<br \/>\na) x as a fraction = 1\/3<br \/>\nb) Explanation (brief): Let x = 0.333&#8230;, then 10x = 3.333&#8230;. Subtracting x from 10x gives 9x = 3, so x = 3\/9 = 1\/3. Therefore, 0.333&#8230; is equivalent to 1\/3.<\/p>\n<p><strong>Question 22.<\/strong><br \/>\na) 7\/8 + 0.3<br \/>\n7\/8 = 0.875, so 0.875 + 0.3 = 1.175.<br \/>\nAs a fraction: 7\/8 + 3\/10 = 35\/40 + 12\/40 = 47\/40 = 1 7\/40.<br \/>\nb) 2\/3 \u2212 0.15<br \/>\n2\/3 \u2248 0.667; 0.667 \u2212 0.15 \u2248 0.517.<br \/>\nExact as a fraction: 2\/3 \u2212 15\/100 = 200\/300 \u2212 45\/300 = 155\/300 = 31\/60 \u2248 0.517.<\/p>\n<p><strong>Question 23.<\/strong><br \/>\nTank is 2\/5 full, add 0.35 of its capacity.<br \/>\n2\/5 as a decimal = 0.4.<br \/>\n0.4 + 0.35 = 0.75, which is 3\/4 of the capacity, not full (1.0).<br \/>\nTherefore, the statement is <strong>not logically correct<\/strong>. To become completely full, you would need to add 3\/5 (0.6) of the tank\u2019s capacity, not 0.35.<\/p>\n<p><strong>Question 24.<\/strong><br \/>\nOriginal price = 640 pesos, mark-up = 1\/4 of original price.<br \/>\na) Mark-up = 640 \u00d7 1\/4 = 160 pesos<br \/>\nb) New selling price = 640 + 160 = 800 pesos<br \/>\nc) 1\/4 as a decimal = 0.25; as a percentage = 25%<\/p>\n<p><strong>Question 25.<\/strong><br \/>\nDecimal value = 0.2<br \/>\na) 0.2 as a fraction = 2\/10 = 1\/5 (simplest form)<br \/>\nb) With denominator 25: 1\/5 = 5\/25<\/p>\n","protected":false},"excerpt":{"rendered":"","protected":false},"author":1,"featured_media":18590,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"_kad_blocks_custom_css":"","_kad_blocks_head_custom_js":"","_kad_blocks_body_custom_js":"","_kad_blocks_footer_custom_js":"","footnotes":""},"categories":[107],"tags":[],"class_list":["post-18587","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-civil-service-exam"],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v25.6 (Yoast SEO v25.6) - 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