UAT Boot Camp 2019

In UAT, Ratio and Percentage can be hidden inside many real life word problem scenarios. Age problems, Money/income problems, Profit and loss, Discount problems, Mixture problems, Students/classroom problems, Population problems, Data interpretation, Time/distance/speed problems, Work and productivity problems, Exam marks/score problems, Price increase/decrease, Salary increase/decrease, Ratio comparison problems, Percentage change problems, Part to whole problems, Sharing/distribution problems .. etc @UATBootcamp

Using Ratio and Percentage concepts, you can answer more than 7 questions on the actual UAT. This also includes questions from the Data Interpretation section. If you’re not confident in these two topics, you could literally miss 7+ questions simply because of weak fundamentals. Master these concepts they can make a significant difference in your UAT score. @UATBootCamp

የዛሬው የግማሽ ቀን ጥናታችን ይሄን ይመስል ነበር እንዴት አገኛችሁት? በኮመንት የተሰማችሁን ጻፉልን👇 ከሰዓት የልምምድ ጥያቄ ይቀጥላል። @UATbootcamp

QUICK PRACTICE 1⃣.In a classroom, there are 12 boys and 16 girls. What is the simplified ratio of boys to girls 3:4 2⃣ Using the same classroom (12 boys and 16 girls), what is the simplified ratio of girls to total students? 4:7 3⃣.A bag contains 3 red marbles and 7 blue marbles. What is the ratio of red to blue marbles, and what fraction of the total marbles are red? 4⃣.Which ratio is larger: 5 : 8 or 3 : 5? 5⃣.Which of the following ratios is equivalent to 4 : 10 Drop your answer in comment.👇 @UATbootcamp

INVERSE PROPORTION ​🔹​​1. WHAT IS INVERSE PROPORTION? Two quantities are in inverse proportion when an increase in one causes a proportional decrease in the other, and vice versa.

• If you double one quantity, the other quantity gets cut in half.

​🔹​​2. CONSTANT PRODUCT (k) In inverse proportion, multiplying the two quantities (x and y) together always equals the same constant value (k).

• Formula: x × y = k  or  y = k / x

• Example: If 2 workers take 6 hours to finish a job, 2 \times 6 = 12. The constant workload value is 12 worker-hours. ​🔹​​3. CORE EXAMPLES

• Workers and Time: More workers on a project = less time needed to complete it.

• Speed and Time: Driving at a higher speed = less time taken to reach the destination.

• Number of People and Workload:

More people sharing a set task = less work for each individual person.

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DIRECT PROPORTION ​🔹​1. WHAT IS DIRECT PROPORTION? Two quantities are in direct proportion when an increase in one leads to a proportional increase in the other, and a decrease in one leads to a proportional decrease in the other.

• If you buy twice as many items, the total cost doubles. • If you buy half as many items, the total cost halves

. ​🔹​2. CONSTANT RATIO (k) In direct proportion, dividing one quantity (y) by the other (x) always gives the same constant value, known as the constant of proportionality (k). • Formula: y / x = k  or  y = kx • Example: If 3 notebooks cost $6, then 6 / 3 = 2. The constant cost is $2 per notebook. ​🔹​3. REAL-LIFE APPLICATIONS

• Shopping: More items purchased = higher total cost. • Fuel Usage: Longer driving distance = more fuel used. • Earnings: More hours worked = higher total pay

. ​🔹DIRECT PROPORTION EXAMPLES ​🔹​1. Quantity and Cost

• Concept: The more items you buy, the higher the total cost.

• Example: If 1 t-shirt costs $15, 3 t-shirts cost $45. • Calculation: Cost= 15 ×Quantity ​🔹​2. Workers and Output

• Concept: Assuming everyone works at the same steady rate, adding more workers increases the total amount produced in a given time.

• Example: If 2 bakers make 50 loaves of bread in a morning, 6 bakers can make 150 loaves in the same time frame. • Calculation: Output= 25 ×Workers ​🔹​3. Distance and Time at Constant Speed

• Concept: When speed stays the same, travelling for a longer duration covers more distance

. • Example: A train moving at a fixed speed of 60 km/h covers 60 km in 1 hour and 180 km in 3 hours. • Calculation: Distance= 60 ×Time @UATbootcamp

➗PROPORTION ​🔹​1. MEANING OF PROPORTION

A proportion is an equation showing that two ratios or fractions are equal

. • Example: 1/2 = 4/8 is a proportion because both ratios represent the exact same value. ​🔹​2. EQUIVALENT PROPORTIONALITY

Two ratios are in an equivalent proportion if they simplify to the same fraction or yield the same decimal.

• Example: Are 3:4 and 9:12 proportional? 3/4 = 0.75 9/12 = 0.75 Yes, they form an equivalent proportion. ​🔹​3. CROSS MULTIPLICATION

For any true proportion a/b = c/d, the diagonal products (cross-products) are always equal

a x d = b x c ​• Example: Check 2/5 = 6/15 2 x 15 = 30 5 x 6 = 30 Since 30 = 30, the proportion is correct. ​🔹​4. FINDING AN UNKNOWN

Use cross multiplication to set up a simple equation when one number is missing

. • Example: Solve for x in 4/7 = x/21 4 x 21 = 7 x x 84 = 7x x = 84 / 7 = 12 ​🔹​5. COMPARING TWO RATIOS

To compare two ratios and determine which is larger, convert both to decimals or cross-multiply

. • Example: Which is larger, 3:5 or 2:3? 3/5 = 0.60 2/3 = 0.66... So, 2:3 is larger than 3:5. @UATbootcamp

📐 EQUIVALENT RATIOS STUDY ​🔹 1. Multiplying Both Terms Multiply both numbers in a ratio by the same non-zero number. Example: 2:3 (×4) ➔ 8:12 ​🔹 2. Dividing Both Terms Divide both numbers by the same common factor. Example: 10:15 (÷5) ➔ 2:3 ​🔹 3. Simplifying Ratios Divide all parts by their Greatest Common Factor (GCF) to reach lowest terms. Example: Simplify 18:24 (÷6) ➔ 3:4 ​🔹 4. Finding Missing Terms Find the multiplier or divisor between known parts to find the unknown value. Example: 4:5 = 12:x (4 × 3 = 12, so 5 × 3) ➔ x = 15 @UATbootcamp

📐 Ratio and Total Quantity ​🔹​1. Finding Total Parts

To find total parts, add all numbers in the ratio together

. Example: Ratio 2:3:5 ➔ Total parts = 2 + 3 + 5 = 10 parts. ​🔹​2. Finding One Part

Divide the total quantity by the total number of parts.

. Example: Total quantity = $100, Total parts = 5. One part = 100 / 5 = $20. ​🔹​3. Finding Individual Quantities

Multiply the value of one part by each specific ratio number.

. Example: One part = $20. Ratio is 2:3. Quantity 1 = 2 * 20 = $40. Quantity 2 = 3 * 20 = $60. ​🔹​4. Dividing a Quantity According to a Ratio

Combine the steps: Add parts, find one part, then multiply across the ratio.

Example: Divide 40 kg in ratio 1:3. Total parts = 1 + 3 = 4. One part = 40 / 4 = 10 kg. Shares = 10 kg and 30 kg. ​🔹​5. Sharing Money According to a Ratio Example: Share $150 between Alex and Sam in ratio 2:3. Total parts = 5. One part = 150 / 5 = $30. Alex = 2 * 30 = $60. Sam = 3 * 30 = $90 ​🔹​6. Sharing Students According to a Ratio Example: 60 students split into two groups in ratio 1:5. Total parts = 6. One part = 60 / 6 = 10. Group A = 10 students. Group B = 5 * 10 = 50 students. @UATbootcamp

RATIOS & PROPORTIONS MASTERCLASS ​1️⃣ BASIC RATIO ​💡 What is a Ratio? = A ratio compares two or more quantities of the same kind. It shows how much of one thing there is compared to another.

​Notation: A ratio can be written in three ways: ​Using a colon: a : b ​As a fraction: a/b ​Using words: "a to b"

​🔹 Part-to-Part vs. Part-to-Whole ​Part-to-Part: Compares one specific group to another group. ​Example: In a fruit basket with 3 apples and 5 oranges, the ratio of apples to oranges is 3 : 5. ​Part-to-Whole: Compares one group to the total combined amount. ​Example: The ratio of apples to total fruit is 3 : (3 + 5) = 3 : 8. ​🔹 Simplifying Ratios To simplify a ratio, divide all terms by their Greatest Common Factor (GCF). ​Example: Simplify 12 : 18. ​Both numbers can be divided by 6: ​(12 ÷6) : (18 ÷6) = 2 : 3. ​​🔹 EQUIVALENT RATIOS ​💡 What are Equivalent Ratios? Equivalent ratios are ratios that show the exact same relationship between numbers, even if the numbers look different.

​You can find equivalent ratios by multiplying or dividing both parts of a ratio by the same number.

​📌 Examples: ​By Multiplying: Start with 2 : 3 Multiply both sides by 2 ➔ 4 : 6 Multiply both sides by 3 ➔ 6 : 9 (2 : 3, 4 : 6, and 6 : 9 are all equivalent ratios!) ​By Dividing (Simplifying): Start with 10 : 15 Divide both sides by 5 ➔ 2 : 3 ​​🔹 COMPARING RATIOS ​💡 How to Compare Ratios? To find out which ratio is bigger or smaller, convert both ratios into fractions with the same denominator, or turn them into decimals. ​📌 Example: Which ratio is bigger: 3 : 4 or 2 : 3? ​Step 1: Convert to Fractions 3 : 4 = 3/4 2 : 3 = 2/3 ​Step 2: Find a Common Denominator (12) 3/4 ➔ (3 × 3) / (4 × 3) = 9/12 2/3 ➔ (2 × 4) / (3 × 4) = 8/12 ​Step 3: Compare Since 9/12 is bigger than 8/12, 3 : 4 is larger than 2 : 3! ​  ​🔹RATIO VS. FRACTION ​💡 What is the Difference? ​🔹 Ratio: ​Compares part to part (or part to whole). ​Shows how two amounts relate to each other. ​Example: A recipe uses 2 cups of sugar and 3 cups of flour. Ratio of sugar to flour = 2 : 3 ​🔹 Fraction: ​Compares a part to the WHOLE total. ​Shows how much of the total you have. ​Example: Total ingredients = 2 cups sugar + 3 cups flour = 5 cups total. Fraction of sugar = 2/5 (2 out of 5 total cups are sugar).

​📝 Quick Summary Tip:​ Ratio (2 : 3) ➔ 2 parts of A for every 3 parts of B.​ Fraction (2/5) ➔ 2 parts of A out of 5 total parts.

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DAY 3 IS HERE! 🎯 Today we’re focusing on one important thing: Do you really know what you’re preparing for? Stay active throughout the session. Take part in the polls, share your thoughts, and ask questions whenever something is not clear. Let’s begin Day 3. @UATbootcamp

ማነው 20/20 የደፈነ? 😄 👇 ደሞ ብቻችሁን ነው የምትፈተኑት አሉ😲 ኸረ ጓደኞቻችሁ ትዝ ይበሏችሁ ለብቻ አይበላም 😂 @UATbootcamp

The last one question remain.