Review of Fractions and Ratio UMI July 15, 2015 10% 30%

Adding Fractions Step 1: Make sure the bottom numbers There are 3 Simple Steps to add fractions: Step 1: Make sure the bottom numbers (the denominators) are the same Step 2: Add the top numbers (the numerators), put the answer over the denominator Step 3: Simplify the fraction (if needed)

1 2 5 + 2 3 = 7 5 + 2 3 = 21 15 + 10 15 = 31 15 =2 1 15

Subtracting Fractions There are 3 simple steps to subtract fractions Step 1. Make sure the bottom numbers (the denominators) are the same. Step 2. Subtract the top numbers (the numerators), Put the answer over the same denominator. Step 3. Simplify the fraction (if needed).

1 3 4 − 4 5 = 7 4 − 4 5 = 35 20 − 16 20 = 19 20

Multiplying Fractions There are 3 simple steps to multiply fractions: Multiply the top numbers (the numerators). 2. Multiply the bottom numbers (the denominators). 3. Simplify the fraction if needed.

1 2 3 × 3 5 = 5 3 × 3 5 =1

Dividing Fractions There are 3 simple steps to Divide fractions: Step 1. Turn the second fraction (the one you want to divide by) upside down (this is now a reciprocal). Step 2. Multiply the first fraction by that reciprocal. Step 3. Simplify the fraction (if needed).

3 2 12 ÷1 5 6 = 38 12 ÷ 11 6 = 38 12 × 6 11 = 19 11 =1 8 11

Please Excuse My Dear Aunt Sally Order of Operations Order of Operations Involving Fraction: Parentheses first-----P Exponents (i.e. Powers and Square Roots, etc.)-E Multiplication and Division (left-to-right)---MD Addition and Subtraction (left-to-right)---AS PEMDAS Please Excuse My Dear Aunt Sally 12/1/2018

2 3 + 4 15 ÷1 1 5 = 2 3 + 4 15 ÷ 6 5 = 2 3 + 4 15 × 5 6 = 2 3 + 2 9 = 6 9 + 2 9 = 8 9

Part-to-Part: "Part-to-Part" and "Part-to-Whole" Ratios: Example: There are 20 students, 5 are girls, and 15 are boys Part-to-Part: The ratio of boys to girls is 15:5=3:1 or 3/1 The ratio of girls to boys is 5:15=1:3 or 1/3

Part-to-Whole: The ratio of boys to all students is 15:20=3:4 or 3/4 The ratio of girls to all students is 5:20=1:4 or 1/4

Proportions Proportion says that two ratios (or fractions) are equal.

Worksheet #20 Solve: Let 𝑏=𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑏𝑜𝑦𝑠 𝑎𝑛𝑑 𝑔=𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑔𝑖𝑟𝑙𝑠 Given 𝑏 𝑡𝑜𝑡𝑎𝑙 = 5 8 , so 𝑏 𝑔 = 5 3 , this implies 3 𝑏=5 𝑔; From the given information we also have 𝑏=𝑔+6, Therefore, 3 (𝑔+6)=5 𝑔, which implies 2 𝑔=18; we have 𝑔=9 𝑎𝑛𝑑 𝑏=15. 𝑡𝑜𝑡𝑎𝑙=24. Answer: There are 24 students in my class.

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