Percentages and Equivalent Fractions

Percentages and Equivalent Fractions

• A percentage is a relationship between 4 numbers, but the fourth number is always 100, which is the bottom number of the equivalent fraction.
• A percentage can be rewritten as a fraction with 100 as the bottom number, e.g. 10 is 20% of 50 can be rewritten as 10/50 = 20/100.

Components of a Percent Problem

• Part: the top number of the fraction (the part we have)
• Total: the bottom number of the fraction (the total)
• Percent: the number in front of the percent sign (the percentage)

Types of Percent Problems

• Type 1: Finding a percent of a number (e.g. what is 20% of 50?)
• Type 2: Finding the percent of a part (e.g. 10 is what percent of 50?)
• Type 3: Finding the total (e.g. 10 is 20% of what?)

Finding the Percent

• Method 1: Convert the fraction to an equivalent fraction with 100 as the bottom number (e.g. 35/50 = 70/100 = 70%)
• Method 2: Divide the part by the total to get the decimal value, then move the decimal point two places to the right to get the percent (e.g. 28 ÷ 80 = 0.35 = 35%)

Percentages and Equivalent Fractions

• A percentage is a relationship between 4 numbers, with 100 as the bottom number of the equivalent fraction.
• Percentages can be rewritten as fractions with 100 as the denominator.

Components of a Percent Problem

• The part is the top number of the fraction, representing the quantity we have.
• The total is the bottom number of the fraction, representing the whole.
• The percent is the number in front of the percent sign, indicating the percentage.

Types of Percent Problems

• Type 1: Finding a percentage of a number (e.g., what is 20% of 50?).
• Type 2: Finding the percentage of a part (e.g., 10 is what percent of 50?).
• Type 3: Finding the total (e.g., 10 is 20% of what?).

Finding the Percent

• Method 1: Convert the fraction to an equivalent fraction with 100 as the denominator.
• Method 2: Divide the part by the total to get the decimal value, then move the decimal point two places to the right to get the percent.

Order of Operations

• A set of rules to ensure consistent math problem solving, preventing multiple answers
• Four rules to follow in this order to avoid confusion

Step 1: Parentheses and Brackets

• Evaluate expressions inside parentheses and brackets FIRST
• Simplify each set of parentheses and brackets before moving on to the next step
• Group numbers and operators together using parentheses and brackets

Step 2: Exponents

• Simplify exponents NEXT, after operations in parentheses and brackets
• Exponents represent repeated multiplication, indicating how many times to multiply a number
• Evaluate exponents before moving on to the next step

Step 3: Multiplication and Division

• Evaluate multiplication and division operations from LEFT TO RIGHT
• Multiplication and division have the same priority, working from left to right
• If a problem has both multiplication and division, work from left to right

Step 4: Addition and Subtraction

• Evaluate addition and subtraction operations LAST, after all other operations
• Addition and subtraction have the same priority, working from left to right
• If a problem has both addition and subtraction, work from left to right