7th Grade Math Final Exam: Basic Operations

Study Notes

Basic Operations with Numbers, Ratios, Rates, Unit Rates, and Percents

• Addition and subtraction with whole numbers involve finding the difference between two numbers. • Multiplication and division with whole numbers involve basic arithmetic operations. • Operations with decimals, fractions, and rational numbers involve performing arithmetic operations with these types of numbers. • Ratios can be written in simplest form by dividing both numbers by their greatest common divisor. • Rates can be calculated by dividing the distance traveled by the time taken. • Unit rates can be found by dividing the distance traveled by the time taken. • Percents can be calculated by dividing a percentage by 100 and multiplying it by the original value.

Discounts, Markups, Percent Change, and Simple Interest

• Discounts can be calculated by finding the percentage of the original price. • Markups can be calculated by adding a percentage to the original price. • Percent change can be calculated by finding the difference between the original and new values and dividing it by the original value. • Simple interest can be calculated by multiplying the principal, rate, and time.

Mixed Problems

• Word problems involving fractions and decimals require applying mathematical operations to real-life scenarios. • Real-life applications of math involve using formulas to solve problems. • Complex fraction operations involve simplifying fractions. • Decimal and fraction conversions involve changing between decimal and fraction forms. • Proportional relationships involve finding equivalent ratios. • Percentage increase or decrease can be calculated by finding the difference between the original and new values and dividing it by the original value. • Interest calculations involve finding the total interest earned over a period of time. • Ratio to fraction conversions involve writing a ratio as a fraction. • Finding percent of a number involves multiplying the number by the percentage. • Combining percent problems involves applying multiple percentage discounts or increases. • Multi-step problems with decimals require applying mathematical operations to solve problems. • Challenging multi-step problems involve solving complex problems with multiple steps.

Basic Operations with Numbers, Ratios, Rates, Unit Rates, and Percents

Perform addition and subtraction with whole numbers, involving subtraction of a number from another.
Multiply and divide whole numbers, and divide a number by another.
Add, subtract, multiply, and divide decimals, involving subtraction of a decimal from another.
Operate with fractions, including multiplication and division, and subtracting a fraction from another.
Calculate with rational numbers, including addition and multiplication.
Write ratios in simplest form, such as 18 apples to 24 oranges.
Calculate rates, such as miles per hour, given a distance and time.
Find unit rates, such as miles per hour, given a distance and time.
Calculate percents, such as finding 25% of a number, and convert to a percent.

Discounts, Markups, Percent Change, and Simple Interest

Calculate discounts, such as finding the sale price of an item with a 25% discount.
Calculate markups, such as finding the new price of an item with a 30% markup.
Calculate percent change, such as finding the percent increase in the price of a book.
Calculate simple interest, such as finding the interest on a loan with a 6% interest rate per year.

Mixed Problems

Solve word problems involving fractions, such as finding the amount of cake left after giving some away.
Apply math to real-life situations, such as finding how many hours a car can run on a tank of gas.
Simplify complex fractions.
Convert decimals to fractions in simplest form.
Identify proportional relationships, such as finding the cost of 7 notebooks given the cost of 3.
Calculate percentage increase or decrease, such as finding the percentage decrease in the price of a laptop.
Calculate interest, such as finding the interest earned on an investment with a 5% interest rate per year.