Podcast
Questions and Answers
What is the simplified form of the fraction $\frac{18}{24}$?
What is the simplified form of the fraction $\frac{18}{24}$?
- $\frac{2}{3}$
- $\frac{3}{8}$
- $\frac{4}{5}$
- $\frac{3}{4}$ (correct)
What is the result of adding the decimal numbers 12.34567 and -4.98765?
What is the result of adding the decimal numbers 12.34567 and -4.98765?
- 7.35802 (correct)
- 8.35820
- 8.35802
- 7.35820
What is $75%$ of 220?
What is $75%$ of 220?
- 165 (correct)
- 175
- 150
- 180
Which of the following represents the percent change when a quantity increases from 50 to 75?
Which of the following represents the percent change when a quantity increases from 50 to 75?
What is the result of multiplying the mixed number $2\frac{1}{2}$ by 4?
What is the result of multiplying the mixed number $2\frac{1}{2}$ by 4?
Flashcards
Improper Fraction
Improper Fraction
A fraction where the numerator is greater than or equal to the denominator, representing a value greater than or equal to one.
Adding and Subtracting Fractions
Adding and Subtracting Fractions
Adding or subtracting fractions with the same denominator: add or subtract the numerators and keep the denominator the same. If the denominators are different, find a common denominator first.
Multiplying Fractions
Multiplying Fractions
To multiply fractions, multiply the numerators and the denominators. If you're multiplying a fraction and a whole number, think of the whole number as a fraction with 1 as the denominator.
Dividing Fractions
Dividing Fractions
Dividing by a fraction is the same as multiplying by its reciprocal. The reciprocal of a fraction is found by flipping the numerator and denominator.
Signup and view all the flashcards
Expressing one quantity as a percentage of another
Expressing one quantity as a percentage of another
To express one quantity as a percentage of another, divide the first quantity by the second quantity and multiply by 100%.
Signup and view all the flashcardsStudy Notes
Fractions
- Proper Fractions: Numerator is smaller than the denominator (e.g., 2/3).
- Improper Fractions: Numerator is greater than or equal to the denominator (e.g., 5/2).
- Mixed Numbers: Combination of a whole number and a fraction (e.g., 1 2/3).
- Simplifying Fractions: Reducing a fraction to its lowest terms by dividing the numerator and denominator by their greatest common factor (GCF).
- Adding/Subtracting Fractions: Find a common denominator, then add/subtract the numerators.
- Multiplying Fractions: Multiply the numerators and the denominators.
- Dividing Fractions: Invert the second fraction and multiply (reciprocal).
- Adding/Subtracting Mixed Numbers: Convert mixed numbers to improper fractions, then proceed as with fractions.
- Multiplying/Dividing Mixed Numbers: Convert mixed numbers to improper fractions, then proceed as with fractions.
- Positive and Negative Fractions: Follow standard rules for multiplying, dividing, adding, and subtracting signed numbers.
Decimals
- Adding/Subtracting Decimals: Align the decimal points and proceed as with whole numbers.
- Multiplying Decimals by Whole Numbers: Multiply as with whole numbers; place the decimal point in the product based on the number of decimal places in the decimal.
- Multiplying Decimals by Decimals: Count the total number of decimal places in both numbers; place the decimal point in the product accordingly.
- Dividing Decimals: Move the decimal point in the divisor to make it a whole number. Move the decimal point in the dividend by the same number of places. Divide as with whole numbers.
- Adding/Subtracting Decimals to 5 decimal places: Carry out the calculation and ensure the result has the specified number of decimal places.
- Positive and Negative Decimals: Follow standard rules for multiplying, dividing, adding, and subtracting signed numbers.
Percentages
- Converting Decimals to Percentages: Multiply the decimal by 100 and add the percent symbol (%).
- Converting Fractions to Percentages: Divide the numerator by the denominator and multiply by 100.
- Converting Percentages to Decimals: Divide the percentage by 100 and remove the percent symbol.
- Expressing One Quantity as a Percentage of Another: Divide the quantity by the total quantity, then convert the decimal to a percentage.
- Calculating Percentage Changes: Find the difference between the original and new values, then express that difference as a percentage of the original value.
- Comparing Quantities Using Percentages: Compare quantities by expressing them as a percentage relative to a benchmark.
- Real-life Problems: Apply percentage concepts to solve practical problems (e.g., discounts, taxes, interest).
General Math
- Simplify fractions: To the simplest (irreducible) form.
- Order of Operations: Follow the correct order of operations when evaluating expressions (PEMDAS/BODMAS).
Test Structure Suggestions
- Multiple Choice: Focus on understanding concepts and applying procedures.
- Short Answer: Emphasis on demonstrating procedures and calculation.
- Word Problems: Incorporate real-life scenarios to assess application of the concepts.
- Problem Solving: Use real-life situations to evaluate the ability to translate, calculate, and interpret results.
Studying That Suits You
Use AI to generate personalized quizzes and flashcards to suit your learning preferences.
