Fractions
A fraction represents a part of a whole or a part of a group. It consists of a numerator (the top number) and a denominator (the bottom number). The numerator represents the number of parts we have, and the denominator represents the total number of parts that make up the whole or the group.
Types of Fractions
There are different types of fractions:
- Proper Fraction: A fraction where the numerator is less than the denominator, e.g., 3/4.
- Improper Fraction: A fraction where the numerator is greater than or equal to the denominator, e.g., 7/4.
- Mixed Number: A whole number combined with a fraction, e.g., 1 3/4.
- Equivalent Fractions: Fractions that represent the same value, e.g., 1/2 and 2/4.
Operations with Fractions
There are four basic operations that can be performed with fractions:
- Addition: To add fractions, make sure the denominators are the same, then add the numerators together and keep the denominator the same, e.g., 1/3 + 1/6 = (2/6) + (1/6) = 3/6 = 1/2.
- Subtraction: To subtract fractions, make sure the denominators are the same, then subtract the numerators and keep the denominator the same, e.g., 5/8 - 3/8 = 2/8 = 1/4.
- Multiplication: To multiply fractions, simply multiply the numerators together to get the new numerator and the denominators together to get the new denominator, e.g., 2/3 * 3/4 = (2*3)/(3*4) = 6/12 = 1/2.
- Division: To divide fractions, multiply the first fraction by the reciprocal of the second fraction, e.g., 2/3 ÷ 4/5 = 2/3 * 5/4 = (2*5)/(3*4) = 10/12 = 5/6.
Comparing Fractions
When comparing fractions, you can use the following methods:
- Common Denominator: Make the denominators the same, then compare the numerators.
- Cross-Multiplication: Multiply the numerator of the first fraction by the denominator of the second fraction and compare it with the product of the numerator of the second fraction and the denominator of the first fraction.
Practice Problems
Now that you understand fractions, try solving the following practice problems:
- Simplify the fraction 10/15.
- Add the fractions 1/4 and 1/3.
- Multiply the fractions 2/5 and 3/8.
- Compare the fractions 2/3 and 3/4 using a common denominator.
Good luck with your practice! If you need further assistance, feel free to reach out to me.
[Fractions] Related Worksheets and Study Guides:
.◂Math Worksheets and Study Guides Seventh Grade. Applying Percents
Study Guide
Applying Percents 
Worksheet/Answer key
Applying Percents Worksheet/Answer key
Applying Percents Worksheet/Answer key
Applying Percents
Worksheet/Answer keyWorksheet/Answer keyWorksheet/Answer keyThe resources above cover the following skills:
Number and Operations (NCTM)
Understand numbers, ways of representing numbers, relationships among numbers, and number systems.
Work flexibly with fractions, decimals, and percents to solve problems.
Grade 7 Curriculum Focal Points (NCTM)
Number and Operations and Algebra and Geometry: Developing an understanding of and applying proportionality, including similarity
Students extend their work with ratios to develop an understanding of proportionality that they apply to solve single and multi-step problems in numerous contexts. They use ratio and proportionality to solve a wide variety of percent problems, including problems involving discounts, interest, taxes, tips, and percent increase or decrease. They also solve problems about similar objects (including figures) by using scale factors that relate corresponding lengths of the objects or by using the fact that relationships of lengths within an object are preserved in similar objects. Students graph proportional relationships and identify the unit rate as the slope of the related line. They distinguish proportional relationships (y/x = k, or y = kx) from other relationships, including inverse proportionality (xy = k, or y = k/x).