How do you add and subtract fractions? Provide an example and demonstrate the steps you would take to arrive at the answer. What strategies would you use to help a student struggling with the concepts of adding and subtracting fractions?
These sites all have excellent explanations of adding and subtracting fractions.
http://www.math.com/school/subject1/lessons/S1U4L3GL.html
http://www.themathpage.com/Arith/add-fractions-subtract-fractions-1.htm
http://www.coolmath.com/fractions/fractions-12-adding-subtracting-different-denominators-01.html
http://jamit.com.au/htmlFolder/FRAC1007.html
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It's easy to add and subtract like fractions, or fractions with the same denominator. You just add or subtract the numerators and keep the same denominator. The tricky part comes when you add or subtract fractions that have different denominators. Since only like fractions can be added or subtracted, we first have to convert unlike fractions to equal like fractions. We want to find the smallest, or least, common denominator, because working with smaller numbers makes doing the math easier. The least common denominator, or LCD, of two fractions is the smallest number that can be divided by both denominators. Rewrite the fractions as equivalent fractions with the LCM as the denominator. Then add or subtract only the numerators and keep the denominator the same. For mixed numbers, you add the whole numbers and add the fractions separately, or change them to improper fractions then find the LCD. Then, add or subtract and simplify.
I prefer to write the multiples of both denominators until I find a common multiple.
Let’s solve the problem: ¾ + 1/6
Simply start writing all the multiples of both denominators, beginning with the numbers themselves. For example: Multiples of 4 are 4, 8, 12, 16, and so on (because 1 × 4=4, 2 × 4=8, 3 × 4=12, 4 × 4=16, etc.). The multiples of 6 are 6, 12, …-- wait, stop! That's the number we're looking for, 12, because it's the first one that appears in both lists of multiples. It's the least common multiple, which we'll use as our least common denominator.
Now that we have our least common denominator, we can make equal like fractions by multiplying the numerator and denominator of each fraction by the factor needed. We multiply 3/4 by 3/3, since 3 times 4 is 12, and we multiply 1/6 by 2/2, since 2 times 6 is 12. This gives the equal like fractions 9/12 and 2/12. Now we can add the numerators, 9 + 2, to find the answer, 11/12. 11/12 is its simplest form, because we cannot divide it by 2 evenly and 11 is a prime number.
To add and subtract fractions, you need to follow a few steps:
1. Ensure that the denominators (the bottom numbers) are the same for both fractions involved. If they are not the same, find a common denominator by finding the least common multiple (LCM) of the denominators.
2. Once you have the same denominators, you can add or subtract the numerators (the top numbers). The numerator is the number that is being added or subtracted in the fraction.
3. Write the resulting fraction with the common denominator.
Here's an example:
Let's say we want to add 1/4 and 2/3.
Step 1: Find a common denominator. The least common multiple of 4 and 3 is 12, so we'll use 12 as the common denominator.
Step 2: Convert the fractions to have the common denominator:
1/4 becomes 3/12 (multiply numerator and denominator by 3)
2/3 becomes 8/12 (multiply numerator and denominator by 4)
Step 3: Add the fractions:
3/12 + 8/12 = 11/12
So, 1/4 + 2/3 = 11/12.
Now, let's discuss some strategies to help a student struggling with adding and subtracting fractions:
1. Visual aids: Use visual models such as fraction bars or circles to demonstrate the concept of adding and subtracting fractions. These models help students understand how fractions combine or separate.
2. Practice with manipulatives: Provide students with physical objects like fraction tiles, cubes, or paper strips. Allow them to physically manipulate the fractions to visualize the addition or subtraction process.
3. Find real-life examples: Relate the concept to real-life scenarios. For example, discussing splitting a pizza into equal parts or sharing a set of objects among friends can make the concept more relatable and engaging.
4. Step-by-step approach: Break down the steps into smaller parts and guide the student through each step. Encourage them to write down the steps and double-check their work.
5. Provide ample practice: Offer plenty of practice problems with different levels of difficulty. Encourage students to practice regularly to improve their skills and build confidence.
6. Individualized support: If a student continues to struggle, provide individualized support. Offer additional mini-lessons, one-on-one time, or access to online resources to cater to their specific needs.
Remember, patience and perseverance are crucial when helping a student struggling with adding and subtracting fractions. With consistent support and practice, most students can grasp the concepts and improve their skills in this area.