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?

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.

I'm a student, but my Mother helped me understand by using toys that I like.

We used LEGOS. There are little “bumps” on top of LEGO elements. These are what makes LEGO “stick” together, called studs. We (LEGO fans) usually refer to parts not by inches or centimeters, but by the number of studs the part has. For example, a brick that has 2 studs on the short side and 4 studs on the longer side is called a 2×4 brick.

A plate with 4 studs on the short side and 8 studs on the long side is called a 4×8 plate.

We added and subtracted each different lego, but changed it to fractions. 2x4 was moved to 1/2.

Hello!

The equation you made for that question was fabulous. I'm a student at Markham Middle School in Placerville and this was so helpful. I had a hard question on one of my homework pieces, it was double points so I really need something to help me. When I read this my mind was blown. I have never seen something so amazing like this Dawson! Thx
- Lela

To add and subtract fractions, you follow some basic steps.

Adding Fractions:
1. Make sure the denominators (the bottom numbers) are the same. If they are not the same, find a common denominator by multiplying the denominators together.
2. Once you have the same denominators, add the numerators (the top numbers) together to get the new numerator.
3. Keep the denominator the same.
4. Simplify the fraction if necessary by finding the greatest common factor (GCF) of the numerator and denominator and dividing both by the GCF.

Subtracting Fractions:
The process for subtracting fractions is the same as adding, except that instead of adding the numerators, you subtract them.

Now, let's look at an example of adding fractions:

Example: 1/4 + 3/8

Step 1: Determine a common denominator. In this case, we can use 8 as the common denominator since both 4 and 8 divide evenly into 8.
1/4 = 2/8 (multiplied numerator and denominator by 2)
3/8 = 3/8 (denominator already matches)

Step 2: Add the numerators together.
2/8 + 3/8 = 5/8

Step 3: Keep the denominator the same.
Final answer: 5/8

When helping a student struggling with adding and subtracting fractions, you can use the following strategies:

1. Explain the concept visually: Use diagrams or visual representations to help them understand the parts and how they are combined or subtracted.

2. Use real-life examples: Relate the concept to everyday situations, such as dividing a pizza or sharing candy, to make it more relatable and understandable.

3. Provide practice problems: Offer a variety of practice problems to reinforce the steps and help them gain confidence and fluency with the process.

4. Break it down: Break the process into smaller steps or components that the student can tackle one at a time. This can make the task less overwhelming.

5. Use manipulatives: Manipulatives, such as fraction bars or circles, can be helpful tools to visually represent fractions and demonstrate operations.

6. Encourage estimation: Encourage students to estimate the answer before performing the calculations. This helps develop number sense and supports the understanding of the relative size of fractions.

7. Provide guided practice: Offer step-by-step guidance and feedback as the student works through problems. Gradually release responsibility as they gain confidence and mastery.

Remember, practice and repetition are crucial in mastering the skills of adding and subtracting fractions.

Chayo, I have never considered fractions the least bit artistic. I like the idea of whole pictures better. Please use the correct title for your posts.

Dawson no one is going to read that.