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### Course: 5th grade > Unit 4

Lesson 1: Strategies for adding and subtracting fractions with unlike denominators# Estimating adding fractions with unlike denominators

Learn all about estimating the sum of fractions with unlike denominators. Practice visualizing fractions and using that understanding to make reasonable estimates when adding them together.

## Want to join the conversation?

- Oml! No matter how hard I try I CANT GET It !(17 votes)
- me too！this is so hard！(8 votes)

- Hi will you teach me more pls(6 votes)
- and for everybody who does not know when estimating you do not need to find the answer.(6 votes)
- The answer is an inpropper fraction. Its 22/15(4 votes)
- So the I just venerated it into

1 and 7/15(2 votes)

- it is so hard! really hard!(4 votes)
- not really that hard tho(4 votes)
- how do you subtract them still i dont get it(3 votes)
- its easy when you figure it out lol(3 votes)
- what is fractions and how can you solve fraction problems(1 vote)
- Fractions are a way to represent parts of a whole or a collection of things. They are like slices of a pie! Here's how they work:

Numerator: The top number (e.g., 3 in 3/4) represents the number of parts you consider. Imagine you have a pie cut into 4 slices, and you take 3 of those slices.

Denominator: The bottom number (e.g., 4 in 3/4) represents the total number of parts the whole is divided into. In our pie example, the denominator is 4 because the pie was cut into 4 slices total.

Common types of fractions:

Proper fractions: When the numerator is smaller than the denominator (e.g., 3/4). The pie slices you consider (3) are fewer than the total slices (4).

Improper fractions: When the numerator is larger than or equal to the denominator (e.g., 5/4). This could represent having more slices (5) than the pie originally had (4), maybe you combined a whole pie with another slice.

Mixed numbers: A combination of a whole number and a fraction (e.g., 1 ½). Here, the 1 represents whole pies you have, and the ½ represents half of another pie.

Solving fraction problems:

There are four main operations we perform with fractions: addition, subtraction, multiplication, and division. Here's a quick guide:

Adding and subtracting fractions:

Fractions must have the same denominator (the number of slices must be the same size) before you can add or subtract the numerators (the number of slices you consider).

If the denominators are different, you need to find a common denominator, a least common multiple that both denominators can divide into evenly. Then, manipulate the fractions to have that common denominator and add/subtract the numerators.

Multiplying fractions:

Multiply the numerators and the denominators separately. (3/4) x (2/5) = (3 x 2) / (4 x 5) = 6/20

Dividing fractions:

Flip the second fraction (divisor) so it becomes its reciprocal (turn the numerator and denominator upside down). Then, multiply the two fractions like normal. (3/4) / (2/5) = (3/4) x (5/2) = 15/8

Tips for solving fraction problems:

Visualize: Use fraction models or draw diagrams to represent the fractions.

Simplify: Before and after calculations, try to simplify fractions to reduce terms with common factors (e.g., 6/12 can be simplified to 1/2).

Practice: The more you practice working with fractions, the more comfortable you'll become with the different operations.

Remember, fractions are a powerful tool for representing and working with parts of a whole. Understanding them unlocks problem-solving abilities in many areas of math and real-world applications.(4 votes)

- i dont know kinda E>Z(2 votes)

## Video transcript

- [Instructor] We are told
that Tony has 2/3 of a bag of dark chocolate chips and 4/5 of a bag of white chocolate chips. Determine a reasonable estimate of the total amount of
chocolate chips Tony has. So pause this video and see if you can figure
out which of these choices is the best reasonable estimate of the total amount of chocolate chips. All right, now let's
work on this together. Now in the future, we will learn how to actually
add something like 2/3 to 4/5, but for the sake of this exercise, we just want to get good at estimating it. And one way to estimate
is to try to visualize. So let's make, so this is a whole right over here, and then this is another
whole right over there. Try to make them the same size. Now what does 2/3 look like? Well, let me divide this
into three equal sections, so that is pretty close. It's hand drawn, so it's not perfect, but I think it gets the job done. And 2/3 would be, that's
1/3 right over there and then that is 2/3 right there, and what does 4/5 looks like? Well, let's see. I can divide this into fifths, so 1/5, 2/5, 3/5, and then 4/5, and 5/5. That is pretty good. And now what does 4/5 look like? Well, it would be 1/5, 2/5, 3/5, and then 4/5. So if we were to add these two together, do we have less than 1/2 of a bag, more than 1/2 of a bag,
but less than one bag, or more than one bag? Well, when you see even the first 2/3, where is a half? A half would have been right around there if we're talking about half of it. So 2/3 is more than a half, and then we also see that
4/5 is more than a half. If you had a half, it would have been like this far. So you can see that you're
adding two things together that are both more than a half. And if you have two halves of
something, that'd be a whole, so if you have two things
that are more than a half, if you add them together, you're gonna have more than
a bag of chocolate chips. So I like this choice right over here. Let's do another example. So here, we are told that a banana weights 3/8 of a kilogram, an apple weighs 2/3 of a kilogram. Determine a reasonable estimate for the weight of both fruits. So pause this video again and see if you can have a go at that. All right, so the key is that we need to determine a reasonable estimate. So let's actually just try
to represent these again, so how could I represent 3/8 of something, of a kilogram, in this case? Well, let me draw a rectangle here and I'm going to try to
divide it into eighths, eight equal sections, so that looks about a half. Let me do it right over there. That looks like about a half, and then if I were to divide those, these would be fourths, and this is hand drawn,
so it's not perfect, but it will help us
understand things a bit. So then let me divide these, and so this would get me to eighths. So I have eight sections here. One, two, three, four,
five, six, seven, eight, and if I'm talking about three of those eight equal sections, I'd have 1/8, 2/8, and 3/8, so that is 3/8 right over there and what does 2/3 looks like? So I'll do that in purple, so if this is a whole, this is a whole like that. If I divide it into three equal sections, it's going to be something like that. I could draw it a little bit better, so something like that, and so two of those three equal sections, that's 1/3, and so that is 2/3. Now what happens if I try to
add these things together? Well one thing I could try
to do to help visualize is I could take that piece there. The wholes are roughly the same length or I tried to draw them so that they are roughly the same length, and if I were to copy and paste that and move that over here, it looks like, if I were to estimate it, I'm getting pretty close
to a whole kilogram here. So it's definitely not just
about 1/3 of a kilogram. 1/3 of a kilogram would be just one of these three equal sections. We're way more than that,
so we rule that out. About one kilogram, that's what we saw. When we, when we take the 2/3 and add to that, 3/8, where it looks like, and
once again, we're estimating. We don't know exactly. It looks like we're a
little bit over a kilogram, so I like this choice, and we're no where close to two kilograms. Two kilograms, we would be
filling in another whole on top of this one right over here. So it's not that choice either.