Test your skills with this online exercise Comparing fractions quiz.
Comparison of two fractions quiz online, greater, less than or equal to
Comparison of two fractions quiz online, greater, less than or equal to. This quiz will also serve as a math game for children. This activity is in line with the curriculum for 3rd, 4th, 5th and 6th grades, hence will serve as a review exercise for children at this level. It is also a free math activity which teachers and parents could use to supplement their math course. After taking this quiz, print out math worksheets on the same topic and get more practice offline.
When we compare fractions, we are looking at two or more fractions and determining which one is larger or smaller. To compare fractions, we need to make sure that the fractions have the same denominator, or bottom number. This is because the denominator tells us how many parts the whole is divided into, and if the denominators are different, it can be difficult to compare the fractions because they are not talking about the same number of parts.
For example, if you wanted to compare the fractions 1/4 and 1/3, you would need to first find a common denominator. A common denominator is a number that both fractions can be converted to, so that they have the same denominator. In this case, a common denominator would be 12 because 4 and 12 have no common factors other than 1 and 3 and 12 is the least common multiple. Now that we have a common denominator, we can convert 1/4 to 3/12 and 1/3 to 4/12. Now we can compare these fractions.
3/12 < 4/12
We can tell that 1/3 is greater than 1/4 because 4 is larger than 3.
Another way to compare fractions is by looking at the numerator, or top number. The numerator tells us how many parts of the whole we have. In general, the larger the numerator, the larger the fraction.
For example, if you wanted to compare the fractions 2/5 and 3/5, you would look at the numerators.
2/5 < 3/5
We can tell that 3/5 is greater than 2/5 because 3 is greater than 2.
We can also convert the fractions to decimal numbers, by dividing the numerator by the denominator, that way is much easier to compare them.
Another example, let’s say we have to compare the fractions 5/8 and 7/12, we can convert them to decimals, 5/8 = .625 and 7/12 = .583, this way we can tell that 5/8 is greater than 7/12
It’s important to notice that when we are comparing fractions with different denominators it’s necessary to have a common denominator, or convert them into decimal numbers, to have a fair comparison.
Another way of comparing fractions is by simplifying them. When a fraction is simplified, it means that the numerator and denominator have no common factors other than 1. Simplifying a fraction makes it easier to compare because it shows the fraction in its simplest form.
For example, let’s compare the fractions 6/12 and 8/16, in order to compare them, we can simplify them first, 6/12 can be simplified to 3/6, which is the same as 1/2, and 8/16 can be simplified to 1/2
1/2 = 1/2
We can tell that both fractions are equal, 6/12 and 8/16 are the same.
In summary, when comparing fractions, it’s necessary to make sure that the fractions have the same denominator, or convert them into decimal numbers, to have a fair comparison. Another way of comparing them is by looking at the numerator, the larger the numerator, the larger the fraction. Also, it’s a good idea to simplify the fractions whenever possible.
Add fractions horizontal arrangement quiz
Learn to add fractions in a horizontal arrangement, math quiz online.
Addition of fractions math test online for children
Addition of fractions math test online for children in 3rd to 7th grades. To successfully take this quiz, children must understand notions of finding the LCM of two numbers. They also have to understand the rules needed in adding fractions. This quiz will improve mental math abilities of children. It will also enable them to self-evaluate their math skills and improve on areas of weakness. This quiz is multiple choice math trivia online and there is no limit as to how many times it could be taken.
When we add fractions, we are finding the total amount when we combine two or more parts together. Imagine you have a pizza and you want to divide it into 4 equal slices. Each slice would be one fourth of the pizza, or 1/4. If you had two slices, the total amount of pizza you would have would be 2/4, which is the same as 1/2. This is because when you add the two parts together (2/4), you are finding the whole (1/2).
When adding fractions, it is important to make sure that the fractions have the same denominator, or bottom number. This is because the denominator tells us how many parts the whole is divided into. If the denominators are different, it can be difficult to add the fractions because they are not talking about the same number of parts.
For example, if you wanted to add 1/4 and 1/3 together, you would need to first find a common denominator. A common denominator is a number that both fractions can be converted to, so that they have the same denominator. In this case, a common denominator would be 12 because 4 and 12 have no common factors other than 1 and 3 and 12 are the least common multiple.
Now that we have a common denominator, we can convert 1/4 to 3/12 and 1/3 to 4/12. Now we can add these fractions, 3/12 + 4/12 = 7/12
It is also possible to add fractions that are arranged horizontally, which means the fractions are lined up next to each other. When adding fractions in this way, it is important to remember that the denominators, or bottom numbers, must still be the same.
For example, if you wanted to add 2/5, 3/5 and 1/5 together, you would line them up horizontally and add the numerators, or top numbers, together:
2/5 + 3/5 + 1/5 = 6/5
It is important to notice in this case, the result of this sum is a mixed number. 6/5 is the same as 1 1/5, which is the same as 6/5.
It’s very important to note that when working with fractions, it is important to simplify the fractions to lowest terms whenever possible.
In general, when adding fractions, you can think of it as combining parts of a whole. The denominators tell us how many parts the whole is divided into, and the numerators tell us how many of those parts we have. By adding the numerators together and keeping the denominator the same, we can find the total amount when we combine the parts together.
In summary, when adding fractions, it’s necessary to have the denominators the same and add the numerators together. In case the denominators are not the same, it’s required to find a common denominator first. Also, it’s always a good idea to simplify the fractions to lowest terms whenever possible.
Addition of fractions vertically arranged quiz
Addition of fractions vertically arranged exercise test your skills.
Interactive math game on adding fractions, 3rd to 7th grade math
This is an interactive math game on adding fractions for kids in 3rd, 4th, 5th, 6th and 7th grades. This takes the form of a multiple choice questions quiz online which kids can use to check their skills on fraction. This is also a drag and drop activity for children at different levels. To the right are the problems and to the left the answers. simply solve the problem and then drag and drop the correct answer that corresponds. At the end of each game, children will get their scores displayed. This is a flexible way to self-evaluate yourself.
When we add fractions, we are finding the total value of two or more parts. In order to add fractions, the denominators (the bottom numbers) of the fractions must be the same. If the denominators are not the same, we must find a common denominator before we can add the fractions.
One way to add fractions is by using a method called “vertical addition.” In this method, we write the fractions one above the other, with the numerators (the top numbers) lined up, and the denominators lined up below them. We then add the numerators together, and keep the denominator the same.
For example, let’s say we want to add the fractions 1/4 and 1/4. We write them vertically, with the numerators lined up and the denominators lined up below:
Now we add the numerators, which in this case are both 1. We get:
We now have the sum of the two fractions which is 2/4. We can simplify this by dividing the numerator and denominator by a common factor of 2, to get the simplified fraction 1/2. So the sum of 1/4 and 1/4 is 1/2.
This method of adding fractions can be used for adding more than two fractions, just keep adding the numerators and keep the denominator same.
As we can see that when we added 1/4 + 1/4 + 1/4 we get 3/4.
It’s also very important to note that the fractions need to be written with the same denominator, and that denominator will be the least common multiple(LCM) of all the fractions, For example:
The LCM for the above fractions is 15. So the fractions will be written as:
Adding fractions can be a bit tricky at first, but with practice and understanding, it becomes easy and fun. It’s also important to understand when to simplify the fraction like we did in 2/4 to 1/2.
When adding or subtracting fractions, it’s important to remember to find a common denominator first, if the denominators are not the same. And always simplify the fraction if possible.
In addition to vertical addition, there are other ways to add fractions, such as finding a common denominator and then adding or subtracting the numerators, or by using a method called “cross-multiplication.” But vertical addition is a useful and straightforward method that students can use to add fractions.
Addition of fractions with large denominators quiz
Learn how to do Addition of fractions with large denominators through this online quiz
Math quiz involving addition of fractions with large denominators
Math quiz involving addition of fractions with large denominators for children in 4th, 5th, 6th and 7th grades. This is an interactive online math test which kids can use to test their skills after school. In each exercise, children have to solve an addition problem and find the corresponding answer. After doing this, players should drag and match to appropriate locations. This quiz could also be used as a math game or as a multiple choice question trivia. Learn math with fun.
When we add fractions, we’re finding the total amount when we combine two or more parts together. One way we can add fractions is by making sure that the denominators, or bottom numbers, are the same.
However, sometimes the denominators can be very large numbers, making it difficult to add the fractions together. In these cases, we can use a method called “finding a common denominator” to help us add the fractions.
A common denominator is a number that both fractions can be converted to, so that they have the same denominator. To find a common denominator for two fractions, we can use the least common multiple (LCM) of the denominators. The least common multiple is the smallest number that both denominators can divide into without leaving a remainder.
For example, let’s say we want to add the fractions 2/15 and 3/20. To find a common denominator, we can use the least common multiple of 15 and 20. The least common multiple of 15 and 20 is 60. This means that we can convert 2/15 to 8/60 and 3/20 to 9/60, so that both fractions have the same denominator of 60.
Now that we have a common denominator, we can add the fractions together: 8/60 + 9/60 = 17/60
In this case, 17/60 is a simplified fraction, we can use the greatest common factor (GCF) to simplify more. The GCF of 17 and 60 is 1.
Another way of achieving the same result is by multiplying the numerator and denominator of the first fraction by the same value, and then doing the same for the second fraction.
For example, you could multiply the numerator and denominator of the first fraction by 4 and the numerator and denominator of the second fraction by 3, this way: (2/15) * (4/4) = 8/60 and (3/20) * (3/3) = 9/60, then add them 8/60 + 9/60 = 17/60
It’s important to note that when working with fractions with large denominators, it is important to simplify the fractions to lowest terms whenever possible, as we showed in the previous example.
Another example let’s say we have to add 2/45 + 5/90, to add them we need to find a common denominator. We can use the LCM of 45 and 90, which is 90. Then we convert the fractions into 9/90 and 5/90, which we can add them together to get 14/90
It’s important to note that sometimes, finding a common denominator for fractions with large denominators can be a bit more difficult and time consuming, but by breaking it down and following these steps, it can be a manageable task.
In summary, when adding fractions with large denominators, it’s necessary to find a common denominator. The least common multiple of the denominators is usually the common denominator. To convert the fractions, we can multiply both the numerator and denominator by the same value. And remember it’s always a good idea to simplify the fractions to lowest terms whenever possible.
Addition of mixed fractions quiz
Practice Addition of mixed fractions math online quiz.
Adding mixed-fractions interactive online test
Adding mixed-fractions interactive online test for children in 4th, 5th, 6th and 7th grades. This is a multiple choice trivia involving drag and drop exercises. Children will improve their math skills through this test. At the end of the quiz a score will be displayed. This is an online practice activity but we also offer the option of downloading worksheets and reviewing while at home. This math quiz could also serve as a cool math game which kids can use both at home and in the classroom.
When we add mixed fractions, we are finding the total value of two or more mixed numbers. A mixed number is a whole number and a fraction combined. For example, 2 1/2 is a mixed number because it is made up of the whole number 2 and the fraction 1/2.
To add mixed fractions, we start by adding the whole numbers together. So in example: 2 3/5 + 3 2/5, First we will add 2 + 3 which equals to 5.
Next, we add the fractions separately, just like we do when adding regular fractions. In the example, 3/5 + 2/5. Since the denominators are the same (5), we can simply add the numerators (the top numbers of the fractions), which gives us 3/5 + 2/5 = 5/5 = 1.
Now, we add the sum of the whole numbers (5) to the sum of the fractions (1) to get the final answer, which is 5 + 1 = 6 1/5. So, the sum of 2 3/5 and 3 2/5 is 6 1/5.
It’s also very important to note that to add mixed fractions, the fractions should have the same denominator. In case they don’t, we need to find the least common denominator (LCD) and change the fraction to have the same denominator before adding them.
Comparing fractions quiz
Test your skills with this online exercise Comparing fractions quiz.
Comparison of two fractions quiz online, greater, less than or equal to
Comparison of two fractions quiz online, greater, less than or equal to. This quiz will also serve as a math game for children. This activity is in line with the curriculum for 3rd, 4th, 5th and 6th grades, hence will serve as a review exercise for children at this level. It is also a free math activity which teachers and parents could use to supplement their math course. After taking this quiz, print out math worksheets on the same topic and get more practice offline.
When we compare fractions, we are looking at two or more fractions and determining which one is larger or smaller. To compare fractions, we need to make sure that the fractions have the same denominator, or bottom number. This is because the denominator tells us how many parts the whole is divided into, and if the denominators are different, it can be difficult to compare the fractions because they are not talking about the same number of parts.
For example, if you wanted to compare the fractions 1/4 and 1/3, you would need to first find a common denominator. A common denominator is a number that both fractions can be converted to, so that they have the same denominator. In this case, a common denominator would be 12 because 4 and 12 have no common factors other than 1 and 3 and 12 is the least common multiple. Now that we have a common denominator, we can convert 1/4 to 3/12 and 1/3 to 4/12. Now we can compare these fractions.
3/12 < 4/12
We can tell that 1/3 is greater than 1/4 because 4 is larger than 3.
Another way to compare fractions is by looking at the numerator, or top number. The numerator tells us how many parts of the whole we have. In general, the larger the numerator, the larger the fraction.
For example, if you wanted to compare the fractions 2/5 and 3/5, you would look at the numerators.
2/5 < 3/5
We can tell that 3/5 is greater than 2/5 because 3 is greater than 2.
We can also convert the fractions to decimal numbers, by dividing the numerator by the denominator, that way is much easier to compare them.
Another example, let’s say we have to compare the fractions 5/8 and 7/12, we can convert them to decimals, 5/8 = .625 and 7/12 = .583, this way we can tell that 5/8 is greater than 7/12
It’s important to notice that when we are comparing fractions with different denominators it’s necessary to have a common denominator, or convert them into decimal numbers, to have a fair comparison.
Another way of comparing fractions is by simplifying them. When a fraction is simplified, it means that the numerator and denominator have no common factors other than 1. Simplifying a fraction makes it easier to compare because it shows the fraction in its simplest form.
For example, let’s compare the fractions 6/12 and 8/16, in order to compare them, we can simplify them first, 6/12 can be simplified to 3/6, which is the same as 1/2, and 8/16 can be simplified to 1/2
1/2 = 1/2
We can tell that both fractions are equal, 6/12 and 8/16 are the same.
In summary, when comparing fractions, it’s necessary to make sure that the fractions have the same denominator, or convert them into decimal numbers, to have a fair comparison. Another way of comparing them is by looking at the numerator, the larger the numerator, the larger the fraction. Also, it’s a good idea to simplify the fractions whenever possible.
Comparing improper fractions quiz
Learn Comparing improper fractions exercise. Online math practice check your skills.
Learn how to compare improper fractions in an online quiz game
Learn how to compare improper fractions in an online quiz game. Improper fractions have numerators that are larger than their denominators. A good way of comparing them is to first reduce them to their lowest terms. This math activity is a good test for children in 4th, 5th, 6th and 7th grades. Comparison of fractions also entail using phrases like less than, greater than and equal to. Learn how to use this vocabulary in real problems. Cool math quiz online for children.
When we compare improper fractions, we are determining which one is greater or smaller than the other. An improper fraction is a fraction where the numerator (the top number) is larger than the denominator (the bottom number).
To compare improper fractions, we have a few methods, one of them is by looking at the numerators (the top numbers) and comparing them. If the numerator of one fraction is larger than the numerator of the other fraction, then the first fraction is larger. for example, 5/3 is larger than 4/3 because 5 is greater than 4.
Another way is by converting them to mixed numbers and then comparing the whole numbers. To convert an improper fraction to a mixed number, we divide the numerator by the denominator and add the remainder as a whole number. For example: 7/4 is smaller than 9/5, because when we convert 7/4 to a mixed number it will be 1 3/4 and 9/5 will be 1 4/5. 1 4/5 is bigger than 1 3/4
Another way is by cross-multiplying the fractions. This method compares the products of the numerators and denominators. For example: 7/4 is smaller than 9/5 because when we cross-multiply we get 35/4 and 36/5. and 36/5 is greater than 35/4
It’s also very important to simplify the fractions if they can be simplified before comparing them.
In conclusion, comparing improper fractions can be done by comparing the numerators, converting them to mixed numbers, or cross-multiplying them. The most important thing to remember is that the fractions need to have the same denominator to be able to compare them directly. It’s also a good idea to practice comparing different improper fractions to become comfortable and confident with the process.
Comparing mixed fractions quiz
In Comparing mixed fractions exercise you will learn how to compare mixed fractions in easy way?
Math quiz online for children to learn how to compare mixed fractions
This is an interactive online math quiz to test kids skills on how to compare mixed fractions. In this quiz, children will solve the problem, fill in the correct answer and submit. This quiz can be taken by children in 3rd, 4th, 5th, 6th and 7th grade who need to test and review their skills. This math quiz could also be perceived as a cool math game suitable for classroom and homeschool use. Have fun online and also learn the notion of comparing mixed fractions.
A mixed fraction, also known as a mixed number, is a whole number combined with a fraction. For example, the mixed fraction 3 1/2 is equal to the whole number 3 plus the fraction 1/2.
Comparing mixed fractions can be a little tricky, but with a few simple steps, it’s easy to do. To compare mixed fractions, you first need to convert them to improper fractions. An improper fraction is a fraction where the numerator (the top number) is larger than the denominator (the bottom number). For example, the mixed fraction 3 1/2 is equal to the improper fraction 7/2.
Once the mixed fractions have been converted to improper fractions, you can use the same method for comparing fractions to compare the mixed fractions. To compare fractions, you compare the numerators (the top numbers) and the denominators (the bottom numbers) separately.
For example, let’s say we want to compare the mixed fractions 2 3/4 and 3 1/2. First, we convert them to improper fractions: 2 3/4 = 11/4 and 3 1/2 = 7/2. Then we compare the numerators: 11 is greater than 7, so we know that 2 3/4 is greater than 3 1/2.
Another method is to convert them to decimals, since it’s very easy to compare decimal numbers.
For example, Let’s compare 3 1/4 and 1 5/6. 3 1/4 = 3+1/4 = 3.25 1 5/6 = 1+5/6 = 1.83333 It is obvious that 3.25 is greater than 1.83333
It’s important to remember that when comparing mixed fractions, you need to make sure that the fractions are in their simplest form (also known as “reduced”) before comparing them. Also, converting to decimals is very useful method when it comes to compare mixed fractions, but you should be careful when converting as it might introduce inaccuracies due to lack of precision with some fractions.
By following these simple steps, you’ll be able to compare mixed fractions with ease and confidence!
Comparing equivalent fractions quiz
Learn Math Comparing equivalent fractions exercise with online quiz.
Math quiz on comparing equivalent fractions
Math quiz on comparing equivalent fractions. Children will through this quiz understand how to find numerators and denominators of equivalent fractions. This quiz makes makes the notion of equivalent fractions easy to understand. This activity is a review option for kids in 3rd, 4th, 5th, 6th and 7th grades. Have fun with comparison of equivalent fractions.
When we compare equivalent fractions, we are determining which one is greater or smaller than the other. Equivalent fractions are fractions that have the same value, even though they might have different numerators and denominators.
To compare equivalent fractions, we can start by simplifying the fractions to their lowest form. To simplify a fraction, we find the greatest common factor (GCF) of the numerator and denominator and divide them both by it. For example, 4/8 and 1/2 are equivalent fractions because they are both simplified to 1/2.
Another way to compare equivalent fractions is by cross-multiplying. This method compares the products of the numerators and denominators, instead of just the numerators or denominators.
For example, let’s compare 2/3 and 4/6:
Cross-multiply 2/3 and 4/6, We get (26) and (34) which equals to 12 and 12, therefore the product of the numerator and denominator of the 2 fractions are equal.
We can also compare the fractions by thinking about it as parts of a whole. If we have a whole pizza and want to split it into 8 pieces, we can represent it as 8/8, or 1. Now if we want to split the pizza into 16 pieces instead, we can represent it as 16/16 or 1 as well. Even though they are represented as different fractions, they are both the same, because they both represent the entire pizza.
It’s also important to remember that equivalent fractions can be found by multiplying or dividing both the numerator and denominator by the same number. For example, 2/3 is equivalent to 4/6, because if we multiply both the numerator and denominator of 2/3 by 2, we get 4/6.
In conclusion, comparing equivalent fractions is easy, because they have the same value. We can compare them by simplifying the fractions to their lowest form, cross-multiplying them, or thinking about them as parts of a whole. It’s also important to remember that equivalent fractions can be found by multiplying or dividing both the numerator and denominator by the same number.
Practicing comparing equivalent fractions is a great way to become more familiar and comfortable with this concept. Encourage kids to practice with different fractions and different methods to become confident and comfortable with comparing equivalent fractions.
Convert decimals to fractions quiz
In this Practice test we will learn how to Convert decimals to fractions?
Math online quiz on how to convert decimals to fractions
Math online quiz on how to convert decimals to fractions. In this exercise children will have to look at decimal numbers and follow the steps needed to convert them to a fraction. This is a multiple choice question quiz in which kids will solve and match appropriate answers. This math test will also serve as a math game for some kids. At the end of the game players will see their scores displayed. This exercise is suitable for 4th, 5th, 6th and 7th graders.
Converting decimals to fractions can seem like a difficult task for kids, but with the right approach and some practice, it can become a simple and fun concept to understand.
First, it’s important to understand what a decimal is. A decimal is a way of expressing numbers as a combination of whole numbers and parts of a whole. For example, the decimal 0.75 represents the fraction 3/4, because 0.75 can be thought of as three fourths.
When converting a decimal to a fraction, the first step is to write the decimal as a fraction with the decimal number as the numerator (the top number) and the number 1 followed by as many zeros as there are digits to the right of the decimal point as the denominator (the bottom number). For example, to convert 0.75 to a fraction, we would write it as 0.75/1.
Next, simplify the fraction by dividing the numerator and denominator by a common factor. In this example, both the numerator and denominator can be divided by 0.25, resulting in the fraction 3/4.
Another example: 0.5 into fraction: 0.5 = 0.5/1 = (5/10) because any decimal can be written as fraction by putting the number after decimal point as numerator and writing 1 followed by as many zeros as there are digits in denominator = (1/2) because 5 and 10 both can be divided by 5
It’s also possible to convert a decimal that has repeating decimal places, like 0.333…, to a fraction. To do this, you can use a technique called long division.
Here is one way to convert 0.333… to a fraction: Multiply both sides of the equation by a power of 10 that will give you a whole number. So in this case it will be 3 as there are 3 decimal places. 0.333… = 0.333… * 3 = 1
0.333… can now be written as a fraction: 1/3
For kids it’s important to make the topic interactive by using examples from real life which they can relate to. Example: When you divide an pizza into 8 equal slices, each slice is one eight (1/8) of the pizza. If we have 3 slice out of 8 then it will be 3/8 of pizza.
In conclusion, converting decimals to fractions can be a fun and easy concept for kids to understand with the right approach and practice. By using real-life examples, and learning techniques like simplifying fractions, kids can develop a deeper understanding of how decimals and fractions work.
Convert fractions to decimals quiz
Math practice through this exercise on how to convert fractions to decimals.
Math quiz on converting fraction to decimal values
This is a math quiz on converting fraction to decimal values. It is a multiple choice math trivia. The principle is to solve all problems correctly, match them and submit. At the end of the quiz, the score will be displayed and kids can figure out where they went wrong. It is an interesting activity for children in 4th, 5th, 6th and 7th grades. It is also an math game depending on how you look at it. This will work well in school and at home as a supplementary material for studying fractions.
Converting fractions to decimals can seem like a difficult task for kids, but with the right approach and some practice, it can become a simple and fun concept to understand.
First, it’s important to understand what a fraction is. A fraction is a way of expressing a part of a whole. For example, the fraction 3/4 represents three fourths of a whole. The top number, called the numerator, tells you how many parts you have, and the bottom number, called the denominator, tells you how many parts the whole is divided into.
When converting a fraction to a decimal, the first step is to divide the numerator by the denominator. This will give you the decimal representation of the fraction. For example, to convert 3/4 to a decimal, we would divide 3 by 4. Using a calculator or long division, we would get 0.75.
It’s important to make the topic interactive by using examples from real life which they can relate to. Example: Suppose you have 5 pencils out of 8 total pencils, you can express it as 5/8. If you want to know how many pencils are missing, you can subtract 5/8 from 1. and 1-5/8 = 3/8
Similarly you can convert the fraction to decimal, 5/8 = 0.625
For example: When you divide an pizza into 8 equal slices, each slice is one eight (1/8) of the pizza. If you want to know how many slices you have, you can convert the fraction to decimal and say that you have 0.125 slices.
Another way to think about converting fractions to decimals is to think of money. For example, if you have $1 and you want to buy an item that cost $3/4, you can think of the fraction as 75 cents.
In conclusion, converting fractions to decimals and vice versa can be a fun and easy concept for kids to understand with the right approach and practice. By using real-life examples and learning techniques like long division or using calculator, kids can develop a deeper understanding of how fractions and decimals work.