How to convert ratios and fractions?

A ratio is a way of comparing two or more numbers. Ratios are often written in the form of a:b, where a and b are whole numbers. To convert a ratio to a fraction, we can use the numbers in the ratio to create a fraction with a numerator of the first number in the ratio and a denominator of the second number in the ratio.

For example, let’s say we have the ratio of 3:4. To convert this ratio to a fraction, we write 3 as the numerator and 4 as the denominator: 3:4 = 3/4

Another example, let’s say we have the ratio of 5:8. To convert this ratio to a fraction, we write 5 as the numerator and 8 as the denominator: 5:8 = 5/8

It’s important to remember that a ratio is a way to compare two or more numbers, while a fraction is a way to represent a part of a whole. Therefore, a ratio can be converted to a fraction as long as the numbers used in the ratio are integers.

You can also simplify the fraction obtained by dividing numerator and denominator with their greatest common divisor (GCD)

For example, let’s say we have the ratio of 6:10. To convert this ratio to a fraction, we write 6 as the numerator and 10 as the denominator: 6:10 = 6/10 =3/5 (using GCD of 6 and 10 is 2)

It’s also important to note that when converting ratios to fractions, it’s often a good idea to write the fraction in its simplest form.

Here are some more examples of converting ratios to fractions: 4:6 = 2/3 7:9 = 7/9 10:12 = 5/6

It’s important to remember that ratios are often used in real-world situations and the ability to convert ratios to fractions is helpful in understanding those situations.

I hope this explanation helps you understand how to convert ratios to fractions. Remember that practice and repetition are key, so be sure to have your child practice converting different ratios to fractions and simplifying them.

Learn to compare mixed fractions

Mixed fractions, also known as mixed numbers, are a combination of a whole number and a fraction. For example, the mixed fraction “3 1/4” represents the number 3 and 1/4. It’s written as a whole number, a space, a numerator, and a denominator. The whole number is the number to the left of the space, and the numerator and denominator represent the fraction to the right of the space.

In order to compare mixed fractions, we first have to convert them to improper fractions. An improper fraction is a fraction where the numerator is larger than the denominator, like 7/4. To convert a mixed fraction to an improper fraction, we use the following steps:

1. Multiply the whole number part of the mixed fraction by the denominator of the fraction part. For example, in the mixed fraction “3 1/4”, we would multiply 3 by 4, which equals 12.
2. Add the product from step 1 to the numerator of the fraction part. In the example above, we would add 12 to 1, which equals 13.
3. Write the sum from step 2 over the denominator of the fraction part. In the example above, the improper fraction is 13/4.

Once the mixed fractions have been converted to improper fractions we can use the same method as comparing regular fractions, which is to compare the numerator and denominator.

Here is an example: Suppose we have two mixed fractions: “4 2/5” and “5 3/4”

1. Converting them to improper fractions: 4 2/5 = 45 + 2 = 22/5 and 5 3/4 = 54 + 3 = 23/4
2. Compare the numerators and denominator: 22/5 is greater than 23/4

It’s important to note that the above method only works if the denominators are the same, which is why we have to convert the mixed fractions to improper fractions first. If the denominators are different, you can use the above method and find a common denominator before comparing.

Another way to compare mixed fractions is to convert them to decimals. We do this by dividing the numerator by the denominator and adding the whole number part. For example, the mixed fraction “3 1/4” would convert to a decimal of 3.25. Once the mixed fractions are in decimal form, it’s easy to compare them just like we do with any decimal number.

It’s also important to note that not all the decimal representation of mixed fractions are exact. And should be rounded as appropriate.

Practicing with a few examples and also by showing them on a number line will help kids better understand and make comparisons between mixed fractions easier.

Learn to compare two fractions with large numerator or denominator

When comparing two fractions, it’s important to make sure that both fractions have the same denominator (the bottom number). If the denominators are different, you’ll need to find a common denominator before you can compare the fractions. A common denominator is a number that both denominators can be divided by evenly.

For example, let’s say you want to compare the fractions 3/4 and 5/6. The denominators are 4 and 6, which are not the same. To find a common denominator, you can think of the smallest number that is a multiple of both 4 and 6, which is 12. This means that you’ll need to multiply both the numerator and denominator of the first fraction by 3, and the numerator and denominator of the second fraction by 2, so that both fractions have a denominator of 12. So the first fraction becomes 9/12, and the second becomes 10/12. Now you can compare the fractions because they have the same denominator.

Another way to find a common denominator is by finding the least common multiple (LCM) of the denominators. To find the LCM you can use prime factorization method, where you write down both denominators as the product of prime numbers and then take the highest exponent of each prime in both numbers and multiply the primes together.

For example, 4 = 2 x 2 and 6 = 2 x 3, so the LCM of 4 and 6 is 2^2 * 3 = 12.

Once the fractions have the same denominator, you can compare the numerators (the top numbers) directly. Whichever numerator is larger, that fraction is larger. For example, in the case of 9/12 and 10/12, 10/12 is the larger fraction because 10 is greater than 9.

It’s also important to keep in mind that when comparing large numerators and denominators, you could simplify the fractions by dividing both the numerator and denominator by the greatest common factor, which is the largest number that divides into both numbers without leaving a remainder, it will make it easier to compare them.

For example, when comparing the fractions 48/72 and 42/56, the GCD of 48 and 72 is 24, so the first fraction can be simplified to 2/3 and the GCD of 42 and 56 is 14 so the second fraction can be simplified to 3/4.

In short, when comparing two fractions with large numerators and denominators, first you need to find a common denominator by either multiplying the numerator and denominator of each fraction by different number or by finding the least common multiple (LCM) of the denominators. Then you can compare the fractions by comparing the numerators directly. And lastly, simplify the fraction to make it easier to compare them.

Adding fractions with common denominator for kids

Adding fractions can seem tricky at first, but it’s actually pretty simple once you understand the basic concept. When adding fractions, it’s important to make sure that the fractions have the same denominator (the bottom number). If the denominators are different, you’ll need to find a common denominator before you can add the fractions.

For example, let’s say you want to add the fractions 2/3 and 1/3. The denominators are already the same, so you can add the fractions directly. To add the fractions, you simply add the numerators (the top numbers) and keep the denominator the same. So, in this case:

(2/3) + (1/3) = (2 + 1)/3 = 3/3

Because both fractions have the same denominator (3), we can simply add their numerators to find the numerator of the answer.

3/3 is a special case because 3/3 is the same as 1. If a numerator is equal to the denominator, it will be the same as 1.

It’s worth mentioning that when you are adding fractions with common denominators, it does not matter if the fractions are simplified or not, because the denominator is common for both and the numerator just needs to be added up.

For example:

• (5/12) + (3/12) = 8/12 = 2/3
• (6/8) + (4/8) = 10/8 = 5/4

When adding fractions with common denominators, it is also important to simplify the final answer by dividing the numerator and denominator by their greatest common factor (GCF). The GCF is the largest number that divides into both the numerator and denominator without leaving a remainder.

For example, when adding fractions (12/15) + (8/15), you get 20/15, if you divide both 20 and 15 by their GCF 5, you get the simplified fraction 4/3.

It’s also worth noting that adding fractions can also be done by converting the fractions to equivalent fractions, this method can be helpful if the denominators of the fractions are large and hard to work with. The concept is that instead of changing the denominator to a common denominator, you change the numerator of one of the fractions in such a way that the denominator remains the same, but the value of the fraction is the same as the other.

For example,

• (1/4) + (1/8) = (1/4) + (2/8) = (3/8)
• (3/5) + (4/10) = (3/5) + (8/20) = (11/20)

In conclusion, Adding fractions is a simple process when the denominators are the same, just add the numerators, and keep the denominator the same. In case the denominators are different, you need to find a common denominator by multiplying the numerator and denominator of each fraction by different numbers or by finding the least common multiple (LCM) of the denominators. And it’s important to remember that the final result should be simplified by dividing the numerator and denominator by their GCF. If the denominators are large you can use equivalent fractions method to add the fractions and keep the denominators the same.

Teaching kids rounding off to nearest hundreds

Rounding is a way to make a number simpler, by replacing it with another number that is close to it. When we round to the nearest hundred, we’re looking for the number that is closest to the original number, but ends in a two-digit number of 00 (like 100, 200, 300, etc.).

To round a number to the nearest hundred, we look at the number in the tens place (the digit in the ones place is the right-most digit). If the number in the tens place is 5 or more, we increase the number in the hundreds place by 1. If the number in the tens place is less than 5, we don’t change the number in the hundreds place.

For example, let’s round 542 to the nearest hundred. The number in the tens place is 4, which is less than 5. So we don’t increase the number in the hundreds place. The rounded number is 500.

Another example is rounding 899, the number in the tens place is 9, which is greater than 5, so we increase the number in the hundreds place by 1. The rounded number is 900.

Let’s look at one more example: rounding 437 to the nearest hundred. The number in the tens place is 3, which is less than 5, so we don’t change the number in the hundreds place. The rounded number is 400.

It’s important to note that when you round up the number will be bigger than the original and when you round down the number will be smaller. The goal of rounding is to make number more simple and easier to work with, but keep in mind that it may not be as accurate as the original number.

Rounding can be used in many real-life situations, like when you’re trying to budget your money or when you’re measuring things. Practice rounding different numbers to the nearest hundred, and you’ll get the hang of it in no time!