Decimals - 6th grade

In this 6th grade math lesson, I solve two word problems that involve both fractions and decimals. The first one has to do with the volume of two olive oil bottles: one bottle contains 0.9 liters and the other 3/4 liter. How much more oil does the first bottle contain? The second problem asks which oil is cheaper per liter. We simply calculate the unit prices (price per liter) by dividing. Lastly, I solve "bonus" problem where we find out how to write the fraction 1/7 as a decimal. It's a bonus problem because this topic is "extra" for 6th grade. Find worksheets and lessons that match this video in my book Math Mammoth Fractions & Decimals 3 at

In this 6th grade math lesson, I solve two word problems that involve both fractions and decimals. The first one has to do with the volume of two olive oil bottles: one bottle contains 0.9 liters and the other 3/4 liter. How much more oil does the first bottle contain? The second problem asks which oil is cheaper per liter. We simply calculate the unit prices (price per liter) by dividing. Lastly, I solve "bonus" problem where we find out how to write the fraction 1/7 as a decimal. It's a bonus problem because this topic is "extra" for 6th grade. Find worksheets and lessons that match this video in my book Math Mammoth Fractions & Decimals 3 at

To divide by a decimal, first change the ENTIRE division problem to another with a whole-number divisor, yet with the same answer. How? Simply multiply both numbers in the division problem (the dividend and the divisor) by 10 repeatedly, until the divisor is a whole number. (The dividend doesn't matter; it can be a decimal). The shortcut for multiplying by 10 is of course that you move the decimal point, and most school books only give you the shortcut, without explaining this principle for division of decimals that in reality, we are MULTIPLYING both the dividend & divisor by 10, 100, 1000 (powers of ten). We can do this process, because in it, the answer (the quotient) does not change. Think about it: 0.2 goes into 0.7 as many times as 2 goes into 7, or 20 goes into 70. Similarly, if you have a division problem with a decimal divisor, such as 4.392 / 0.7, you're solving how many times 0.7 goes into 4.392. But that is the same as finding how many times 7 goes into 43.92. This process

To divide by a decimal, first change the ENTIRE division problem to another with a whole-number divisor, yet with the same answer. How? Simply multiply both numbers in the division problem (the dividend and the divisor) by 10 repeatedly, until the divisor is a whole number. (The dividend doesn't matter; it can be a decimal). The shortcut for multiplying by 10 is of course that you move the decimal point, and most school books only give you the shortcut, without explaining this principle for division of decimals that in reality, we are MULTIPLYING both the dividend & divisor by 10, 100, 1000 (powers of ten). We can do this process, because in it, the answer (the quotient) does not change. Think about it: 0.2 goes into 0.7 as many times as 2 goes into 7, or 20 goes into 70. Similarly, if you have a division problem with a decimal divisor, such as 4.392 / 0.7, you're solving how many times 0.7 goes into 4.392. But that is the same as finding how many times 7 goes into 43.92. This process

Basic lesson for beginners on converting fractions into decimals. Some fractions are easy to write as decimals, because their denominator is a power of ten (10, 100, 1000, etc.), or because you can find an equivalent fraction with a denominator that is a power of ten. For example, 3/4 = 75/100, and then you just write 75/100 as 0.75. Or, 3/8 = 375/1000 = 0.375. But most of the time we need to use division to change a fraction into a decimal. This means either long division or dividing with a calculator. For example, to convert 5/13 into a decimal, you divide 5 by 13. In long division, you might add decimal zeros to the dividend (5) before you even start, for example so it becomes 5.00000. Often, these divisions don't terminate, but we do notice a PATTERN in the decimal digits -- and also in the remainders that show up in long division. In fact, any fraction (rational number), when written as a decimal, either has a repeating pattern in the digits that goes on forever, or the decimal te

Basic lesson for beginners on converting fractions into decimals. Some fractions are easy to write as decimals, because their denominator is a power of ten (10, 100, 1000, etc.), or because you can find an equivalent fraction with a denominator that is a power of ten. For example, 3/4 = 75/100, and then you just write 75/100 as 0.75. Or, 3/8 = 375/1000 = 0.375. But most of the time we need to use division to change a fraction into a decimal. This means either long division or dividing with a calculator. For example, to convert 5/13 into a decimal, you divide 5 by 13. In long division, you might add decimal zeros to the dividend (5) before you even start, for example so it becomes 5.00000. Often, these divisions don't terminate, but we do notice a PATTERN in the decimal digits -- and also in the remainders that show up in long division. In fact, any fraction (rational number), when written as a decimal, either has a repeating pattern in the digits that goes on forever, or the decimal te

A beginner lesson on how to divide decimals using long division, when the divisor is a whole number and the dividend is a decimal number. Actually, it is super easy: you divide normally, and then put the decimal point in the answer in the same place where it is in the dividend. The situation is altogether different if the DIVISOR is a decimal - please see this video to learn that: In this lesson, we also look at whole-number divisions that turn into decimal divisions, if we don't want a remainder. For example, to divide 52 by 7, one could say the answer is 7 remainder 3. But, there is also the possibility of continuing the division into the decimal digits. Lastly, we briefly look at how to convert fractions into decimals, because it ties in. A fraction IS a division, so any fraction can be considered as a division problem. To write a fraction as a decimal, you simply divide. In this lesson, we use long division to do that, but you could of course use a calculator for the same end. This

A beginner lesson on how to divide decimals using long division, when the divisor is a whole number and the dividend is a decimal number. Actually, it is super easy: you divide normally, and then put the decimal point in the answer in the same place where it is in the dividend. The situation is altogether different if the DIVISOR is a decimal - please see this video to learn that: In this lesson, we also look at whole-number divisions that turn into decimal divisions, if we don't want a remainder. For example, to divide 52 by 7, one could say the answer is 7 remainder 3. But, there is also the possibility of continuing the division into the decimal digits. Lastly, we briefly look at how to convert fractions into decimals, because it ties in. A fraction IS a division, so any fraction can be considered as a division problem. To write a fraction as a decimal, you simply divide. In this lesson, we use long division to do that, but you could of course use a calculator for the same end. This

The shortcut for multiplying decimals by decimals is this: you multiply as if there were no decimal points, and then you place a decimal point in the answer in such a manner that the number of decimal digits in the answer is the SUM of the decimal digits in all the factors. We practice using this rule with several problems, and then I show where the rule comes from, using fraction multiplication. Consider this example: 2/10 x 6/100 = 12/1000. The number of zeros in the denominator (in the power of ten) corresponds to the number of decimal digits: 2/10 is 0.2 (one decimal digit) 6/100 is 0.06 (two decimal digits) The answer, 12/1000, is 0.012 (three decimal digits). As we multiply powers of ten (the denominators), we simply ADD the number of zeros to get the answer. And that is why we ADD the decimal digits to get the amount of decimal digits for the answer. This lesson is meant for 5th grade math (and onward). Check out also the 1st part of this lesson, where we explore SCALING, at

The shortcut for multiplying decimals by decimals is this: you multiply as if there were no decimal points, and then you place a decimal point in the answer in such a manner that the number of decimal digits in the answer is the SUM of the decimal digits in all the factors. We practice using this rule with several problems, and then I show where the rule comes from, using fraction multiplication. Consider this example: 2/10 x 6/100 = 12/1000. The number of zeros in the denominator (in the power of ten) corresponds to the number of decimal digits: 2/10 is 0.2 (one decimal digit) 6/100 is 0.06 (two decimal digits) The answer, 12/1000, is 0.012 (three decimal digits). As we multiply powers of ten (the denominators), we simply ADD the number of zeros to get the answer. And that is why we ADD the decimal digits to get the amount of decimal digits for the answer. This lesson is meant for 5th grade math (and onward). Check out also the 1st part of this lesson, where we explore SCALING, at