Homeschool Math Blog

Decimals, decimals, decimals... math curricula spend a LOT of time with decimals in grades 4-6. And yes, a lot of it is necessary. But perhaps your child can grasp the concepts quicker with these videos , and then be able to progress faster and easier. Decimal division in particular can be a stumbling block. So, check out my new videos and bookmark the page for later use!

Here are some of my recent additions to Math Mammoth Youtube channel .  - videos about decimal arithmetic. Add and subtract decimals I explain the main principle in adding or subtracting decimals: we can add or subtract "as if" there was no decimal point IF the decimals have the same kind of parts--either tenths, hundredths, or thousandths. Many students have a misconception of thinking of the "part" after the decimal point as "plain numbers." Such students will calculate 0.7 + 0.05 = 0.12, which is wrong, and I explain why in the video. Multiply decimals by whole numbers I explain how to multiply decimals by whole numbers: think of your decimal as so many "tenths", "hundredths", or "thousandths", and simply multiply as if there was no decimal point. Compare to multiplying so many "apples". For example, 5 x 0.06 is five copies of six "hundredths". Multiply 5 x 6 = 30. The answer has to be 30 hun...

I have now been able to get back to shooting videos after a long break. These three videos (titled Tenths, Hundredths, and Thousandths) deal with what decimals are (they're fractions!) and in that sense are tied together. The first video explains about decimal numbers with one decimal digit ( tenths ) using fractions and a number line. I also include some easy addition problems. In the second video below, I explain decimals with two decimal digits—or hundredths —using fractions and a number line. Also included an explanation of why you can "tag" or "add" zeros to the end of a decimal and its value does not change. Lastly, I explain decimals with three decimal digits—or thousandths —using fractions and a number line. Then I show examples of converting fractions to decimals and vice versa.

I have two new books available for the Math Mammoth Blue Series: 1) British Money Math Mammoth British Money is a worktext that covers money-related topics usually encountered during years 2-4. The book contains both textbook explanations and exercises, and is designed to be very easy to teach from, requiring very little teacher preparation (you do need to find practise coins before the lessons). Please read more, and see free sample pages. 2) Fractions & Decimals 3 Math Mammoth Fractions & Decimals 3 continues the study of fraction and decimal topics, on the 6th grade level . This book assumes the student already has studied fractions and decimals in the past, for example using Math Mammoth Fractions 2 and Math Mammoth Decimals 2. The goal of the book is to go through all of the fraction and decimal arithmetic , using up to six decimal digits and larger denominators in fractions than what is commonly encountered in 4th and 5th grade materials. Read more, and see free sample...

When dividing decimals by decimals, such as 45.89 ÷ 0.006, we are told to move the decimal point in both the dividend and the divisor so many steps that the divisor becomes a whole number. Then, you use long division. But why? Schoolbooks often don't tell us the "why", just the "how". This video explores this concept. Divide decimals - why do we move the decimal point? It has to do with the fact that when we move the decimal point, we are multiplying both numbers by 10, 100, 1000, or some other power of ten. When the dividend and the divisor are multiplied by the same number, the quotient does not change. This principle makes sense: 0.344 ÷ 0.004 can be thought of, "How many times does four thousandths fit into 344 thousandths?" The same number of times as what four fits into 344! So, 0.344 ÷ 0.004 can be changed into the division problem 344 ÷ 4 without changing the answer. Both 0.344 and 0.004 got multiplied by 1000. When we simplify fractions or wr...

In this video I show, first of all, the common shortcut: you move the decimal point in the number as many steps as there are zeros in the number 10, 100, 1000 etc. For example: 2.16 × 10,000 = 21,600.0 It is as if the point moved four steps from between 2 and 1 to between zeros. You can see better examples of this in my lesson Multiply and Divide Decimals by 10, 100, and 100 at HomeschoolMath.net. Then, I also show where this shortcut originates , using PLACE VALUE charts. In reality, it's not the decimal point moving (it's sort of an illusion), but the digits of the number move within the place value chart (to the opposite direction from the way the decimal point seems to "move"). This explanation can really help students to understand the reason behind the "trick" of moving the decimal point. Multiply & Divide Decimals by powers of ten

To multiply decimals, we are told to multiply as if there were no decimal points, and then make the answer have as many decimal digits as there are decimal digits in the factors. In the video below, I compare multiplying decimals by decimals to fraction multiplication: Multiply decimals by decimals Do you know where this rule or "shortcut" comes from? It comes from fraction multiplication. For example, 1.1 × 0.005 becomes (11/10) × (5/1000) when it is written with fractions. One decimal digit means the denominator is 10. Three decimals means the denominator is 1,000. When you multiply the fractions, you get 55/10,000. Ten thousand as a denominator means the corresponding decimal has four decimal digits. So, the answer is 0.0055. If you are a teacher, you can approach the rule for decimal multiplication by starting out with fractions, and using examples like the one above or the ones in the video to show students where the rule comes from.

I got an advance notice of a new games website called Mangahigh.com . It's more than just simple math games, though. These games are designed extremely well, both from mathematical and "enjoyment" perspective. Mangahigh is led by a team of mathematicians, educationalists, and games designers so the games feature commercial-quality gameplay. I wanted to highlight two of the free games here: Flower Power This is the one that I liked most... it's addictive! Grow flowers and harvest them to make money. Practice ordering decimals, fractions, and percentages. The game starts with ordering decimals (daisies), and proceeds into fractions (tulips or roses) and percents. Each time you get a full stem, you need to decide whether to pick the flowers to sell (earn money) or to let them be pollinated and thus get more flowers to grow. Grades 3-8. Save Our Dumb Planet Defend Earth from deadly meteorites using missiles. A team of dumb scientists are on hand to suggest possible trajec...

This is the COOLEST fractions to decimals calculator I've seen! It will convert a fraction into a decimal to any number of decimal places, and TELL you if it is a recurring decimal, and how many digits its period is. I tried 2/10392, and it said "2/10392=1/5196 has 2 initial digits followed by a period of 432 digits." I won't copy the actual digits here... Hat Tip goes to MathNotations Blog .

I feel students need to get grounded conceptually in this topic. So many times, all they learn about decimal division are the rules of how to go about decimal division when using long division, and it becomes an "empty" skill - a skill that lacks the conceptual foundation. So for starters, we can do two different kinds of mental math division problems. Division by a whole number - using mental math Here it is easy to think, "So much is divided between so many persons". 0.9 ÷ 3 is like "You have nine tenths and you divide it between three people. How much does each one get?" The answer is quite easy; each person "gets" 0.3 or three tenths. And... remember ALWAYS that you can check division problems by multiplication. Since 3 × 0.3 = 0.9, we know the answer was right. 0.4 ÷ 100 turns out to be an easy problem if you write 0.4 as 0.400: 0.400 ÷ 100 is like "You have 400 thousandths and you divide it between 100 people; how much does each one ...

This is a tough topic... in a sense. It is not difficult at all, if you just follow the rule given in your math textbook, because the rule is pretty straightforward: To multiply decimal numbers, multiply them as if there were no decimal points, and then put as many decimal digits in the answer as there are total in the factors. The difficulty is only if you try to understand why we have such a rule - where does it come from? Understanding the rule for decimal multiplication is actually fairly simple, because it comes from fraction multiplication. But, I will propose here a little different way of explaining all this. First, look over this decimal multiplication lesson that is taken from Math Mammoth Decimals 2 book. It talks about how 0.4 × 45 is like taking 4/10 part of 45. The same applies if you have 0.4 × 0.9 - you can think of it as taking 4/10 part of 0.9. Can you see now why the answer to 0.4 × 0.9 has to be smaller than 0.9? Or, turn it around: 0.9 × 0.4 is taking 9/10 of 0....

UPDATED! My Decimal worksheets generator just got better. Now you can vary the number of decimals randomly in the problems. Also, the page now includes a bunch of ready-made worksheets that you generate just by clicking on links - what could be easier than that? Of course you can still use the generator to tailor-make worksheets to your exact needs. This generator makes worksheets for decimal addition, subtraction, multiplication, and division.

Someone asked, how can you use models to multiply decimals? Learning to multiply decimals, I feel, is built on students' previous understanding of multiplying whole numbers and fractions. So models wouldn't necessarily be the focus, but instead relating decimals to fractions first, and learning from that. Multiply a decimal by a whole number Of course, when multiplying a decimal by a whole number, you could use the same models as for fractions: say you have a problem 2 × 0.34 You can use little hundredths cubes, or draw something that's divided to 100 parts. BUT you can also just use fractions, and justify the calculation that way: 2 × 0.34 = 2 × 34/100 = 68/100 = 0.68. OR you can explain it as repeated addition: 2 × 0.34 = 0.34 + 0.34 = 0.68. I employ that idea in these lessons: Multiply mentally decimals that have tenths and Multiply decimals that have hundredths Multiply a decimal by a decimal When students are learning to multiply a decimal by a decimal, th...

is 9/56 rational? when converted to a decimal it seems to be never ending and it seems like there's no pattern (at least as far as the calculator shows) Well, relying on a calculator is leading this person astray. Obviously the number is rational - it's a fraction (!); it fits the definition of a rational number. The calculator gives 0.160714286 (to nine decimal digits), but if you use long division and continue it till you get just a few digits more, you get 0.16071428571428..., or 0.160 714285 .