How To Teach Decimals Conceptually
Decimals are a huge part of your math curriculum. They are connected to so many standards in various domains; place value, fractions, and measurement. Teaching this topic conceptually will give your students the exposure and confidence they need to see beyond standard algorithms and truly understand the reasoning behind their work. It’s easy to teach the algorithms for adding, subtracting, multiplying, and dividing decimals and breeze through this content, but you’re missing out on an opportunity to bring concrete understanding to these four operations.
Here is a breakdown of how I teach the four operations in connected to decimals in my classroom.
Addition and Subtraction of Decimals:
Adding decimals – the easiest of the four, addition of decimals seems to be a nice starting point for students. Before I start on addition I really want my students to have a strong conceptual understanding of decimal place values, how they relate to one another (the hundredths place is one-tenth the value of the tenths place, but 10 times greater than the thousandths place), and be able to visually represent decimals using models.
We use place value disks and a place value chart to represent the decimals we are adding. Students will regroup disks when needed and see how that act changes the value of their numbers.
We also practice representing addition and subtraction of decimals with hundredth grids. Students will use different colored highlighters to represent the values being combined and cross out values when subtracting.
Multiplication of Decimals:
I think multiplication and division of decimals are far more “fun” than addition and subtraction. There are various ways to model and represent decimals using pattern blocks, fraction tiles, hundredth grids, and base ten blocks.
Here are some examples of the types of questions we review in class.
Our Power Problems have rigorous questions for you to implement in your classroom!
We work on these visual representations long before I introduce any algorithms. With a concrete understanding of multiplication with decimals your students will be able to understand the work behind the formula.
Division of Decimals:
You want to continue modeling and requiring students to conceptually understand this operation, just like the other three. Again, we use models to represent dividing a decimal by a decimal, decimal by a whole number, and a whole number by a decimal. Your students should be able to represent each of these scenarios using a hundredth grid. I integrate word problems anywhere I can so students have practice identifying which operation to use.
If you set your students up with conceptual understanding of decimals, this will help with fraction and measurement standards later on in the year. Next year’s teacher will also appreciate your efforts and you’re building number sense too!
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Picture Books That Teach Fractions, Ratios, Percentages, and Decimals
You will love this list of picture books that teach fractions, ratios, percentages, and decimals! These topics can be tough for children to grasp…until you bring them to life through picture books.
You’ve heard me say it a million times, but picture books can go a long way in helping children understand tough topics. Math is abstract. That means it isn’t something that our children can easily grasp if they have no prior knowledge or some frame of reference to start with. Picture books (and hands-on activities) are great for doing just that.
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Even if your children don’t seem to be having trouble understanding fractions, ratios, percentages, and decimals, it never hurts to add an extra layer of connection through picture books.
Picture Books to Teach Fractions
It wasn’t until I started teaching fractions using picture books and hands-on manipulatives that I truly begin understanding them. Seriously. My experiences in school had been too abstract and I usually ended up in tears anytime fractions came around throughout my learning. Books like these and “playing” with manipulatives like fraction bars and circles turned on the light bulb!
You can easily play with fractions in your kitchen, too! Whip up a pizza or a pie and have the kids help cut it in halves, fourths, eighths, etc. Using measuring cups while cooking is also a great way to practice fractions. Your children will be able to see how they can use fractions in the “real world” if they accidentally put a teaspoon of salt into a recipe that only calls for 1/4 teaspoon of salt. Several of these books include food fractions!
- A Fractions Goal – Parts of a Whole by Brian P. Cleary
- Apple Fractions by Jerry Pallotta
- Clean-Sweep Campers by Lucille Recht Penner
- The Doorbell Rang by Pat Hutchins
- Fraction Action by Loreen Leedy
- Fraction Fun by David Adler
- Fractions, Decimals, and Percents by David A. Adler
- Fractions in Disguise by Edward Einhorn
- Full House: An Invitation to Fractions by Dayle Ann Dodds
- Gator Pie by Louise Mathews
- Give Me Half! by Stuart J. Murphy
- How Many Ways Can You Cut a Pie by Jane Belk Moncure
- Mulitplying Menace: The Revenge of Rumplestiltskin by Pam Calvert
- Rabbit and Hare Divide an Apple by Harriet Ziefert
- Sir Cumference and the Fraction Faire by Cindy Neuschwander
- The Hershey’s Milk Chocolate Fractions by Jerry Pallotta
- Whole-y Cow! Fractions are Fun by Taryn Souders
Picture Books to Teach Ratios and Proportions
Ratios and proportions are basically fractions, although they explain different information. A ratio is a comparison of two quantities and a proportion is a statement that two ratios are equal. So, for instance, if there are 2 computers in your house and 5 people live in your house, the ratio of computers to people is 2/5. A proportion of 2/5 would be something that is equal to 2/5 like 4/10 or 6/15.
Ratios and proportions sound hard, but they can be understood by most elementary students who have a basic understanding of fractions and multiplication. These books can help bring the concepts to life.
- A Very Improbable Story by Edward Einhorn
- Beanstalk: The Measure of a Giant by Ann McCallum
- Cut Down To Size at High Noon by Scott Sundby
- If You Hopped Like a Frog by David M. Schwartz
- Is a Blue Whale the Biggest Thing There Is? by Robert E. Wells
- Pythagoras and the Ratios by Julie Ellis
- Ratios and Rates Reasoning by Melanie Alvarez
- The Warlord’s Puppeteers by Virginia Pilegard
Picture Books to Teach Percentages
Percentages are basically fractions, too! They are based on parts of 100, which can make them a little easier to understand once the concept of fractions is down pat. There are only a few books to help specifically with percentages, so be sure to read them all!
- Fractions, Decimals, and Percents by David A. Adler
- The Grizzly Gazette by Stuart J. Murphy
- Twizzlers Percentage Book by Jerry Pallotta
Picture Books to Teach Decimals and Place Value
You guessed it, decimals are basically fractions, too, and they are great to teach right alongside place value. I’ve included books specifically for decimals and place value in this fun list.
Consider using place value blocks, decimal disks, and decimal dominoes to help further visualize these topics!
- A Fair Bear Share by Stuart J. Murphy
- A Place for Zero by Angeline Sparagna LoPresti
- Do You Know Dewey?: Exploring the Dewey Decimal System by Brain P. Cleary
- Earth Day – Hooray! by Stuart J. Murphy
- Fractions, Decimals, and Percents by David A. Adler
- How Much is a Million? by David M. Schwartz
- Parting Is Such Sweet Sorrow: Fractions and Decimals by Linda Powley
- Penguin Place Value by Kathleen L. Stone
- Place Value by David A. Adler
- Sir Cumference and All the King’s Tens by Cindy Neuschwander
- The King’s Commissioners by Aileen Friedman
- Zero the Hero by Joan Holub and Tom Litchenheld
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Multiplication of fractions: a simple instruction — Lifehacker
January 15, 2021
A simple cheat sheet for those who have forgotten the school curriculum in mathematics.
Multiplying fractions with each other
It’s simple: multiply the numerator by the numerator, and the denominator by the denominator. Then check if the fraction can be reduced. For example:
The rule works for fractions with both different and the same denominators. If the fraction is large, let’s say 24 / 35 , try to shorten it right away — it will be easier to keep count.
If there is a mixed number in the example, first convert it to an improper fraction, and then multiply it in the way described above. Convert the result back to a mixed number.
Remember the basics 💡
- What are fractions and how to add them
The multiplication process takes place in three steps:
- Write the fractions in a column and multiply as natural numbers, without thinking about commas for now.
- Find out how many decimal places were in each fraction and add them up.
- Moving from right to left, count as many digits as a result of multiplication as in the previous step. Put a comma there. This is the answer. For example:
If you multiply by 0.1, 0.01, 0.001 and so on, then move the decimal point to the left as many places as there are after the decimal point in the multiplier: 0.18 × 0.1 = 0.018; 0.5 × 0.001 = 0.0005.
Refresh your knowledge 👈
- How to convert a fraction to decimal
Multiplying fractions by natural numbers
Only the numerator needs to be multiplied, and the denominator is left unchanged. If the result is an improper fraction, subtract the integer part from it to get a mixed number. For example:
If you need to multiply a mixed number, convert it to an improper fraction and multiply in the same way. That is:
There is a second way: divide the denominator by the natural number given to you, and do not touch the numerator. This method is more convenient to use when the denominator is divisible by this natural number without a remainder. For example:
Compare this method with the first one — the result is the same.
In this case, use the same method as for multiplying a fraction by a fraction. Multiply the numbers in a column, then count as many digits as there were after the decimal point in the decimal fraction, and put a comma there. That is:
If you need to multiply a decimal by 10, 100, 1000, and so on, just move the comma to the right as many places as there are zeros after the one. For example: 0.045 × 10 = 0.45; 0.045 x 100 = 4.5.
Read also 🧮👌🤓
- Multiply, divide, add like Sheldon Cooper? Math Hacks…
- How to Teach Your Child to Count Easily
- 6 ways to calculate the percentage of the amount with and without a calculator
- How to learn the multiplication table easily and quickly
- How to master mental counting for schoolchildren and adults
How to teach a child to convert fractions to decimals? – Wiki Reviews
Just like how do you convert a fraction to a decimal for kids? So, to convert a fraction to a decimal, divide the numerator by the denominator . If necessary, you can use a calculator for this. This will give us our answer as a decimal.
How do you turn a mixed fraction into a decimal? How to convert mixed number to decimal
- Convert a fraction to a decimal: Divide the numerator by the denominator.
- Add this decimal number to the integer part of the mixed number.
How to convert a fraction to a decimal without a calculator? Find a number that can be multiplied by the denominator to get 10, 100, 1000, or any 1 followed by 0. This can be an easy way to replace a common fraction with a decimal without using a calculator or doing up division.
Second, how do you turn a mixed fraction into a decimal? How to convert mixed number to decimal? To convert a mixed number to decimal form, find the decimal value of the fractional part of the number, and then add it to the integer part of . For example, 1 4/5 can be converted to decimal as 1 + 4/5 = 1 + 0.8 = 1.8.
How do I change a common fraction to a decimal?
To convert a common fraction to a decimal, divide the numerator by the denominator , So 3 / 4 can be changed to decimal 0.75. However, not all common fractions can be converted to such exact decimals: 2 / 3 as a decimal is an endless series of sixes to the right of the decimal point.
then how do you turn .33 into a fraction? Simplified 1/3 is actually equivalent to 33 and 1/3 percent. Some instructors do not allow students to round up to this number. In this case, 33/100 is the exact equivalent.
What is 46 in a fraction? Because there are 46 digits in 2, the last digit is the «100th» decimal place. So we can just say that. 46 same as 46/100 . dividing the numerator and denominator by 2.
What is 39 in a fraction?
Thirty-nine percent expressed as a fraction, 39/100 . This can also be written in decimal as 0.39.
What is 94 as a fraction?
94% shot 94/100 . If you want, you can simplify it to 47/50.
What is 11% as a fraction?
Answer: The value of 11% as a fraction in its simplest form is 11/100 .
What is 75 as a fraction?
Answer: 75% is written as 3/4 as a fraction in its simplest form.
How to multiply fractions? There are 3 easy steps to multiply fractions
- Multiply the top numbers (numerators).
- Multiply the bottom numbers (denominators).
- Simplify the fraction if necessary.
What is 58 in a fraction? Since there are 58 digits in 2, the last digit is the «100th» decimal place. So we can just say that. 58 same as 58/100 .
Is 93 older than 100 in its simplest form?
As you can see, 93/100 is not further simplified by , so the result is the same as at the beginning.
What is 66.6% as a fraction? What is 66.6% as a fraction? 66.6% as fraction 66.6/100 . If you want, you can simplify it to 333/500. 3.
How to turn 0.916 into a fraction?
- 0.91666…= 0.91¯6.