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Numbers And Operations In Base Ten: Decimal Operations CCSS 5.NBT.7 Facts & Worksheets

Adding and subtracting decimals is a very simple process and is very similar to adding and subtracting whole numbers.

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Worksheets /Math /Grade 5 (ages 10-11) /Numbers And Operations In Base Ten: Decimal Operations CCSS 5.NBT.7 Facts & Worksheets

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Adding and subtracting decimals is a very simple process and is very similar to adding and subtracting whole numbers. The only difference is, we always have to remember to align the decimal points with each other when adding or subtracting!

See the fact file below for more information on the decimal operations or alternatively, you can download our 30-page Numbers And Operations In Base Ten: Decimal Operations CCSS 5.NBT.7 worksheet pack to utilise within the classroom or home environment.

Key Facts & Information

LEARNING OBJECTIVE:

  • At the end of the lesson, students will be able to add, subtract, multiply, and divide decimals to hundredths using strategies on place value, properties of operations, models, and the number line.

A NOTE FOR THE TEACHER

  • When working with different decimal operations, take note of the following:
    • When adding or subtracting, always align the decimals with each other and add numbers in the same place value.
    • When multiplying decimals, don’t forget to double-check if you have the right number of place values in the product.
    • When dividing decimals, it usually helps to write the decimals in word form.

THEORY:

  • Adding and subtracting decimals is a very simple process and is very similar to adding and subtracting whole numbers. The only difference is, we always have to remember to align the decimal points with each other when adding or subtracting! Take for example: 19.9 + 6.89 and 19.9 – 6.89.

  • Notice how we added at 0 to the hundredths place value of 19.90. This was just used as a placeholder, and we can do this since we are not changing the value of the original number.
  • Multiplying decimals, on the other hand, can be a bit more confusing. One way we can do this is by simply treating the decimals as whole numbers.
  • Take for example 25.5 x 3.42

  • We start by treating the decimals as whole numbers. In this case, we multiply 255 to 342, where the product will be 87 210. In the original decimal numbers, 25.5 had 1 decimal place, while 3.42 had 2 decimal places. Get the total number of decimal places and then apply this to the final product. In the example, 1 decimal place + 2 decimal places result in 3 decimal places. Thus, we add a decimal point in 87 210 in order to apply the 3 decimal places. After doing so, we get our final product which is 87.210. You can verify this using a calculator.
  • We can also use the number line when multiplying whole numbers to decimal numbers. Take, for example, 0.03 x 2

  • Starting from zero, we moved 0.3 units two times. From this, we can see how the product of 0.3 and 2 is 0.6. This can also be verified using the previous technique wherein we treat both numbers as whole numbers.
  • When dividing using decimals, there are a number of techniques we can use. The first technique uses models and the number line to divide whole numbers by decimals and vice versa. Take, for example, 3 ÷ 0.5. Remember that 0.5 is also the same as ½, so we can rephrase the example into “how many ½ or 0.5s are there in 3?

  • In the models above, each block contains two halves. So if we have 3 blocks, we have a total of 6 halves. Thus, we can conclude in our example that
  • 3 ÷ 0.5 = 6 since there are 6 halves in 3. We can verify this by multiplying 6 by 0.5, which in turn will give us 3!
  • We can also use the number line when dividing decimal numbers by whole numbers. Take, for example, 0.6 ÷ 3. We can interpret this as dividing 0.6 into 4 equal portions and determining how much is in each portion.

  • In the model, we divided the interval from 0.0-0.6 into 3 equal intervals. Notice how each interval has 0.2 units. Thus, we can conclude that 0.6 ÷ 3 = 0.2, which can be interpreted as “When dividing 0.6 into 3 portions, there will be 0.2 units per portion”.
  • The last technique involves dividing a decimal by another decimal number. In this technique, we simply write the decimals into words based on their place values and then dividing normally. To better illustrate this, take, for example, 1.5 ÷ 0.5. We can write this as 15 tenths divided by 5 tenths.
  • 15 tenths divided by 5 tenths will be equal to 3 tenths or 0.3.
  • Thus, 1.5 ÷ 0.5 = 0.3.
  • When doing the different decimal operations, we can also estimate the final answer by rounding off the given decimals to the nearest whole number to make solving much easier. Take for example, 1.86 x 35.10
  • 86 can be rounded off to 2, while 35.10 can be rounded off to 35. Thus, our simplified equation will become 2 x 35, which can be easily solved to get 70.
  • We can verify that 70 is close to the true value by solving for 1.86 x 35.10. Doing so will result in 65.286, which isn’t too far off from 70.

Numbers And Operations In Base Ten: Decimal Operations CCSS 5.NBT.7 Worksheets

This is a fantastic bundle that includes everything you need to know about Numbers And Operations In Base Ten: Decimal Operations across 30 in-depth pages. These are ready-to-use worksheets that align with the Common Core CCSS code 5.NBT.7 for Numbers And Operations In Base Ten: Decimal Operations.

Table of contents

  • A lesson plan
  • Warm up activity
  • Math theory explained
  • Assisted learning activities
  • Independent learning activities
  • Extension activities and games
  • Answer keys

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Use With Any Curriculum

These worksheets have been specifically designed for use with any international curriculum. You can use these worksheets as-is, or edit them using Google Slides to make them more specific to your own student ability levels and curriculum standards.

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