Number & Operations in Base Ten

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5th Grade Math › Number & Operations in Base Ten

Questions 1 - 10
1

Explanation

Subtracting decimals is just like subtracting whole numbers. But, you must remember your decimal in your answer.

You start subtracting on the far right which in this case is the hundredths place. Screen shot 2020 09 11 at 8.31.19 am

Next, subtract the tenths place Screen shot 2020 09 11 at 8.31.37 am

The decimal will be carried down and remain between the tenths place and the one' place. Screen shot 2020 09 11 at 8.31.48 am

The final subtraction portion is the ones place. Screen shot 2020 09 11 at 8.31.54 am

2

300 is how many times greater than 3? Using the same logic, 40 is how many times greater than 4?

300 is 100 times greater than 3, and 40 is 10 times greater than 4.

300 is 100 times greater than 3, and 40 is 100 times greater than 4.

300 is 10 times greater than 3, and 40 is 10 times greater than 4.

300 is 10 times greater than 3, and 40 is 100 times greater than 4.

300 is 30 times greater than 3, and 40 is 4 times greater than 4.

Explanation

3

Subtract:

Explanation

We can use base ten blocks to help us solve this problem. Let's review what our base ten blocks are by using a whole number

Base ten blocks

When we put this together, we add:

To use base ten blocks to add decimal numbers, we need to think of the base ten blocks a little differently. We think of the hundreds block as one whole. The tens block as tenths because you would need ten of these to make one whole. Finally, the ones block as hundredths because you would need a hundred of these to make one whole:

Base ten blocks decimal

Let's look at this problem:

First, we want to represent the with four tenths blocks and five hundredths blocks:

45

Next, we want to take away , which means taking away one of the tenths and one of the hundredths:

34

We can see that we now have three tenths blocks and four hundredths blocks, which means our answer is

Answer chart 4

4

Multiply:

Explanation

When multiplying decimals, we can use our base ten blocks to create an area model. To do this, we want to use our hundreds, or one whole, block:

One whole

is equal to five tenths. Remember, our one whole block is made up of ten tenths. We can shade in , or five tenths blocks, of the whole. Let's shade of the vertical tenths blocks. Let's use blue to shade:

5

Next, we want to shade four of the tenths blocks to represent the . Since we shaded vertical for the first step, we need to shade horizontal for this step. Let's use yellow to shade:

4

Notice the green shading. This is where the yellow and the blue shading overlapped. (Remember, yellow and blue make green). The overlapping section is our answer. There are twenty green hundredths blocks; therefore, our answer is which is equal to two tenths, :

20

5

Screen shot 2020 09 16 at 1.44.48 pm

Explanation

The problem that you are challenged to solve is .

is the dividend, this is what is being broken up into groups. is our divisor which is the number of groups you are making. We need to split in half to see how many are in each group.

The first step is to place your decimal above your equation in the same place. It will line up with the decimal inside of your "long-division house".
Screen shot 2020 09 16 at 1.44.52 pm

Next, we need to use or multiplication facts to determine what can be multiplied by to make or get close to it without going over. is the fact that works best ( is too large). We will place the numeral directly above the in the ones place to indicate that groups of fit into the . We will put the product of which was underneath the in the ones place and subtract the difference. The numbers above the "house" are our quotient or answer to the division problem.

Screen shot 2020 09 16 at 1.44.57 pm

Next, we will carry the in the tenths place down and put it next to the . We will work with the numbers as if they were when thinking of multiplication facts, but it should be noted this is actually when you consider the decimal placement. so we place the above the "house" in the tenths place of our quotient and subtract the . We are left with remaining so there is no remainder.

Screen shot 2020 09 16 at 1.56.57 pm

Our final answer is , which means that half of is

6

Divide:

Explanation

We can use base ten blocks to help us solve this problem. First, we want to use base ten blocks to represent

Screen shot 2020 07 01 at 7.51.55 pm

Because we are dividing by , we need to split up our into groups of

Screen shot 2020 07 01 at 7.55.20 pm

We can see that we have 2 groups of 2, thus the answer is 2.

7

Divide:

Explanation

We can use base ten blocks to help us solve this problem. First, we want to use base ten blocks to represent

9

Because we are dividing by , we need to split up our into groups of :

3

As you can see, we have groups; thus,

8

Divide:

Explanation

We can use base ten blocks to help us solve this problem. First, we want to use base ten blocks to represent

Screen shot 2020 07 01 at 7.51.55 pm

Because we are dividing by , we need to split up our into groups of

Screen shot 2020 07 01 at 7.55.20 pm

We can see that we have 2 groups of 2, thus the answer is 2.

9

Explanation

10

Explanation

Subtracting decimals is just like subtracting whole numbers. But, you must remember your decimal in your answer.

You start subtracting on the far right which in this case is the hundredths place. Screen shot 2020 09 11 at 8.31.19 am

Next, subtract the tenths place Screen shot 2020 09 11 at 8.31.37 am

The decimal will be carried down and remain between the tenths place and the one' place. Screen shot 2020 09 11 at 8.31.48 am

The final subtraction portion is the ones place. Screen shot 2020 09 11 at 8.31.54 am

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