Examples with solutions for Associative Property: Only addition and subtraction

Exercise #1

13+7+100= 13+7+100=

Video Solution

Step-by-Step Solution

First, we'll solve the left exercise, since adding the numbers will give us a round number:

13+7=20 13+7=20

Now we'll get an easier exercise to solve:

20+100=120 20+100=120

Answer

120

Exercise #2

8+2+7= 8+2+7=

Video Solution

Step-by-Step Solution

First, we'll solve the left exercise, since adding the numbers will give us a round number:

8+2=10 8+2=10

Now we'll get an easier exercise to solve:

10+7=17 10+7=17

Answer

17

Exercise #3

4+9+8= 4+9+8=

Video Solution

Step-by-Step Solution

Let's break down 4 into a smaller addition problem:

3+1 3+1

Now we'll get the exercise:

3+1+9+8= 3+1+9+8=

Since the exercise only involves addition, we'll use the commutative property and start with the exercise:

1+9=10 1+9=10

Now we'll get the exercise:

3+10+8= 3+10+8=

Let's solve the exercise from right to left:

10+8=18 10+8=18

18+3=21 18+3=21

Answer

21

Exercise #4

13+2+8= 13+2+8=

Video Solution

Step-by-Step Solution

We will use the commutative property and first solve the addition exercise on the right:

2+8=10 2+8=10

Now we get:

13+10=23 13+10=23

Answer

23

Exercise #5

13+5+5= 13+5+5=

Video Solution

Step-by-Step Solution

First, we'll solve the right-hand exercise, since adding the numbers will give us a round number:

5+5=10 5+5=10

Now we'll get an easier exercise to solve:

13+10=23 13+10=23

Answer

23

Exercise #6

38+2+8= 38+2+8=

Video Solution

Step-by-Step Solution

First, we'll solve the right-hand exercise, since adding the numbers will give us a round number:

2+8=10 2+8=10

Now we'll get an easier exercise to solve:

38+10=48 38+10=48

Answer

48

Exercise #7

32+5+1= 32+5+1=

Video Solution

Step-by-Step Solution

First, we'll combine the lower numbers using the commutative property:

5+1=6 5+1=6

Now we'll get the exercise:

32+6=38 32+6=38

Answer

38

Exercise #8

24+2+562= 24+2+562=

Video Solution

Step-by-Step Solution

Let's break down 560 into a smaller addition exercise and we get:

24+2+560+2= 24+2+560+2=

Now let's use the commutative property and add the smaller numbers:

24+2+2=26+2=28 24+2+2=26+2=28

Now we get the exercise:

28+560= 28+560=

Let's break down 28 into a smaller addition exercise:

20+8+560 20+8+560

Let's group the round numbers:

20+560=580 20+560=580

And we get the exercise:

580+8=588 580+8=588

Answer

588

Exercise #9

0.85+7.61+2.3= 0.85+7.61+2.3=

Video Solution

Step-by-Step Solution

According to the order of operations, we will solve the exercise from left to right.

We will first calculate the addition exercise in the vertical column, since it contains two numbers after the decimal point:

0.85+7.61=8.46 0.85+7.61=8.46

Now we will get the exercise:

8.46+2.3= 8.46+2.3=

Let's remember that:

2.3=2.30 2.3=2.30

We will calculate in the vertical column and get:

10.76 10.76

Answer

10.76

Exercise #10

8.5+5.2+8.4= 8.5+5.2+8.4=

Video Solution

Step-by-Step Solution

We will break down each of the factors in the exercise into a whole number and its remainder.

We get:

8+0.5+5+0.2+8+0.4= 8+0.5+5+0.2+8+0.4=

Now we'll combine only the whole numbers:

8+5+8=13+8=21 8+5+8=13+8=21

Now we'll calculate the remainder:

0.5+0.2+0.4=0.7+0.4=1.1 0.5+0.2+0.4=0.7+0.4=1.1

And now we'll get the exercise:

21+1.1=22.1 21+1.1=22.1

Answer

22.1

Exercise #11

0.2x+8.6x+0.65x= 0.2x+8.6x+0.65x=

Video Solution

Step-by-Step Solution

According to the order of operations rules, we'll solve the exercise from left to right:

0.2x+8.6x=8.8x 0.2x+8.6x=8.8x

We'll break down 8.8 into a smaller addition exercise that will be easier for us to calculate:

8x+0.8x+0.65x= 8x+0.8x+0.65x=

Now we'll use the commutative property since the exercise only involves addition.

Let's focus on the leftmost addition exercise, remembering that:

0.8=0.80 0.8=0.80

We'll calculate the following exercise:

0.80x+0.65x=1.45x 0.80x+0.65x=1.45x

And finally, we'll get the exercise:

8x+1.45x=9.45x 8x+1.45x=9.45x

Answer

9.45X

Exercise #12

10.1x+5.2x+2.4x= 10.1x+5.2x+2.4x=

Video Solution

Step-by-Step Solution

We will factor each of the terms in the exercise into a whole number and its remainder.

We get:

10x+0.1x+5x+0.2x+2x+0.4x= 10x+0.1x+5x+0.2x+2x+0.4x=

Now we'll combine only the whole numbers:

10x+5x+2x=15x+2x=17x 10x+5x+2x=15x+2x=17x

Now we'll calculate the remainder:

0.1x+0.2x+0.4x=0.3x+0.4x=0.7x 0.1x+0.2x+0.4x=0.3x+0.4x=0.7x

And now we'll get the exercise:

17x+0.7x=17.7x 17x+0.7x=17.7x

Answer

17.7X

Exercise #13

56x+78x+24x= \frac{5}{6}x+\frac{7}{8}x+\frac{2}{4}x=

Video Solution

Step-by-Step Solution

First, let's find a common denominator for 4, 8, and 6: it's 24.

Now, we'll multiply each fraction by the appropriate number to get:

5×46×4x+7×38×3x+2×64×6x= \frac{5\times4}{6\times4}x+\frac{7\times3}{8\times3}x+\frac{2\times6}{4\times6}x=

Let's solve the multiplication exercises in the numerator and denominator:

2024x+2124x+1224x= \frac{20}{24}x+\frac{21}{24}x+\frac{12}{24}x=

We'll connect all the numerators:

20+21+1224x=41+1224x=5324x \frac{20+21+12}{24}x=\frac{41+12}{24}x=\frac{53}{24}x

Let's break down the numerator into a smaller addition exercise:

48+524=4824+524=2+524=2524x \frac{48+5}{24}=\frac{48}{24}+\frac{5}{24}=2+\frac{5}{24}=2\frac{5}{24}x

Answer

2524x 2\frac{5}{24}x

Exercise #14

756+623+13= 7\frac{5}{6}+6\frac{2}{3}+\frac{1}{3}=

Video Solution

Step-by-Step Solution

Note that the right addition exercise between the fractions gives a result of a whole number, so we'll start with it:

623+13=7 6\frac{2}{3}+\frac{1}{3}=7

Now we get:

756+7=1456 7\frac{5}{6}+7=14\frac{5}{6}

Answer

1456 14\frac{5}{6}

Exercise #15

12+312+424= \frac{1}{2}+3\frac{1}{2}+4\frac{2}{4}=

Video Solution

Step-by-Step Solution

According to the order of operations, we will solve the exercise from left to right.

Let's note that in the first addition exercise, we have an addition between two halves that will give us a whole number, so:

12+312=4 \frac{1}{2}+3\frac{1}{2}=4

Now we will get the exercise:

4+424= 4+4\frac{2}{4}=

Let's note that we can simplify the mixed fraction:

24=12 \frac{2}{4}=\frac{1}{2}

Now the exercise we get is:

4+412=812 4+4\frac{1}{2}=8\frac{1}{2}

Answer

812 8\frac{1}{2}

Exercise #16

13+23+234= \frac{1}{3}+\frac{2}{3}+2\frac{3}{4}=

Video Solution

Step-by-Step Solution

According to the order of operations rules in arithmetic, we will solve the exercise from left to right.

Let's note that:

13+23=33=1 \frac{1}{3}+\frac{2}{3}=\frac{3}{3}=1

Now we'll get the exercise:

1+234=334 1+2\frac{3}{4}=3\frac{3}{4}

Answer

334 3\frac{3}{4}

Exercise #17

67x+87x+323x= \frac{6}{7}x+\frac{8}{7}x+3\frac{2}{3}x=

Video Solution

Step-by-Step Solution

Let's solve the exercise from left to right.

We will combine the left expression in the following way:

6+87x=147x=2x \frac{6+8}{7}x=\frac{14}{7}x=2x

Now we get:

2x+323x=523x 2x+3\frac{2}{3}x=5\frac{2}{3}x

Answer

523x 5\frac{2}{3}x

Exercise #18

13.4+4.5+0.1= 13.4+4.5+0.1=

Video Solution

Answer

18