Examples with solutions for Associative Property: More than two fractions

Exercise #1

4.5×3.2×5.6= 4.5\times3.2\times5.6=

Video Solution

Step-by-Step Solution

According to the order of operations rules, we will solve the exercise from left to right since multiplication is the only operation in it.

We will solve the left exercise vertically to avoid confusion and get:

4.5×3.2=14.40 4.5\\\times3.2\\=14.40 It is important to maintain correct positioning of the exercise, with the decimal point serving as an anchor.
Then we can multiply in order, first the ones digit of the first number by the ones digit of the second number,
then the tens digit of the first number by the ones digit of the second number, and so on.

Now we will get the exercise:

14.40×5.6= 14.40\times5.6=

Let's remember that:

14.40=14.4 14.40=14.4

We will solve the exercise vertically as well, and remember the rules of keeping the decimal point and multiplying in order (ones, tens, and so on)

And we will get:

14.4×5.6=80.64 14.4\\\times5.6\\=80.64

Answer

80.64 80.64

Exercise #2

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

Video Solution

Step-by-Step Solution

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

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

Giving us:

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

Answer

1456 14\frac{5}{6}

Exercise #3

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 #4

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

Video Solution

Step-by-Step Solution

According to the rules of the order of operations in arithmetic, we 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

We should obtain the following exercise:

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

Answer

334 3\frac{3}{4}

Exercise #5

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 #6

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 #7

8.5+5.2+8.4= ? 8.5+5.2+8.4=\text{ ?}

Video Solution

Step-by-Step Solution

First we will break down each of the factors in the exercise into a whole number and its remainder:

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

Then 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

Finally, we are left with the following:

21+1.1=22.1 21+1.1=22.1

Answer

22.1

Exercise #8

11.2×5.6×7.3= 11.2\times5.6\times7.3=

Video Solution

Step-by-Step Solution

According to the order of operations rules, we will solve the exercise from left to right since multiplication is the only operation in it.

We will solve the left exercise vertically to avoid confusion and get:

11.2×5.6=62.72 11.2\\\times5.6\\=62.72 It's important to maintain correct positioning of the exercise, with the decimal point serving as an anchor.
Then we can multiply in order, first the ones digit of the first number by the ones digit of the second number,
then the tens digit of the first number by the ones digit of the second number, and so on.

Now we'll get the exercise:

62.72×7.3= 62.72\times7.3=

Let's remember that:

7.3=7.30 7.3=7.30

We will solve the exercise vertically as well, remembering the rules about keeping the decimal point aligned and multiplying in order (ones, tens, and so on)

And we'll get:

457.856 457.856

Answer

457.856 457.856

Exercise #9

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 #10

10.1x+5.2x+2.4x= ? 10.1x+5.2x+2.4x=\text{ ?}

Video Solution

Step-by-Step Solution

The first step is factorising each of the terms in the exercise into a whole number and its remainder:

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

Next, we will 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

Finally, we are left with the following:

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

Answer

17.7x x

Exercise #11

34×23×214x= \frac{3}{4}\times\frac{2}{3}\times2\frac{1}{4}x=

Video Solution

Step-by-Step Solution

Let's begin by combining the simple fractions into a single multiplication exercise:

3×24×3×214x= \frac{3\times2}{4\times3}\times2\frac{1}{4}x=

Let's now proceed to solve the exercise in the numerator and denominator:

612×214x= \frac{6}{12}\times2\frac{1}{4}x=

Finally we'll simplify the simple fraction in order to obtain the following:

12×214x=118x \frac{1}{2}\times2\frac{1}{4}x=1\frac{1}{8}x

Answer

118x 1\frac{1}{8}x

Exercise #12

15×78×223= \frac{1}{5}\times\frac{7}{8}\times2\frac{2}{3}=

Video Solution

Step-by-Step Solution

First, let's convert the mixed fraction to an improper fraction as follows:

15×78×3×2+23= \frac{1}{5}\times\frac{7}{8}\times\frac{3\times2+2}{3}=

Let's solve the equation in the numerator:

15×78×6+23= \frac{1}{5}\times\frac{7}{8}\times\frac{6+2}{3}=

15×78×83= \frac{1}{5}\times\frac{7}{8}\times\frac{8}{3}=

Since the only operation in the equation is multiplication, we'll combine everything into one equation:

1×7×85×8×3= \frac{1\times7\times8}{5\times8\times3}=

Let's simplify the 8 in the numerator and denominator of the fraction:

1×75×3= \frac{1\times7}{5\times3}=

Let's solve the equations in the numerator and denominator and we get:

715 \frac{7}{15}

Answer

715 \frac{7}{15}

Exercise #13

15.6×5.2x×0.3= 15.6\times5.2x\times0.3=

Video Solution

Step-by-Step Solution

Let's look at the exercise, and we'll see that we have two "regular" numbers and one number with a variable.
Since this is a multiplication exercise, there's no problem multiplying a number with a variable by a number without a variable.

In fact, it's important to remember that a variable attached to a number represents multiplication by itself, for example in this case: 5.2×x 5.2\times x
Therefore, we can use the distributive property to separate the variable, and come back to it later.
We'll solve the exercise from left to right.

We'll solve the left exercise vertically to avoid confusion and get:

     15.6×    5.2= 81.12 ~~~~~15.6 \\\times~~~~5.2 \\=~81.12 It's important to be careful with the correct placement of the exercise, where the decimal point serves as an anchor.
Then we can multiply in order, first the ones digit of the first number by the ones digit of the second number,
then the tens digit of the first number by the ones digit of the second number, and so on.

Now we'll get the exercise:

81.21×0.3= 81.21\times0.3=

Let's remember that:

0.3=0.30 0.3=\text{0}.30

And we'll get:

24.336 24.336

Let's not forget to add the variable at the end, and thus the answer will be:

24.336x 24.336 x

Answer

24.336x 24.336x

Exercise #14

0.5×6.7×6.31= 0.5\times6.7\times6.31=

Video Solution

Step-by-Step Solution

According to the order of operations rules, we will solve the exercise from left to right since multiplication is the only operation in it.

We will solve the left exercise vertically to avoid confusion and get:

0.5×6.7=3.35 0.5\\\times6.7\\=3.35 It is important to maintain correct positioning of the exercise, with the decimal point serving as an anchor.
Then we can multiply in order, first the ones digit of the first number by the ones digit of the second number,
then the tens digit of the first number by the ones digit of the second number, and so on.

Now we will get the exercise:

3.35×6.31= 3.35\times6.31=

We will solve the exercise vertically as well, remembering the rules of keeping the decimal point and multiplying in order (ones, tens, and so on)

And we will get:

3.35×6.31=21.1385 3.35\\\times6.31\\=21.1385

Answer

21.1385 21.1385

Exercise #15

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 #16

356×556×13x= 3\frac{5}{6}\times5\frac{5}{6}\times\frac{1}{3}x=

Video Solution

Step-by-Step Solution

First, let's convert all mixed fractions to simple fractions:

3×6+56×5×6+56×13x= \frac{3\times6+5}{6}\times\frac{5\times6+5}{6}\times\frac{1}{3}x=

Let's solve the exercises with the eight fractions:

18+56×30+56×13x= \frac{18+5}{6}\times\frac{30+5}{6}\times\frac{1}{3}x=

236×356×13x= \frac{23}{6}\times\frac{35}{6}\times\frac{1}{3}x=

Since the exercise only involves multiplication, we'll combine all the numerators and denominators:

23×356×6×3x=805108x \frac{23\times35}{6\times6\times3}x=\frac{805}{108}x

Answer

805108x \frac{805}{108}x

Exercise #17

23×723×312= \frac{2}{3}\times7\frac{2}{3}\times3\frac{1}{2}=

Video Solution

Step-by-Step Solution

First, we'll convert the mixed fractions to simple fractions as follows:

23×7×3+23×3×2+12= \frac{2}{3}\times\frac{7\times3+2}{3}\times\frac{3\times2+1}{2}=

Let's solve the exercises in the fraction multiplier:

23×21+23×6+12= \frac{2}{3}\times\frac{21+2}{3}\times\frac{6+1}{2}=

23×233×72= \frac{2}{3}\times\frac{23}{3}\times\frac{7}{2}=

Since the only operation in the exercise is multiplication, we'll combine everything into one exercise and get:

2×23×73×3×2=46×79×2=32218 \frac{2\times23\times7}{3\times3\times2}=\frac{46\times7}{9\times2}=\frac{322}{18}

Answer

1789 17\frac{8}{9}

Exercise #18

78×278×14= \frac{7}{8}\times2\frac{7}{8}\times\frac{1}{4}=

Video Solution

Step-by-Step Solution

First, let's convert the mixed fraction to a simple fraction as follows:

78×8×2+78×14= \frac{7}{8}\times\frac{8\times2+7}{8}\times\frac{1}{4}=

Let's solve the exercise in the numerator:

78×16+78×14= \frac{7}{8}\times\frac{16+7}{8}\times\frac{1}{4}=

78×238×14= \frac{7}{8}\times\frac{23}{8}\times\frac{1}{4}=

Since the only operation in the exercise is multiplication, we'll combine everything into one exercise:

7×23×18×8×4= \frac{7\times23\times1}{8\times8\times4}=

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

7×2364×4=161256 \frac{7\times23}{64\times4}=\frac{161}{256}

Answer

161256 \frac{161}{256}

Exercise #19

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

Video Solution

Answer

18