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1

Answer:

#(7x)/4-(4x)/5=(23x)/20#

Explanation:

In order to add or subtract fractions, they must have the same denominator, called the least common denominator (LCD). To find the least common denominator, write the multiples for each denominator. The lowest (least) multiple in common is the LCD.

#4:##4,8,12,16,color(red)20,24#
#5:##5,10,15,color(red)20,25#

The LCD is #20#. Now we need to multiply each fraction by an equivalent fraction that is equal to #1#. For example, #2/2=1#, #8/8=1#.

The first fraction needs to be multiplied by #color(red)(5/5# so that its new denominator will be #20#. The second fraction needs to be multiplied by #color(red)(4/4# so that its new denominator will be #20#.

#(7x)/4xxcolor(red)(5/5)-(3x)/5xxcolor(red)(4/4#

Multiply.

#(35x)/20-(12x)/20#

Place the numerators over the denominator #20#.

#(35x-12x)/20#

Simplify.

#23/20#

#23# is a prime number so the fraction cannot be further reduced.

2

Answer:

The answer is #0#.

Explanation:

Use the order of operations #("PEMDAS")#.

#color(red)"P"# = parentheses
#color(blue)"E"# = exponents
#color(orange)"MD"# = multiplying and dividing
#color(violet)"AS"# = adding and subtracting

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

#2+6 color(red)((9-3^2)) -2 color(white)"XXX"# Evaluate the #color(red)"P"#arentheses

within parentheses, we start over with #"PEMDAS"#

#(9-3^2) color(white)"XXXXXXX"# No #color(red)"P"#arentheses
#(9-color(blue)(3^2)) color(white)"XXxxxxxxx"# Evaluate the #color(blue)"E"#xponents
#(9-9) color(white)"xxXXxxxxxx"# No #color(orange)"M"#ultiplication or #color(orange)"D"#ivision
#(color(violet)(9-9))color(white)"xxXXxxxxxx"# Evaluate the #color(violet)"A"#ddition and #color(violet)"S"#ubtraction
#=(0)#

#2 + 6(0) - 2 color(white)"XXXXXX"# No #color(blue)"E"#xponents

#2 + color(orange)(6(0)) - 2 color(white)"XXXXXX"# Evaluate the #color(orange)"M"#ultiplication and #color(orange)"D"#ivision

#color(violet)(2+0-2) color(white)"XXXXXXX/"# Evaluate the #color(violet)"A"#ddition and #color(violet)"S"#ubtraction

#=0#

Final Answer

1

Answer:

No, #2/5!=5/8#

Explanation:

First, find a common denominator between the two. If one is not immediately obvious, you can always find one by multiplying the two denominators (the bottom numbers) together.

In this case, #8*5=40# so a common denominator is #40#. multiply the two fractions by a modified version of #1#

To get the denominator of #2/5# to #40#, the fraction should be multiplied by #8/8#

#2/5*8/8=16/40#

To get the denominator of #5/8# to #40#, the fraction should be multiplied by #5/5#.

#5/8*5/5=25/40#

#16/40!=25/40#

So, #2/5!=5/8#

1

Answer:

# 120 #

Explanation:

The easiest way to do this is to find the prime factorization of each number first.

# 8 = 4 * 2 #
# 8 = 2 * 2 * 2 #
# 8 = 2^3 #

# 12 = 6 * 2 #
# 12 = 3 * 2 * 2 #
# 12 = 3 * 2^2 #

# 15 = 5 * 3 #

Now that we have reduced all numbers to their prime factorizations, we will look for the factors with the highest exponent and multiply them all together to get our LCM.

There is # 2^3 # from # 8 #, # 3^1 # from # 12 # and # 15 #, and # 5^1 # from # 15 #.

So now we must do the following:

# 2^3 * 3 * 5 #
# 2 * 2 * 2 * 3 * 5 #
# 120 #

Therefore, the LCM of # 8 #, # 12 #, and # 15 # is # 120 #.

1

Answer:

#88#

Explanation:

Identify the individual terms and simplify each to a final answer.
These will be added or subtracted in the last step.

Within each term, the order of operations has to be followed:
Powers and roots, then multiply and divide.

#color(red)(12^2) +color(blue)(24div3) - color(forestgreen)(4^3#

#=color(red)(144) +color(blue)(8) - color(forestgreen)(64#

#= 152-64 #

#=88#

1

Answer:

#1.749 rarr 1.7#

Explanation:

The nearest 'tenth' means the same as to one decimal place.

To decide whether to round up to the next tenth or down to the same tenth, look at the digit in the second decimal place (hundredths).

If it is #5# or more, round up.
If it is #4# or less, round down.

#1.7color(red)(4)9# will round to #1.7#

The #color(red)(4)# is not big enough to affect the #7#.

Note that the thousands place is not considered at all.

1

Answer:

8

Explanation:

The lowest common multiple is the lowest number which is a multiple of both numbers.

Since 8 * 1 = 8 and 2 * 4 = 8, 8 is the lowest common multiple.

An easy way to find the LCM is to list all multiples of each number, up to the product of both numbers (in this case, 16).

For 2:
- 2, 4, 6, 8, 10, 12, 14, 16

For 8:
- 8, 16,

8 is the lowest number they both have in common.

The highest possible value of an LCM is both numbers multiplied by each other. This is why for both lists i stopped at 16, because
2*8 = 16

0

Answer:

#41/4#

Explanation:

1) Put mixed numbers in fraction form

#5 3/4 = (4 * 5 + 3)/4 = 23/4" "# (keep denominator)

#4 1/2 = (2 * 4 + 1)/2 = 9/2" "# (keep denominator

Problem:

#23/4 + 9/2#

2) Put both denominators in prime factorization and find LCD

#4 = 2 * 2 #

#2 = 2#

#LCD: 4#

3) Divide each denominator by LCD and multiply it with fractions

#23/4 = 23/4" "# (keep denominator; it is the same result because we want the denominator to be #4#)

#9/2 * 2/2 = 18/4#

4) Finally, add and solve

#23/4 + 18/4 = 41/4 = 10 1/4#

1

Answer:

#LCM = 36#

Explanation:

Write each number as the product of its prime factors, then you know what you are working with.

Notice that you do not even need to consider #4#, because #4# is a factor of #12#, so any multiple of #12# will be a multiple of #4# as well.

#color(white)(............) 4 = 2xx2#
#color(white)(............) 9 = " "3xx3#
#color(white)(..........) 12 = 2xx2xx3#
#color(white)(.................) darrcolor(white)(.)darrcolor(white)(m)darrcolor(white)(.)darr#

#LCM =" " 2xx2xx3xx3 = 36#

Notice that in factor form:

#2xx2# is there for the #4#
#2xx2xx3# is there for the #12#
#3xx3# is there for the #9#

All the numbers are in the LCM, but there are no unnecessary factors.

1

Answer:

#31.5# litres

Explanation:

Find the total volume first:

#450# glasses each contain #350# ml

#450 xx 350 = 157,500# ml.

Convert to litres immediately (#div 1000#)

#157,500 div 1000 =157# litres

The ratio: #" water : juice "# is #" "4" : "1#

This means that #4/5# is water and only#1/5# is juice.

The volume of juice is therefore:

#1/5 xx 157 = 31.5# litres