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1

Answer:

#7.5/10#

Explanation:

Given:

The answer must be equivalent to #3/4#, however the denominator must be a 10.

To solve this, we can use a proportion.

#3/4 = x/10# Where x is the unknown value we are solving for

#color(red)(3)/color(blue)(4) = color(blue)(x)/color(red)(10)# Now we cross multiply

#color(red)(3)(color(red)(10)) = color(blue)(4)(color(blue)(x))#

#30 = 4x# Divide 4 from both sides to isolate x

#x = 7.5#

0

Answer:

#2/5#

Explanation:

You find a number that you can divide the denominator and numerator by and then you divide it by that number until you cant divide it no more.

In the above context we have;

#8/20#

#(4 xx 2)/(4 xx 5)#

#(cancel4 xx 2)/(cancel4 xx 5)#

#(1 xx 2)/(1 xx 5)#

#2/5#

1

Answer:

#2/5#

Explanation:

Divide both the numerator and denominator by the HCF.

#8/20#

IN this case:

#(8div4)/(20div4) = 2/5#

2

Answer:

#7.5/10#

Explanation:

You need to multiply the numerator and denominator by the same number.

#4 xx 2.5 = 10#

#(3 xx2.5)/(4xx2.5) = 7.5/10#

3

Answer:

A few thoughts...

Explanation:

Here are a few ideas:

  • If you know that #6 xx 8 = 48# then it follows that #48 -: 8 = 6#

  • If you know that #7^2 = 49# then note that #48 = 49-1 = 7^2-1^2 = (7-1)(7+1) = 6 xx 8#

  • Notice that #48 = 40+8 = (10xx4)+8 = (10xx1/2xx8)+8 = (5xx8)+(1xx8) = (5+1)xx8 = 6xx8#

  • Add #8#'s until you get #48# and count the number of #8#'s you had to use: #48=overbrace(8+8+8+8+8+8)^(6 xx 8)#

  • The other way round, we could count the number of times we need to subtract #8# from #48# until we get to #0#: #48 rarr 40 rarr 32 rarr 24 rarr 16 rarr 8 rarr 0#. That was #6# times.

1

Answer:

I have one thought to add to George's excellent answer.

Explanation:

#48 -: 8# can also be written #48/8#

And I can reduce the fraction because both numbers are even:

#48/8 = (2 xx 24)/(2 xx 4) = 24/4#

If I notice that #24/4 = 6#, then I can finish. If not, then I see that the numbers are both even, so I can reduce again:

#48/8 = 24/4 = 12/2#.

And finish with #6#.

1

Answer:

See a solution process below:

Explanation:

First, using the standard order of operation or PEDMAS, execute the operations with the Parenthesis first:

#1 xx (color(red)(50) + color(red)(1779)) -: (color(blue)(81) -: color(blue)(9)) =>#

#1 xx 1829 -: 9#

Next, execute the Multiplication and Division operations left to right:

#color(red)(1) xx color(red)(1829) -: 9 =>#

#color(red)(1829) -: color(red)(9) =>#

#color(red)(1829)/color(red)(9) =>#

#(1827 + 2)/9 =>#

#1827/9 + 2/9 =>#

#203 + 2/9 =>#

#203 2/9#

or

#203.2222....#

or

#203.bar2#

1

Answer:

#10,000#

Explanation:

The question essentially asks what is #500# divided by #0.05#, since the answer, #a# we'll call it, is #0.05 * a#.

So, #500/0.05 = 10,000#.

The key point you need to note in this question is the phrase, times smaller, which tells you that the answer is #0.05 + 0.05# until you reach #500#. This is equal to #500/0.05#.
For future reference, any question following this format you'll need to use division.

2

Answer:

180

Explanation:

Find the unique prime factors for each number and multiply the factors together.

# 12 = 2 xx 2 xx 3 #
# 18 = 2 xx 3 xx 3 #
# 45 = 5 xx 3 xx 3 #

There are two factors of 2 needed ( the factor of 2 for 18 is a repeat.)

There are two factors of 3 needed ( the factors of 3 in 12 and 45 are repeats.)

There is one unique factor of 5

Multiplying the non repeated or unique factors gives.

The Least Common Multiply # = 2 xx 2 xx 3 xx 3 xx 5#

# 2 xx 2 xx 3 xx 3 xx 5 = 180#

1

Answer:

See a solution process below:

Explanation:

First, we can write #5 1/4" hours"# as #(5" hours" + 1/4" hours")#

So, first we can add the #5" hours"# to 7:00 PM giving:

#7:00" PM" + 5 = 12:00" AM"#

If #1" hour" = 60" minutes"# then we can divide each side of the equation by #color(red)(4)# to find out how many minutes in a #1/4# of an hour:

#(1" hour")/color(red)(4) = 60/color(red)(4)" minutes"#

#1/4" hour" = 15" minutes"#

We can now add the 15 minutes to the result we had from the previous step giving:

#12:00" AM" + 15" minutes" = 12:15" AM"#