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Answer:

#23# has only 2 factors - it is prime.

Explanation:

A prime number can be defined as:

"A natural number which has only 2 factors - itself and 1".

23 has only 2 factors:#" "23 = 1 xx23#

There are no other natural numbers which are factors.
#23# is therefore a prime number.

If it had 3 or more factors it would be composite.

1 is the only number which has 1 factor - it is neither prime nor composite.

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.

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 =157.5# 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 157.5 = 31.5# litres

Answer:

#550/3000 = 11/60#

Explanation:

When you write a fraction you are showing :

#("part")/("whole")#

In order to do this the units have to be the same, so you can write #3km # as #3000m#

#550m# is the 'part' and #3000m# is the 'whole'.

The fraction is : #(550m)/(3000m)#

Note:

  • the units are the same, so they will cancel.
    The fraction does not have a unit, it merely indicates how the two quantities compare with each other.

  • 'fraction' generally refers to a common fraction.

  • fractions should be given in the simplest form, Divide the numerator and denominator by the highest common factor

#(550 div 50)/(3000 div 50) = 11/60#

Answer:

The answer is #45#.

Explanation:

We use BODMAS to help solve this. There are no Brackets and no Orders, so we go straight to Division and then Multiplication, before going on to Addition and then Subtraction. The direction is left to right.

#20+6-:2xx10-5#

There are no Brackets and nor Orders, so we go directly to Division.

There is one Division: #6-:2=3#

Hence:

#20+3xx10-5#

Next comes Multiplication: #3xx10=30#

Hence:

#20+30-5#

Next comes Addition: #20+30=50#

#50-5#

Last is Subtraction: #50-5=45#

#45#

Answer:

Bill has to run #2 7/8# laps on Friday to reach his target.

Explanation:

First we calculate the distance Bill has run on each day of the week from Monday to Thursday. We do that by converting the mixed fractions into improper fractions (by multiplying the whole number by the denominator and adding the product to the numerator) and multiplying them by #400#, the distance of each lap in metres.

Monday:

Number of laps: #1 1/4=5/4#

Distance: #5/4xx400=5/(1cancel4)xx100cancel400=5xx100=500m#

Tuesday:

Number of laps: #1 3/4=7/4#

Distance: #7/4xx400=7/(1cancel4)xx100cancel400=7xx100=700m#

Wednesday:

Number of laps: #1 5/8=13/8#

Distance: #13/8xx400=13/(1cancel8)xx50cancel400=13xx50=650m#

Thursday:

Number of laps: #2 1/2=5/2#

Distance: #5/2xx400=5/(1cancel4)xx200cancel400=5xx200=1000m#

Now we add the four distances to determine the total distance run by Bill in four days.

The total distance is #(500+700+650+1000)=2850m#

Bill wants to run a total of #4000m# in five days, so he would have to run #(4000-2850)=1150m# on Friday to achieve that total.

Since #1# lap is #400m#, we divide that distance by #400# to calculate how many laps Bill has to run.

#1150/400=(115cancel0)/(40cancel0)=(23cancel115)/(8cancel40)=2 7/8#

Bill has to run #2 7/8# laps on Friday to reach his target.

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