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32

Answer:

#GCF = 18#
Common factors:# " " 1 , 2, 3, 6, 9, 18#

Explanation:

There can be several common factors, but there is only one Greatest Common factor.

Write 36 and 90 as the product of their prime factors.

#36 = 2xx2xx3xx3#

#90= color(white)(xxx)2xx3xx3xx5#

#GCF =color(white)(x)2xx3xx3 color(white)(xxx) =18#

As for all the common factors, it is probably easiest to write all the factors of 36 and then select which are factors of 90 as well.

Factors of 36: #" "color(red)(1, 2, 3), 4, " "color(red)(6, 9)," " 12," " color(red)(18), " "36#
Factors of 90#" "color(red)(1,2,3)" ",5,color(red)(6,9),10," "15,color(red)(18),30," "45,90#

Common factors:#" "color(red)(1, 2, 3, 6, 9, 18)#

1

Answer:

25/3 oz or 8.33 oz

Explanation:

(2/5) of a jar of peanut butter needs #3(1/3) oz# of peanuts
1 full jar of peanut butter will require #(3(1/3))/(2/5) oz# of peanuts.
#=(10/3)/(2/5)=(10/3)*(5/2)=(10*5)/(3*2)=(5*cancel2*5)/(3*cancel2)#
= 25/3 oz = 8.33 oz

1

Answer:

47 is a positive integer and has no factors other than 1 and itself; hence a prime number and not composite.

Explanation:

A composite number is a positive integer which is not prime (I.e. which has factors other than one and itself). 47 has no factors other than 1 and itself, and hence a prime number and not composite.

1

Answer:

See a solution process below:

Explanation:

1 dozen is 12, therefore 3 dozen is #3 xx 12 = 36#

We can write the correlation:

#(1.5"tsp")/8 = b/36#

Multiply each side of the equation by #color(red)(36)# to solve for #b# while keeping the equation balanced:

#color(red)(36) xx (1.5"tsp")/8 = color(red)(36) xx b/36#

#(54"tsp")/8 = cancel(color(red)(36)) xx b/color(red)(cancel(color(black)(36)))#

#((2 xx 27)"tsp")/(2 xx 4) = b#

#((color(red)(cancel(color(black)(2))) xx 27)"tsp")/(color(red)(cancel(color(black)(2))) xx 4) = b#

#27/4"tsp" = b#

#(24 + 3)/4"tsp" = b#

#(24/4 + 3/4)"tsp" = b#

#(6 + 3/4)"tsp" = b#

#6 3/4"tsp" = b#

The answer is: b. 6 and 3 fourths tsp

1

Answer:

B

Explanation:

Given:
8 jumbo blueberry muffins need 1.5 tsp of baking powder
3 dozen (36 pcs) need how many tsp of baking powder?

#36   "muffins" * (1.5   tsp)/(8   "muffins") = (54)/8 = 6 6/8 = 6 3/4#

Another way of looking at this is ratio and proportion.
Let x = amount of baking powder needed for 3 dozen

#(1.5   tsp)/(8   "muffins") = x/(36   "muffins")#

#x = ((1.5   tsp)*(36   "muffins"))/(8   "muffins")#

#x = (54)/8 = 6 3/4#

1

Answer:

See a solution process below:

Explanation:

First, convert each number of yards from mixed numbers to improper fractions:

Needs:

#2 1/2 = 2 + 1/2 = (2/2 xx 2) + 1/2 = 4/2 + 1/2 = (4 + 1)/2 = 5/2#

Has:

#1 3/4 = 1 + 3/4 = (4/4 xx 1) + 3/4 = 4/4 + 3/4 + (4 + 3)/4 = 7/4#

To find out how much more fabric Sarah needs we can subtract how much Sarah has from how much total fabric Sarah needs:

#5/2 - 7/4#

To add or subtract fractions the must be over a common denominator. We can multiply the fraction on the left by the appropriate form of #1# to put it over a common denominator without changing the value of the fraction:

#(2/2 xx 5/2) - 7/4 =>#

#(2 xx 5)/(2 xx 2) - 7/4 =>#

#10/4 - 7/4#

We can now subtract the numerators over the common denominator:

#(10 - 7)/4 => 3/4#

Sarah needs #3/4# more yards of fabric to complete the dress.

2

Answer:

78

Explanation:

To the find the LCM factor both number and use each unique factor only once

# 26 = 2 xx 13#

# 39 = 3 xx 13# each has a factor of 13 so that is not unique

The unique factors are 2, 3 and 13 so the LCM is

# 2 xx 3 xx 13 = 78#

1

Answer:

#lcm(16,20)#=60

Explanation:

another way is to simply list the multiples of the numbers and pick out the common ones

multiples of#" "15:{15,30,45color(red)(,60),75,90,105,color(red)(120),.....}#

multiples of #" "20:{20,40color(red)(,60),80,100,color(red)(120),...}#

common multiples:#" "{60,120,..}#

#lcm(16,20)#=60

1

Answer:

G C F 18
It’s also called Greatest Common Divisor G C D

Explanation:

To find G C F of 36, 90:

First write the factors of both terms :
Factors of #36 = 2*color(red)(2*3*3)#

Factors of #90=color(red)(2*3*3*)5#

Select the common factors in both terms as marked redabove.
#color(red)(2*3*3)=#18 is the G C F

1

Answer:

#gcf(15,45)=15#

Explanation:

Another way is to list the factors and then pick out the common ones.

factors of #15:{color(red)(1,3,5,15),}#

factors of #45:{color(red)(1,3,5),9,color(red)(15),45}#

common factors #{1,3,5,15}#

#gcf(15,45)=15#