Question #be08b

2 Answers
Jul 3, 2017

#A->" Mary bought "7/12 pounds#
#B->"Total weight bought is "1 1/3 pounds#

Solution given in a lot of detail.

Explanation:

#color(blue)("Important facts")#

A fraction's structure is that of:

#("count")/("indicator of size of what you are counting")->("numerator")/("denominator")#

You can not #ul("directly")# add or subtract the 'counts' unless the size indicators are the same.

Multiply by 1 and you do not change the value. However, 1 comes in many forms so you can change the way something looks without changing its true value.

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#color(blue)("Answering question A")#
Badly worded but you will get my point.

#Mary = Jessica-1/6#

#Mary=3/4-1/6 larr" in pounds"#

Note that both 4 and 6 will divide exactly into 12

#color(green)(Mary=[3/4color(red)(xx1)]-[1/6color(red)(xx1)]#

#color(green)(Mary=[3/4color(red)(xx3/3)]-[1/6color(red)(xx2/2)]#

#color(green)(Mary=" "9/12" "-" "2/12)#

#9-2=7# giving

#Mary=7/12 pounds#
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#color(blue)("Answering question B")#

Total weight bought #=3/4+7/12#

#color(green)("Total weight bought "=[3/4color(red)(xx1)]+7/12#

#color(green)("Total weight bought "=[3/4color(red)(xx3/3)]+7/12#

#"Total weight bought "= 9/12+7/12=16/12 pounds#

but 4 will divide exactly into both 16 and 12

#16/12-=(16-:4)/(12-:4)=4/3=1 1/3#

Total weight bought is #1 1/3 pounds#

#1/3# as a decimal is not precise so leave it in fraction form

Jul 16, 2017

a) Mary bought #7/12# lb

b) they bought #1 1/3# lb together

Explanation:

Identify the operations first. Many people are put off by the fractions.

Here's a similar but easier question.

John bought #8# lb of berries and Mark bought #2# lb less than John

So Mark bought: #8-2 = 6# lb. (This is a subtraction.)

Together they bought #8+6 = 14# lb (This is an addition.)

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Do exactly the same with the fractions:

Jessica bought #3/4# lb and Mary bought #1/6# lb less than Mary.

Mary bought:

#3/4 - 1/6" "larr# convert to a common denominator #(12)#

#=9/12 - 2/12 = 7/12# lb of berries

Together they bought:

#3/4 + 7/12" "larr# convert to a common denominator

#=9/12 +7/12 = 16/12#lb

Convert to a mixed number:

#16/12= 12/12 +4/12#

#= 1 1/3# lb of berries