Core Connections Course 1 Student 1st Edition Chapter 5 Multiplying Fractions and Area
Page 225 Problem 1 Answer
Given a situation, Mandy has a coupon of 40% and there is 70% sale on sunglasses that means she pays 110%.
Another situation is if there is 70% than means, she has to pay 30% and she has a coupon of 40% which means she has to pay 60% so 30% and 60% means 90% so she would pay 90% .
Find at least two ways to represent this situation using diagrams or numbers.
Use our representations to make sense of the situation and figure out if the sunglasses really are free.
Representation of Lorna’s explanation i.e.110% or in fractions,110/100=11/10.
Representation of Mandy’s explanation i.e.90% or in fractions,90/100=9/10 From 2 diagram we conclude that Mandy has to play less than price of sunglasses and Lorna has to pay 10%
more than the price of sunglasses.
Page 226 Problem 2 Answer
Given Tony purchased sunglasses by taking advantage of sale.
We have to write the result of calculating 60% of 30% as decimal.
We will use percentage to convert it in decimal.
We will calculate 60% of 30%
30% in decimal is 30/100 = 0.30 (in decimal)
60/100 =0.60 (in decimal)
So, 60%⋅30%=0.6⋅0.3
=6/10⋅3/10
=18/100
=0.18
=18%
Tony first calculated discount from sale i.e.70%.
Now the price to be paid is 30%.
The discount coupon of 40% is applied then on the price after the sale discount i.e. on 30%.
So, 60% of 30% of original price is to be paid.
Tony first calculated discount from sale i.e. 70%.
Now the price to be paid is 30%.
The discount coupon of 40% is applied then on the price after the sale discount i.e. on 30%.
So, 60% of 30% of original price is to be paid.
Page 226 Problem 3 Answer
Given 40% of 20%.We have to find the value of 40% of 20%.
We will use decimal multiplication.
the Given 40% of 20%, Chika used decimal multiplication as 0.4(0.2)=0.8
The result is wrong because since the number is divided by 100, the decimal will come before hundredth place.
Chika used wrong way to multiply decimal. The correct answer of 40% of 20% is 0.08.
Page 226 Problem 4 Answer
We have to find what happens when we multiply one-tenth by one-tenth.
We will use fraction-multiplication to find it out.
We will also represent the problem solution in decimal.
One-tenth is 1/10. So, one-tenth of one-tenth is
1/10⋅1/10=1/100
In decimal terms, 1/10=0.1 because decimal will be put before tenth place.
So, 0.1⋅0.1=0.01
One-tenth of one-tenth is 1/100 and in decimal is 0.01.
Page 226 Problem 5 Answer
Given 1/10.4/100.
We will use fraction multiplication to find it out.
We will also represent the problem solution in decimal.
The fraction-multiplication
1/10⋅4/100=4/1000
1/10 =0.1 and 4/100
=0.04 in decimal terms. So,0.1×0.04=0.004
Hence, the multiplication of given expression 1/10.4/100=4/1000 and in decimal form is 0.004.
Page 226 Problem 6 Answer
Given 40% of 20%.We have to calculate the correct answer.
We will use fraction multiplication to find it out.
40% of 20%,Chika used decimal multiplication as 0.4(0.2)=0.8
The correct calculation is0.4⋅0.2=4/10⋅2/10
=8/100
=0.08
Hence,40% of 20% the correct calculation is 0.08.
Page 226 Problem 7 Answer
From the part (a) to (f), we multiplied parts by parts.
We have to compare the products to the numbers that were multiplied.
There is no case such that the product of the multiplication is greater than any of the number.
There is no case such that the product of the multiplication is greater than any of the number.
Page 226 Problem 8 Answer
Given 20% Justify why ben write 2/10
We will use fraction-multiplication.
20% infraction is
20%=20/100
Reducing into the lowest term, 20% reducing to the lowest term is 2/10.
Page 226 Problem 9 Answer
Given a figure and 20% of 4.312.
We have to label the missing dimensions and areas with fractions and find the product and then express it as a decimal.
We will use fraction multiplication.
The rectangle is ABCD.4.312 is written as 4+0.3+0.01+0.002 which infraction term is
4+3/10+1/100+2/1000
20%⋅4.312=2/10⋅4312/1000
=8624/10000
=0.8624
The labeled figure is here
The value of 20% of 4.312=0.8624 and the labeled figure is
Page 226 Problem 10 Answer
Given a rough work by Ben We have to explain his work.
We will use fraction-multiplication.
4.312 can be written as 4.000+0.300+0.010+0.002.
Now 20% is 2/10 or 0.2 as written in part (a). So, 20% of 4.312 is 0.2×4.312
=0.2×(4.000+0.300+0.010+0.002)
=0.8+0.06+0.002+0.0004
Hence, the rough work done by Ben is 0.8+0.06+0.002+0.0004.
Page 226 Problem 11 Answer
Given 20% of 4.312
We have to help Ben complete his work by writing the answer to his multiplication problem.
We will use fraction-multiplication.
4.312 can be written as 4.000+0.300+0.010+0.002.
Now 20% is 2/10 or 0.2 as written in part (a). So, 20% of 4.312 is 0.2×4.312
=0.2×(4.000+0.300+0.010+0.002)
=0.8+0.06+0.002+0.0004……(1)
Now, solving (1) 0.8+0.06+0.002+0.0004=0.8624
Ben complete his work by writing the answer to his multiplication problem which is 0.8624
Page 226 Problem 12 Answer
Given20% of 4.312 Explain why did Ben line up the decimals points in his method as shown in figure
In the figure Ben lined up the decimals points in his method since addition will be easier as in digits at the ones place will be added, then digits at the tenth place will be added and so on.
Ben lined up the decimals points in his method since addition will be easier as in digits at the ones place will be added easily.
Page 227 Problem 13 Answer
Given0.2(4.312)
We have to use a generic rectangle, to sum up the product.
We will use a fraction of addition.
Given 0.2(4.312)
Solving them,
0.2(4.312)
=4⋅2/10+3/10⋅2/10+1/100⋅2/10+2/1000⋅2/10
=8/10+6/100+2/1000+4/10000
=0.8624
Hence, the product of 0.2(4.312) is 0.8624.
Page 227 Problem 14 Answer
Given 0.2(4.312) Conn or has shown his figure through the figure.
We have to explain where he has decided to place the decimal point in his answer.
Given 0.2(4.312)=0.8624
From the figure, we notice the first fraction 8/10. Since there is 10 in the denominator it will belong to tenths in the final result.
The decimal point is placed on the left side of tenths.
Connor has placed decimal point is placed on the left side of tenths.
Page 227 Problem 15 Answer
Given 3.9(0.6) Mohammed has calculated the answer as shown in figure.
We have to explain the answer be more than 2 or less than 2.
From the figure, we see the answer is 1.8 which will be added to 0.54 which makes it more than 2.
The answer is greater than 2 since in the solution part 1.8 is added to 0.53 which makes it greater than 2.
Page 227 Problem 16 Answer
Given the figure where Mohammed has multiplied the number.
We have to check whether the multiplication is correct or not.
We will use decimal-multiplication.
The calculation is 3.9×0.6
=(3+0.9)×0.6
=(3+9/10)×6/10
=3×6/10+9/10×6/10
=18/10+54/100
=1.8+0.54
The calculation done my Mohammed is correct as result is same in both case.
Page 227 Problem 17 Answer
Given the calculation of Mohammed’s work.
He noticed that he will need to add 5 tenths and 8 tenths.
calculate the sum for him.
From the calculation of Mohammed’s work
Five tenths and eighth tenths will be added in a usual way e.g. 0.5+0.8=1.3 and then 1 will be added to the number after the decimal of 1.8.
Mohammed will add Five tenths and eighth tenths will be added in a usual way e.g. 0.5+0.8=1.3 and then 1 will be added to number after the decimal of 1.8.
Page 227 Problem 18 Answer
Given the calculation of Mohammed’s work
We have to find the product 3.9(0.6).
We will use decimal multiplication.
Mohammed’s work to find the product of 3.9(0.6) can be completed as follows:
3.9×0.6 / 0.54+1.8 / 2.34
Hence, the product of 3.9(0.6) is 2.34.
Page 227 Problem 19 Answer
Given 0.3(0.0001).We have to find the product without using a calculator.
We will use fractions to solve.
Given0.3(0.0001)/0.3×0.0001
=3/ 10×1/10000
=3/100000
=0.00003
Therefore the product of 0.3(0.0001)=0.00003 we have calculated without calculator.
Page 227 Problem 20 Answer
Given1486(0.25).
We have to find the product without using the calculator.
We will use fractions to solve.
Given1486(0.25)
0.25×1.486
=25/100×(1.000+0.400+0.080+0.006)
=25/100×1+25/100×4/10+25/100×8/100+25/100×6/1000
=25/100+100/1000+200/10000+150/100000
=0.25+0.1+0.02+0.0015
=0.3715
Therefore the product of 1486(0.25) without using calculator is 0.3715.
Page 227 Problem 21 Answer
Given2.8(0.902).
We have to find the product without using the calculator.
We will use fractions to solve.
Given2.8(0.902)
0.28×0.902
=28/100×(0.900+0.000+0.002)
=28/100×9/10+28/100×0+28/100×2/1000
=252/1000+0+56/100000
=0.252+0.00056
=0.25256
Therefore the product of 2.8(0.902) without using calculator is 0.25256.
Page 227 Problem 22 Answer
Given Jack designed a bridge that is 0.2 miles and 3/5 of bridge has been built.
We have to find how much section of bridge is finished.
We will use fraction- multiplication.
Jack designed a bridge that will be 0.2 miles long, and 3/5 the bridge has been built.
Section of the bridge that is finished is
0.2×3/5
=2/10×3/5
=6/50
=6×2/50×2
=12/100
=0.12
Therefore Jack build 0.12 section of the bridge.
Page 227 Problem 23 Answer
Given Brianna thinks that3%⋅4%=12%.
But Caitlyn is not sure.We have to explain who is correct.
We will use fraction-multiplication.
Brianna thinks that3%⋅4%=12%.
It can also be written as 3%⋅4%
=3/100×4/100
=12/10000
=0.12%≠12%
Caitlyn is right.
Therefore, Caitlyn is right as 3%⋅4%≠12%.
Page 228 Problem 24 Answer
We have to create an entry with “Multiplication of Decimals” and label it with today’s date.
We will include at least two examples and we will explain the steps.
Multiplication of decimals Suppose we need to multiply 0.2 with 3.524.
Firstly, open 3.524as3.000+0.500+0.020+0.004. After writing these into fractions, multiply each term with0.2
0.2×3.524
=0.2×(3.000+0.500+0.020+0.004)
=2/10×(3+5/10+2/100+4/1000)
=6/10+10/100+4/1000+8/10000
Convert the above terms into decimals and then add up to get the final solution.
6/10+10/100+4/1000+8/10000
=0.6+0.1+0.004+0.0008
=0.7048
Multiplication of decimals Suppose we need to multiply 0.5 with 0.425.
Firstly, open 0.425 as 0.400+0.020+0.005. After writing these into fractions, multiply each term with0.5.
0.5×0.425
=0.5×(0.400+0.020+0.005)
=5/10×(4/10+2/100+5/1000)
=20/100+10/1000+25/10000
Convert the above terms into decimals and then add up to get the final solution.
20/100+10/1000+25/10000
=0.2+0.01+0.0025
=0.2125
Therefore, two examples of “decimal of multiplication” are 0.2×3.54=0.7048 and 0.5×0.425=0.2125.
Page 228 Problem 25 Answer
Given Ethan gave 10% of his income to charity.
This month, he wrote the calculation as shown in the figure.
We have to explain why this calculation is appropriate and finish the calculation for him.
Calculate how much he gave this month.
Ethan decided to give his monthly income to charity. His monthly income is $1526. So, the money given to charity is
1526×10/100
=1526×10/10×10
=1526×1/10
=152.6
The fraction multiplied is one-tenth. So, the decimal point is added before tenth place after multiplication.
Ethan gave $152.6 for the charity every month.