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Bridges in Mathematics Grade 5 Home Connections Answer Key Unit 5 Module 1
Bridges in Mathematics Grade 5 Home Connections Unit 5 Module 1 Session 1 Answer Key
Multiplication & Division Review
Question 1.
Complete the following multiplication tables.
a.
Answer:
Explanation:
Completed the given table above using multiplication method as
60 X 2 = 120,
60 X 9 = 540,
60 X 6 = 360,
60 X 5 = 300,
60 X 7 = 420,
60 X 20 = 1,200,
60 X 40 = 2,400,
60 X 30 = 1,800.
b.
Answer:
Explanation:
Completed the given table above using multiplication method as
40 X 2 = 80,
40 X 9 = 360,
40 X 6 = 240,
40 X 5 = 200,
40 X 7 = 280,
40 X 20 = 8,000,
40 X 40 = 1,600,
40 X 30 = 1,200.
Question 2.
Complete the following division tables.
Answer:
Explanation:
Completed the given table above using division method as
1,200 ÷ 30 = 40,
900 ÷ 30 = 30 ,
60 ÷ 30 = 2,
210 ÷ 30 = 70,
1,500 ÷ 30 = 500,
1,800 ÷ 30 = 600,
270 ÷ 30 = 9,
2,400 ÷ 30 = 800.
Question 3.
Solve these multiplication problems using the standard algorithm.
Answer:
Explanation:
Solved the given multiplication problems using the standard algorithm as shown above.
Question 4.
Whitney’s 9 cousins are coming to visit, and she wants to make them each a little gift bag. She wants to put an equal number of little candies in each bag, eat 3 candies herself, and have none left over.
a. Which bag of candies should she buy? Show all of your work.
Hint: Can you remember a divisibility rule to help?
Answer:
Lemon Sours,
Explanation:
Given Whitney’s 9 cousins are coming to visit and she wants to make them each a little gift bag, She wants to put an equal number of little candies in each bag, eat 3 candies herself and have none left over. So bag of candies should she buy are
1. Lemons Sours 147 divided by 9 as 147/9 =
9)147(16
09
57
54
3
2. Strawberry Kisses 216 divided by 9 as 216/9 =
9)216(24
18
36
36
0
3. Pineapple Sweets 193 divided by 9 as 193/9 =
9)193(21
18
13
09
4
As remainder is 3 in 1 bit therefore she should buy Lemons Sours.
b. How many candies will each cousin get? Show all your work.
Answer:
Each cousin will get 16 candies,
Explanation:
As given Whitney’s 9 cousins are coming to visit and she wants to make them each a little gift bag, She wants to put an equal number of little candies in each bag, eat 3 candies herself and have none left over. So bag of candies should she buy are Lemons Sours 147 divided by 9 as 147/9 =
9)147(16
09
57
54
3
So each cousin will get 16 candies.
Bridges in Mathematics Grade 5 Home Connections Unit 5 Module 1 Session 3 Answer Key
More Fractions of Wholes
Question 1.
Find the products.
a. \(\frac{1}{4}\) of 6 = _______________
Answer:
\(\frac{3}{2}\),
Explanation:
The products of \(\frac{1}{4}\) of 6 is \(\frac{6}{4}\) = \(\frac{3}{2}\).
b. \(\frac{1}{5}\) × 30 = _______________
Answer:
6,
Explanation:
The products of \(\frac{1}{5}\) X 30 is \(\frac{30}{5}\) = 6.
c. \(\frac{1}{3}\) of 27 = _______________
Answer:
9,
Explanation:
The products of \(\frac{1}{3}\) of 27 is \(\frac{27}{3}\) = 9.
d. \(\frac{3}{4}\) of 6 = ______________
Answer:
\(\frac{9}{2}\) or 4\(\frac{1}{2}\),
Explanation:
The products of \(\frac{3}{4}\) of 6 is \(\frac{18}{4}\) = \(\frac{9}{2}\) = 4\(\frac{1}{2}\).
e. \(\frac{4}{5}\) × 30 = _________________
Answer:
24,
Explanation:
The products of \(\frac{4}{5}\) X 30 is \(\frac{4}{5}\) X 30 = \(\frac{4 X 30}{5}\) = \(\frac{120}{5}\) = 24.
f. \(\frac{2}{3}\) × 27 = ________________
Answer:
18,
Explanation:
The products of \(\frac{2}{3}\) X 27 is \(\frac{2 X 27}{3}\) = \(\frac{2 X 9}{1}\) = 18.
Question 2.
True or False?
a. \(\frac{1}{4}\) × 9 = 2\(\frac{1}{4}\)
T
F
Answer:
True,
Explanation:
Given to check \(\frac{1}{4}\) X 9 = 2\(\frac{1}{4}\) so \(\frac{9}{4}\) = \(\frac{2 X 4 + 1}{4}\) = \(\frac{9}{4}\) its true.
b. \(\frac{3}{5}\) of 25 = 15
T
F
Answer:
True,
Explanation:
Given to check \(\frac{3}{5}\) X 25 = \(\frac{3 X 25}{5}\) so \(\frac{3 X 5}{1}\) = 15 so it is true.
c. \(\frac{2}{5}\) of 15 = 5\(\frac{2}{5}\)
T
F
Answer:
False,
Explanation:
Given to check \(\frac{2}{5}\) of 15 = \(\frac{2 X 15}{5}\) so \(\frac{30}{5}\) = 6 now right side 5\(\frac{2}{5}\) is \(\frac{5 X 5 + 2}{5}\) = \(\frac{27}{5}\) both sides it is not equal so its false.
d. 18 × \(\frac{1}{5}\) = \(\frac{5}{18}\)
T
F
Answer:
False,
Explanation:
Given to check 18 X \(\frac{1}{5}\) = \(\frac{18 X 1}{5}\) so \(\frac{18}{5}\) now right side \(\frac{5}{18}\) is \(\frac{18}{5}\) not equal to \(\frac{5}{18}\) both sides it is not equal so its false.
e. \(\frac{2}{6}\) × 24 = 14
T
F
Answer:
False,
Explanation:
Given to check \(\frac{2}{6}\) X 24 = \(\frac{2 X 24}{6}\) so \(\frac{2 X 4}{1}\) = 8 now right side it is 14 both sides it is not equal so its false.
f. 17 × \(\frac{1}{3}\) = \(\frac{17}{3}\)
T
F
Answer:
True,
Explanation:
Given to check 17 X \(\frac{1}{3}\) = \(\frac{17 X 1}{3}\) so \(\frac{17}{3}\) now right side is also \(\frac{17}{3}\) both sides are equal so its true.
Question 3.
Pete rode his dirt bike \(\frac{2}{3}\) of the 150-mile course. How many miles did Pete ride? Show your work.
Answer:
100 miles,
Explanation:
Given Pete rode his dirt bike \(\frac{2}{3}\) of the 150-mile course. Number of many miles did Pete ride are \(\frac{2}{3}\) X 150 miles = \(\frac{2 X 150}{3}\) miles = \(\frac{300}{3}\) miles = 100 miles.
Question 4.
Kim says that multiplying \(\frac{1}{4}\) × 12 is the same as dividing 12 by 4. Do you agree with Kim? Explain your answer.
Answer:
Yes,
Explanation:
Given Kim says that multiplying \(\frac{1}{4}\) X 12 is the same as dividing 12 by 4. As \(\frac{1}{4}\) X 12 is \(\frac{12}{4}\) = 3 and 12/ 4 = 3, So I agree with Kim.
Review
Question 5.
Round each number to the nearest tenth and hundredth.
Answer:
Explanation:
Rounded each number to the nearest tenth and hundredth.
Question 6.
Evaluate each of the following.
a. 6 × (5 × 12) = ________________
Answer:
360,
Explanation:
Given to evaluate 6 X (5 X 12) so which is equal to 6 X 60 = 360.
b. (18 × 13) + (2 × 13) = _______________
Answer:
260,
Explanation:
Given to evaluate (18 X 13) + (2 X 13) = 234 + 26 = 260.
c. (75 ÷ 3) × 10 = ________________
Answer:
250,
Explanation:
Given to evaluate (75 ÷ 3) X 10 = 25 X 10 = 250.
d. (117 × 4) – (7 × 4) = ________________
Answer:
440,
Explanation:
Given to evaluate (117 X 4) – (7 X 4) = 468 – 28 = 440.
Question 7.
Six friends had lunch together and decided to split the bill evenly.
a. If the bill was $48.60, what was each person’s share? Show your work.
Answer:
$8.10,
Explanation:
Given six friends had lunch together and decided to split the bill evenly. If the bill was $48.60, So each person’s share is
6)$48.60($8.10
48
0.60
0.60
0
b. After tax and tip, the bill totaled $63.00. What was each person’s share? Show your work.
Answer:
$10.5,
Explanation:
Given after tax and tip the bill totaled $63.00. So each person’s share is
6)$63.00($10.50
60
3.00
3.00
0
Question 8.
CHALLENGE Vivian loves to paint in the evenings after school. She is working on three paintings. She needs 4 brushes, 3 canvases, and 12 small tubes of paint. Brushes cost $0.75 each, canvases cost $5.99 each, and tubes of paint costs $1.89 each.
a. Write an expression to determine Vivian’s cost, then solve the problem.
Answer:
Expression: (4 X $0.75) + (3 X $5.99) + (12 X $1.89),
Vivian’s cost is $43.65,
Explanation:
Given Vivian loves to paint in the evenings after school. She is working on three paintings. She needs 4 brushes, 3 canvases, and 12 small tubes of paint. Brushes cost $0.75 each, canvases cost $5.99 each, and tubes of paint costs $1.89 each. An expression to determine Vivian’s cost is (4 X $0.75) + (3 X $5.99) + (12 X $1.89) = $3.00 + $17.97 + $22.68 = $43.65.
b. Help Vivian determine the average cost per painting. Write an expression and then solve the problem.
Answer:
Expression: ((4 X $0.75) + (3 X $5.99) + (12 X $1.89) ÷ 3),
Average cost per painting : $14.55,
Explanation:
The expression for the average cost per painting is ((4 X $0.75) + (3 X $5.99) + (12 X $1.89) ÷ 3) = ($3.00 + $17.97 + $22.68) ÷ 3 = $43.65 ÷ 3 = $14.55.
Bridges in Mathematics Grade 5 Home Connections Unit 5 Module 1 Session 5 Answer Key
Games, Cards & More
In Target One Fractions, players choose three numbers to create a whole number and a fraction that have a product close to 1. Their score is the difference between their product and 1, and the lowest score wins the round.
Question 1.
Erica is playing Target One Fractions. She has these cards: 1, 2, 3, 4, 6.
a. Which three cards should she choose to make a whole number and a fraction that have a product close to 1?
Answer:
Three cards are : 1,2,3,
Fraction close to 1 is 1.2,
Explanation:
We have Erica is playing Target One Fractions. She has these cards: 1, 2, 3, 4, 6. So three cards should she choose to make a whole number and a fraction that have a product close to 1 will be substituting and checking
1. (1,2,3) ÷ 5 = 1 + 2 + 3 ÷ 5 = 6 ÷ 5 = 1.2 close to 1,
2. (1,3,4) ÷ 5 = 1 + 3 + 4 ÷ 5 = 8 ÷ 5 = 1.6 not close to 1,
3. (1,2,4) ÷ 5 = 1 + 2 + 4 ÷ 5 = 7 ÷ 5 = 1.4 not equal to 1,
4. (1,2,6) ÷ 5 = 1 + 2 + 6 ÷ 5 = 9 ÷ 5 = 1.8 not equal to 1,
5. (1,3,6) ÷ 5 = 1 + 3 + 6 ÷ 5 = 10 ÷ 5 = 2 not equal to 1,
6. (2,3,4) ÷ 5 = 2 + 3 + 4 ÷ 5 = 9 ÷ 5 = 1.8 not close to 1,
7. (2,3,5) ÷ 5 = 2 + 3 + 5 ÷ 5 = 10 ÷ 5 = 2 not close to 1,
8. (2,4,6) ÷ 5 = 2 + 4 + 6 ÷ 5 = 12 ÷ 5 = 2.4 not equal to 1,
9. (3,4,5) ÷ 5 = 3 + 4 + 5 ÷ 5 = 12 ÷ 5 = 2.4 not close to 1,
10. (3,4,6) ÷ 5 = 3 + 4 + 6 ÷ 5 = 13 ÷ 5 = 2.6 not close to 1,
11. (3,5,1) ÷ 5 = 3 + 5 + 1 ÷ 5 = 9 ÷ 5 = not close to 1,
12. (4,5,1) ÷ 3 = 4 + 5 + 1 ÷ 3 = 10 ÷ 3 =3.33 not close to 1,
13. (4,2,3) ÷ 3 = 4 + 2 + 3 ÷ 3 = 9 ÷ 3 = 3 not close to 1,
14. (4,5,6) ÷ 3 = 4 + 5 + 6 ÷ 3 = 15 ÷ 3 = 5 not close to 1,
15. (5,1,2) ÷ 3 = 5 + 1 + 2 ÷ 3 = 8 ÷ 3 = 2.66 not close to 1,
16. (5,3,4) ÷ 3 = 5 + 3 + 4 ÷ 3 = 12 ÷ 3 = 4 not close to 1,
17. (5,2,6) ÷ 3 = 5 + 2 + 6 ÷ 3 = 13 ÷ 3 = 4.33 not close to 1,
18. (6,4,5) ÷ 3 = 6 + 4 + 5 ÷ 3 = 15 ÷ 3 = 5 not close to 1,
19. (6,2,3) ÷ 3 = 6 + 2 + 3 ÷ 3 = 11 ÷ 3 = 3.66 not close to 1,
20. (6,3,5) ÷ 3 = 6 + 3 + 5 ÷ 3 = 14 ÷ 3 = 4.66 not close to 1.
b. Write an expression for the problem Erica will solve.
Answer:
Expression: 1,2,3 ÷ 5,
Explanation:
An expression for the problem Erica will solve is 1,2,3 ÷ 5.
c. Solve the problem.
Answer:
1.2 approximately equal to 1,
Explanation:
Given numbers 1,2,3 so 1 + 2 + 3 ÷ 5 = 6 ÷ 5 = 1.2 close to 1,
d. What is Erica’s score for this round?
Answer:
1.2 approximately equal to 1,
Explanation:
Erica’s score for this round is 1.2 approximately equal to 1.
Question 2.
Jamal is playing Beat the Calculator: Fractions. Help Jamal solve the following problems. Show your work.
a. 1\(\frac{1}{5}\) – \(\frac{3}{10}\) = _______________
Answer:
\(\frac{9}{10}\),
Explanation:
Given Jamal is playing Beat the Calculator: Fractions. Helping Jamal to solve the following problems is 1\(\frac{1}{5}\) – \(\frac{3}{10}\) = \(\frac{1 X 5 + 1}{5}\) – \(\frac{3}{10}\) = \(\frac{6}{5}\) – \(\frac{3}{10}\) as denominators multiplying numerator and denominator with 2 as \(\frac{6 X 2}{5 X 2}\) – \(\frac{3}{10}\) = \(\frac{12}{10}\) – \(\frac{3}{10}\) = \(\frac{12 – 3}{10}\) = \(\frac{9}{10}\).
b. \(\frac{1}{3}\) + \(\frac{1}{4}\) + \(\frac{1}{2}\) = _______________
Answer:
\(\frac{13}{12}\) or 1\(\frac{1}{12}\),
Explanation:
Given to solve \(\frac{1}{3}\) + \(\frac{1}{4}\) + \(\frac{1}{2}\) as denominators are not the same we multiply numerators and denominators to have common denominators first with same number \(\frac{1}{3}\) X 4 = \(\frac{4}{12}\), \(\frac{1}{4}\) X 3 = \(\frac{3}{12}\), \(\frac{1}{2}\) X 6 = \(\frac{6}{12}\) all have denominators 12 so we add numerators as \(\frac{4 + 3 + 6}{12}\) = \(\frac{13}{12}\) as numerator is greater than denominator we write in mixed fraction \(\frac{1 X 12 + 1}{12}\) we get 1\(\frac{1}{12}\).
c. (\(\frac{7}{8}\) – \(\frac{1}{4}\)) – (\(\frac{5}{5}\) – \(\frac{3}{3}\)) = ______________
Answer:
– \(\frac{11}{8}\) or -1\(\frac{3}{8}\),
Explanation:
Given to solve (\(\frac{7}{8}\) – \(\frac{1}{4}\)) – (\(\frac{5}{5}\) – \(\frac{3}{3}\)) =
(\(\frac{7}{8}\) – \(\frac{1}{4}\)) – 1 – 1) = (\(\frac{7}{8}\) – \(\frac{1}{4}\)) – 2) as denominators are not the same we multiply numerators and denominators to have common denominators first \(\frac{7 X 1 – 2 X 1 -16}{8}\) = \(\frac{-11}{8}\) as numerator is greater than denominator we write in mixed fraction as \(\frac{8 X 1 + 3}{12}\) we get -1\(\frac{3}{8}\).
d. \(\frac{12}{24}\) + \(\frac{18}{36}\) + \(\frac{24}{48}\) = ________________
Answer:
\(\frac{3}{2}\),
Explanation:
Given \(\frac{12}{24}\) + \(\frac{18}{36}\) + \(\frac{24}{48}\) to solve all denominators have common factor 6 we divide by it, we get \(\frac{6 X 2}{6 X 4}\) + \(\frac{6 X 3}{6 X 6}\) + \(\frac{6 X 4}{6 X 8}\) =
\(\frac{1}{2}\) + \(\frac{1}{2}\) + \(\frac{1}{2}\) = 3 times \(\frac{1}{2}\) so \(\frac{3}{2}\).
Question 3.
Billy made 60 cards to give away on Valentine’s Day. Help Billy figure out how many cards he will give to his family, his teachers, and his friends. Show your work.
a. If Billy gives \(\frac{1}{3}\) of his cards to his family, how many cards does Billy give his family?
Answer:
20 cards,
Explanation:
Given Billy made 60 cards to give away on Valentine’s Day, If Billy gives \(\frac{1}{3}\) of his cards to his family, Number of cards does Billy gives his family are 60 X \(\frac{1}{3}\) = \(\frac{60}{3}\) = 20 of his cards to his family.
b. If Billy gives \(\frac{1}{4}\) of his cards to his teachers, how many cards does Billy give his teachers?
Answer:
15 cards,
Explanation:
Given Billy made 60 cards to give away on Valentine’s Day, If Billy gives \(\frac{1}{4}\) of his cards to his teachers, Number of cards does Billy gives his teachers are 60 X \(\frac{1}{3}\) = \(\frac{60}{3}\) = 20 of his cards to his teachers.
c. If Billy gives \(\frac{5}{12}\) of his cards to his friends, how many cards does Billy give his friends?
Answer:
Given Billy made 60 cards to give away on Valentine’s Day, If Billy gives \(\frac{5}{12}\) of his cards to his friends, Number of cards does Billy gives his friends are 60 X \(\frac{5}{12}\) = \(\frac{60 X 5}{12}\) = 25 of his cards to his friends.
Question 4.
True or False?
a. 3 × \(\frac{4}{5}\) = 4 × \(\frac{3}{5}\)
T
F
Answer:
True,
Explanation:
Given to find 3 X \(\frac{4}{5}\) = 4 X \(\frac{3}{5}\) we get left side as \(\frac{3 X 4}{5}\) and right side \(\frac{4 X 3}{5}\) result is \(\frac{12}{5}\) = \(\frac{12}{5}\) both side are equal so its true.
b.
3 × \(\frac{4}{5}\) = 5 × \(\frac{3}{4}\)
T
F
Answer:
False,
Explanation:
Given to find 3 X \(\frac{4}{5}\) = 5 X \(\frac{3}{4}\) we get left side as \(\frac{3 X 4}{5}\) and right side \(\frac{5 X 3}{4}\) result is \(\frac{12}{5}\) = \(\frac{15}{4}\) both side are not equal its false.
c. 3 × \(\frac{4}{5}\) = \(\frac{4}{5}\) × 3
T
F
Answer:
True,
Explanation:
Given to find 3 X \(\frac{4}{5}\) = \(\frac{4}{5}\) X 3 we get left side as \(\frac{3 X 4}{5}\) and right side \(\frac{4 X 3}{5}\) result is \(\frac{12}{5}\) = \(\frac{12}{5}\) both side are equal so its true.
Question 5.
Madison and Noah are reading new books from the library. Noah has read \(\frac{3}{8}\) of his book, which has 72 pages. Madison has read \(\frac{3}{5}\) of her book, which has 55 pages. Who has read more pages? How do you know? Show your work.
Answer:
Madison read more number of pages,
Explanation:
As Madison and Noah are reading new books from the library. Noah has read \(\frac{3}{8}\) of his book, which has 72 pages. Madison has read \(\frac{3}{5}\) of her book, which has 55 pages. So Noah read \(\frac{3}{8}\) X 72 pages = \(\frac{3 X 72}{8}\) pages = \(\frac{3 X 9 X 8}{8}\) pages = 3 X 9 pages = 27 pages and Madison read \(\frac{3}{5}\) X 55 pages = \(\frac{3 X 55}{5}\) = \(\frac{3 X 11 X 5}{5}\) = \(\frac{3 X 11}{5}\) = 33 pages, now comparing who read more pages are 27 pages & 33 pages we get Madison read more number of pages.
Question 6.
CHALLENGE A rectangular solid that is 6 cm-by-6 cm-by-6 cm is painted on all six faces. Then the solid is cut into cubes that measure 2 cm on each side. How many cubes have only one face painted? Show your work.
Answer:
6,
Explanation:
Given that the dimension of a rectangular solid is 6 cm X 6 cm X 6 cm. It is painted on all six faces and is cut into smaller cubes that measure 2 cm on each side. We are to calculate the number of cubes that have only one face painted.
The volume of the rectangular solid is given by V = 6 cm X 6 cm X 6 cm = 216 cubic cm and the volume of each small cube is
2 cm X 2 cm X 2cm = 8 cubic cm, Therefore, the number of small cubes that are made after cutting the solid will be 216/8 = 27,
So, there will be 27 small cubes. On one face of the solid, there will be 9 small cubes, out of which only the middle one is painted on one face. Since there are six faces, so number of cubes that have only one face painted = 1 X 6 = 6.