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## Bridges in Mathematics Grade 5 Home Connections Answer Key Unit 5 Module 3

**Bridges in Mathematics Grade 5 Home Connections Unit 5 Module 3 Session 1 Answer Key**

**Comparing, Simplifying & Adding Fractions Review**

Question 1.

Find the least common multiple of each pair of numbers.

ex:

The least common multiple of 8 and 28 is 56.

multiples of 28: 28,

multiples of 8: 8, 16, 24, 32, 40, 48,

a. The least common multiple of 8 and 12 is ______________.

multiples of 12:

multiples of 8:

Answer:

The least common multiple of 8 and 12 is 24,

multiples of 12: 12, 24, 36, 48, 60,

multiples of 8: 8,16, 24, 32, 40,

Explanation:

Asked to find the least common multiple of 8 and 12 we get 24 as multiples of 12 are 12, 24, 36, 48, 60,

multiples of 8 are 8,16, 24, 32, 40.

b. The least common multiple of 6 and 15 is ______________.

multiples of 15:

multiples of 6:

Answer:

The least common multiple of 6 and 15 is 30,

multiples of 15: 15, 30, 45, 60, 75,

multiples of 6: 6, 12, 18, 24, 30, 36,

Explanation:

Asked to find the least common multiple of 6 and 15 we get 30 as multiples of 15 are 15, 30, 45, 60, 75,

multiples of 6 are 6,12, 18, 24, 30, 36.

c. The least common multiple of 6 and 14 is _______________.

multiples of 14:

multiples of 6:

Answer:

The least common multiple of 6 and 14 is 42,

multiples of 14: 14, 28, 42, 56, 70,

multiples of 6: 6, 12, 18, 24, 30, 36, 42, 48,

Explanation:

Asked to find the least common multiple of 6 and 14 we get 42 as multiples of 14 are 14, 28, 42, 56, 70,

multiples of 6 are 6, 12, 18, 24, 30, 36, 42, 48.

Question 2.

Rewrite each pair of fractions with a common denominator. (Use the least common multiples above to help.) Then use a <, >, or = to compare them in two expressions.

ex:

a.

Answer:

Explanation:

Rewritten each pair of fractions with a common denominator. Used the least common multiples above to help. Then used a < to compare them in two expressions as shown above.

b.

Answer:

Explanation:

Rewritten each pair of fractions with a common denominator. Used the least common multiples above to help. Then used a < to compare them in two expressions as shown above.

c.

Answer:

Explanation:

Rewritten each pair of fractions with a common denominator. Used the least common multiples above to help. Then used a > to compare them in two expressions as shown above.

Question 3.

Rewrite each fraction in simplest form by dividing the numerator and denominator by the greatest common factor. A fraction is in its simplest form when its numerator and denominator have no common factor other than 1. You do not have to show your work if you can do it in your head.

ex:

a.

Answer:

Explanation:

Rewritten the fraction in simplest form by dividing the numerator and denominator by the greatest common factor 2 as shown above.

b.

Answer:

Explanation:

Rewritten the fraction in simplest form by dividing the numerator and denominator by the greatest common factor 3 as shown above.

c.

Answer:

Explanation:

Rewritten the fraction in simplest form by dividing the numerator and denominator by the greatest common factor 6 as shown above.

d.

Answer:

Explanation:

Rewritten the fraction in simplest form by dividing the numerator and denominator by the greatest common factor 4 as shown above.

e.

Answer:

Explanation:

Rewritten the fraction in simplest form by dividing the numerator and denominator by the greatest common factor 4 as shown above.

Question 4.

Rewrite each pair of fractions so they have the same denominator. Then find their sum. Sometimes, you will need to find the least common multiple. Sometimes you might be able to reduce each fraction to its simplest form to find a common denominator.

ex: \(\frac{5}{8}\) + \(\frac{7}{12}\)

\(\frac{15}{24}\) + \(\frac{14}{24}\) = \(\frac{29}{24}\) and \(\frac{29}{24}\) = 1\(\frac{5}{24}\)

ex: \(\frac{2}{6}\) + \(\frac{8}{12}\)

\(\frac{1}{3}\) + \(\frac{2}{3}\) = \(\frac{3}{3}\) ans \(\frac{3}{3}\) = 1

a. \(\frac{3}{4}\) + \(\frac{2}{8}\)

Answer:

1,

Explanation:

Given to find \(\frac{3}{4}\) + \(\frac{2}{8}\) we make common denominator as \(\frac{3}{4}\) X \(\frac{2}{2}\) + \(\frac{2}{8}\) = \(\frac{3 X 2}{4 X 2}\) + \(\frac{2}{8}\) = \(\frac{6}{8}\) + \(\frac{2}{8}\) as we have common denominators we write as \(\frac{6 + 2}{8}\) = \(\frac{8}{8}\) = 1.

b. \(\frac{6}{8}\) + \(\frac{9}{12}\)

Answer:

\(\frac{3}{2}\),

Explanation:

Given to find \(\frac{6}{8}\) + \(\frac{9}{12}\) we make common denominator as \(\frac{6}{8}\) X \(\frac{3}{3}\) + \(\frac{9}{12}\) X \(\frac{2}{2}\) = \(\frac{6 X 3}{8 X 3}\) + \(\frac{9 X 2}{12 X 2}\) = \(\frac{18}{24}\) + \(\frac{18}{24}\) as we have common denominators we write as \(\frac{18 + 18}{24}\) = \(\frac{36}{24}\) both goes by 6 we get \(\frac{6 X 6}{6 X 4}\) = \(\frac{6}{4}\) now again both goes by 2 so \(\frac{3 X 2}{2 X 2}\) we get \(\frac{3}{2}\).

c. 3\(\frac{6}{12}\) + 4\(\frac{1}{2}\)

Answer:

8,

Explanation:

Given to find 3\(\frac{6}{12}\) + 4\(\frac{1}{2}\) we make common denominator as \(\frac{3 X 12 + 6}{12}\) + \(\frac{4 X 2 + 1}{2}\) X \(\frac{6}{6}\) = \(\frac{42}{12}\) + \(\frac{9 X 6}{2 X 6}\) = \(\frac{42}{12}\) + \(\frac{54}{12}\) as we have common denominators we write as \(\frac{42 + 54}{12}\) = \(\frac{96}{12}\) both goes by 12 we get so \(\frac{8 X 12}{1 X 12}\) = 8.

d. 1\(\frac{5}{8}\) + 2\(\frac{3}{4}\)

Answer:

\(\frac{35}{8}\) = 4\(\frac{3}{8}\),

Explanation:

Given to find 1\(\frac{5}{8}\) + 2\(\frac{3}{4}\) we first change mixed fractions into fractions then make common denominator as \(\frac{1 X 8 + 5}{8}\) + \(\frac{2 X 4 + 3}{4}\) X \(\frac{2}{2}\) = \(\frac{13}{8}\) + \(\frac{11 X 2}{4 X 2}\) = \(\frac{13}{8}\) + \(\frac{22}{8}\) as we have common denominators we write as \(\frac{13 + 22}{8}\) = \(\frac{35}{8}\) as numerator is greater than denominator we write as mixed fraction \(\frac{4 X 8 + 3}{8}\) = 4\(\frac{3}{8}\).

**Bridges in Mathematics Grade 5 Home Connections Unit 5 Module 3 Session 3 Answer Key**

**Fraction Multiplication Models**

Question 1.

Circle the picture that best represents each equation. Then solve the equation.

a. \(\frac{1}{2}\) × \(\frac{3}{6}\) = _______________

Answer:

Explanation:

Given \(\frac{1}{2}\) X \(\frac{3}{6}\) = \(\frac{1 X 3}{2 X 6}\) = \(\frac{1}{2 X 2}\) = \(\frac{1}{4}\) so circled C bit as shown above.

b. \(\frac{1}{2}\) × \(\frac{1}{3}\) = _______________

Answer:

Explanation:

Given \(\frac{1}{2}\) X \(\frac{1}{3}\) = \(\frac{1 X 1}{2 X 3}\) = \(\frac{1}{6}\), so circled C bit as shown above.

c. \(\frac{2}{5}\) × \(\frac{3}{4}\) = _______________

Answer:

Explanation:

Given \(\frac{2}{5}\) X \(\frac{3}{4}\) = \(\frac{2 X 3}{5 X 4}\) = \(\frac{6}{20}\) or \(\frac{3}{10}\), so circled A bit as shown above.

Question 2.

Use the grid to model and solve each combination. Remember to outline a rectangle to represent the whole first.

ex:

a. \(\frac{5}{6}\) × \(\frac{5}{6}\) = _______________

Answer:

Explanation:

Given \(\frac{5}{6}\) X \(\frac{5}{6}\) = \(\frac{5 X 5}{6 X 6}\) = \(\frac{25}{36}\), Used the grid to model and solved the combination. Outlined a rectangle to represent the result.

b. \(\frac{3}{7}\) × \(\frac{2}{4}\) = _______________

Answer:

Explanation:

Given \(\frac{3}{7}\) X \(\frac{2}{4}\) = \(\frac{3 X 2}{7 X 4}\) = \(\frac{3}{14}\), Used the grid to model and solved the combination. Outlined a rectangle to represent the result.

Question 3.

Betsy has $14.25 and her brother has $16.00. They want to buy two water guns that cost $12.99 each and a bag of water balloons that costs $4.79.

a. Do they have enough money? If so, how much money will they have left over? If not, how much more money do they need? Show your work.

Answer:

Betsy needs more is $3.53, Her brother needs $1.78,

Explanation:

Given Betsy has $14.25 and her brother has $16.00. They want to buy two water guns that cost $12.99 each and a bag of water balloons that costs $4.79, Betsy total costs is guns cost + Bag of water balloons costs = $12.99 + $4.79 = $17.78 so more Betsy needs is $17.78 – $14.25 = $3.53, Betsy brother needs $17.78 – $16.00 = $1.78.

b. If Betsy earns another $6, will they have enough money to buy two water guns and two bags of water balloons? Show your work.

Answer:

No, Betsy does not have enough money to buy two water guns and two bags of water balloons,

Explanation:

If Betsy earns another $6 they will have enough money to buy two water guns and two bags of water balloons so

it is 2 X $12.99 + 2 X $4.79 = $25.98 + $6.79 = $32.77 So adding to Betsy earnings we get $14.25 + $6 = $20.25

as $20.25 < $32.77. Therefore Betsy does not have enough money to buy two water guns and two bags of water balloons.

Question 4.

Betsy made a cake for Josie’s birthday party. After the party, 1/3 of the cake was left. Later that afternoon, Betsy ate another 1/12 of the cake. Then, that evening, Josie ate another 1/12 of the cake. How much of the cake was eaten in all? Show your work.

Answer:

Josie ate 5/6 of cake in all,

Explanation:

Given Betsy made a cake for Josie’s birthday party. After the party, 1/3 of the cake was left. Later that afternoon, Betsy ate another 1/12 of the cake. Then, that evening, Josie ate another 1/12 of the cake. Let the cake be x so

cake eaten is x + 1/12 + 1/12 – 1/3 so x = 1 + 1/12 + 1/12 – 1/3 = (12 + 1 + 1 – 4)/12 = 10/12 = 5/6.

Question 5.

**CHALLENGE** Three friends were talking about races they entered over the weekend. Sherry said she ran \(\frac{3}{5}\) of her 12 kilometer course before she started walking. Kyle said he ran \(\frac{7}{8}\) of his 5 kilometer course before he started walking. Evan said he ran \(\frac{3}{4}\) of his 8 kilometer course before he started walking. The boys argued that they each ran more than Sherry because \(\frac{3}{4}\) and \(\frac{7}{8}\) are greater fractions that \(\frac{3}{5}\). Do you agree? Explain your thinking.

Answer:

No, we don not agree as Sherry ran more than the boys,

Explanation:

Given three friends were talking about races they entered over the weekend. Sherry said she ran \(\frac{3}{5}\) of her 12 kilometer course before she started walking. Kyle said he ran \(\frac{7}{8}\) of his 5 kilometer course before he started walking. Evan said he ran \(\frac{3}{4}\) of his 8 kilometer course before he started walking. The boys argued that they each ran more than Sherry because \(\frac{3}{4}\) and \(\frac{7}{8}\) are greater fractions that \(\frac{3}{5}\) comparing Sherry with Evan we get Sherry \(\frac{3}{5}\) X 12 = \(\frac{3 X 12}{5}\) =\(\frac{36}{5}\) = 7\(\frac{1}{5}\) and Evan \(\frac{3}{4}\) X 8 = \(\frac{3 X 8}{4}\) = 6 as 7\(\frac{1}{5}\) > 6,Next comparing Sherry with Kyle we get \(\frac{7}{8}\) X 5 = \(\frac{7 X 5}{8}\) = 4\(\frac{3}{8}\) as 7\(\frac{1}{5}\) > 4\(\frac{3}{8}\) so we don not agree as Sherry ran more than the boys.