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## Bridges in Mathematics Grade 5 Home Connections Answer Key Unit 2 Module 1

**Bridges in Mathematics Grade 5 Home Connections Unit 2 Module 1 Session 2 Answer Key**

**Comparing Fractions**

Question 1.

Color in the grid to show the fractions below. Each grid represents 1 whole.

a.

\(\frac{1}{2}\)

Answer:

Color half of the grid to show the fraction \(\frac{1}{2}\).

b.

\(\frac{1}{4}\)

Answer:

Color the quarter of the grid to show the fraction \(\frac{1}{4}\).

c.

\(\frac{3}{10}\)

Answer:

d.

\(\frac{16}{10}\)

Answer:

\(\frac{16}{10}\) = \(\frac{8}{5}\)

e.

\(\frac{6}{4}\)

Answer:

\(\frac{6}{4}\) = \(\frac{3}{2}\) = 1 \(\frac{1}{2}\)

Question 2.

Use the pictures above to help complete each comparison below using <, >, or =.

ex \(\frac{1}{2}\) > \(\frac{3}{10}\)

a.

\(\frac{6}{4}\) 1\(\frac{1}{2}\)

Answer:

From the above figure we can say that,

\(\frac{6}{4}\) = 1\(\frac{1}{2}\)

b.

\(\frac{6}{10}\) \(\frac{3}{4}\)

Answer:

\(\frac{6}{10}\) = 0.6

\(\frac{3}{4}\) = 0.75

\(\frac{6}{10}\) < \(\frac{3}{4}\)

c.

\(\frac{16}{10}\) 1\(\frac{1}{2}\)

Answer:

\(\frac{16}{10}\) = 1\(\frac{6}{10}\)

1\(\frac{1}{2}\)

1\(\frac{6}{10}\) > 1\(\frac{1}{2}\)

\(\frac{16}{10}\) > 1\(\frac{1}{2}\)

d.

\(\frac{6}{10}\) \(\frac{6}{4}\)

Answer:

\(\frac{6}{10}\) = 0.6

\(\frac{6}{4}\) = 1\(\frac{1}{2}\)

0.6 < 1\(\frac{1}{2}\)

\(\frac{6}{10}\) < \(\frac{6}{4}\)

e.

\(\frac{3}{10}\) \(\frac{1}{4}\)

Answer:

\(\frac{3}{10}\) = 0.3

\(\frac{1}{4}\) = 0.25

0.3 > 0.25

\(\frac{3}{10}\) > \(\frac{1}{4}\)

Question 3.

Add these fractions. (Hint: Think about money to help.)

a.

\(\frac{1}{2}\) + \(\frac{1}{4}\) = __________

Answer:

\(\frac{1}{2}\) + \(\frac{1}{4}\)

LCD of 2, 4 = 4

\(\frac{2}{4}\) + \(\frac{1}{4}\) = \(\frac{2+1}{2}\) = \(\frac{3}{4}\)

b.

1\(\frac{1}{2}\) + \(\frac{3}{4}\) = __________

Answer:

1\(\frac{1}{2}\) + \(\frac{3}{4}\)

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

\(\frac{3}{2}\) + \(\frac{3}{4}\)

LCD of 2, 4 = 4

\(\frac{6}{4}\) + \(\frac{3}{4}\) = \(\frac{6+3}{4}\) = \(\frac{9}{4}\)

c.

\(\frac{1}{2}\) + \(\frac{1}{10}\) = __________

Answer:

\(\frac{1}{2}\) + \(\frac{1}{10}\)

LCD of 2, 10 is 10.

\(\frac{5}{10}\) + \(\frac{1}{10}\) = \(\frac{5+1}{10}\) = \(\frac{6}{10}\) = \(\frac{3}{5}\)

d.

\(\frac{3}{10}\) + \(\frac{1}{4}\) = __________

Answer:

\(\frac{3}{10}\) + \(\frac{1}{4}\)

LCD of 4, 10 is 20.

\(\frac{6}{20}\) + \(\frac{5}{20}\) = \(\frac{6+5}{20}\) = \(\frac{11}{20}\)

Question 4.

Francisco and his mother bought some fruit yesterday. They bought 2 \(\frac{1}{2}\) pounds of peaches, \(\frac{7}{10}\) of a pound of raspberries, and 1 \(\frac{1}{4}\) pounds of apricots. How many pounds of fruit did they buy in all? Show all your work.

Answer:

Given,

Francisco and his mother bought some fruit yesterday. They bought 2 \(\frac{1}{2}\) pounds of peaches, \(\frac{7}{10}\) of a pound of raspberries, and 1 \(\frac{1}{4}\) pounds of apricots.

2 \(\frac{1}{2}\) + \(\frac{7}{10}\) + 1 \(\frac{1}{4}\)

Convert from mixed fraction to the improper fraction.

2 \(\frac{1}{2}\) = \(\frac{5}{2}\)

1 \(\frac{1}{4}\) = \(\frac{5}{4}\)

\(\frac{5}{2}\) + \(\frac{5}{4}\)

LCD of 2, 4 = 4

\(\frac{10}{4}\) + \(\frac{5}{4}\) = \(\frac{10+5}{2}\) = \(\frac{15}{4}\)

Question 5.

**CHALLENGE** Write three fraction addition problems in which the fractions have different denominators and the sum is 1.

ex \(\frac{1}{2}\) + \(\frac{2}{4}\) = 1

a

b

c

Answer:

\(\frac{1}{2}\) + \(\frac{2}{4}\) = 1

\(\frac{3}{8}\) + \(\frac{5}{8}\) = 1

\(\frac{2}{5}\) + \(\frac{3}{5}\) = 1

\(\frac{1}{4}\) + \(\frac{3}{4}\) = 1

Question 6.

**CHALLENGE** Fill in the missing numerators and denominators to make each comparison true.

a.

Answer:

\(\frac{4}{2}\) = 2

The denominator of the given fractions are same. So, the numerator should be greater than 4.

So, the missing number is 5.

\(\frac{5}{2}\) > \(\frac{4}{2}\)

b.

Answer:

Given,

1\(\frac{1}{4}\)

\(\frac{1}{4}\) can be written as \(\frac{3}{12}\)

1\(\frac{1}{4}\) = 1\(\frac{3}{12}\)

c.

Answer:

\(\frac{16}{32}\) = \(\frac{1}{2}\)

\(\frac{3}{8}\)

\(\frac{1}{2}\) < \(\frac{3}{8}\)

\(\frac{16}{32}\) < \(\frac{3}{8}\)

**Bridges in Mathematics Grade 5 Home Connections Unit 2 Module 1 Session 4 Answer Key**

**More Adding Fractions**

Question 1.

Show the fractions on the strips or clocks. Then add them and report the sum.

Answer:

\(\frac{1}{2}\) + \(\frac{3}{8}\) = \(\frac{7}{8}\)

\(\frac{3}{4}\) + \(\frac{3}{8}\) = \(\frac{9}{8}\)

\(\frac{5}{8}\) + \(\frac{1}{2}\) = 1 \(\frac{1}{8}\)

\(\frac{3}{4}\) + \(\frac{7}{8}\) = 1 \(\frac{5}{8}\)

\(\frac{1}{4}\) + \(\frac{2}{3}\) = \(\frac{11}{12}\)

\(\frac{3}{4}\) + \(\frac{2}{3}\)

LCD is 12

\(\frac{9}{12}\) + \(\frac{8}{12}\) = \(\frac{17}{12}\)

\(\frac{1}{2}\) + \(\frac{5}{6}\) = 1 \(\frac{1}{3}\)

Show your work for each problem using numbers, sketches, or words.

Question 2.

Abby and Lauren are preparing for a dance performance. On Monday, they practiced for \(\frac{2}{3}\) of an hour. On Tuesday, they practiced for \(\frac{5}{6}\) of an hour. How long did they practice on Monday and Tuesday together?

Answer:

Given,

Abby and Lauren are preparing for a dance performance.

On Monday, they practiced for \(\frac{2}{3}\) of an hour.

On Tuesday, they practiced for \(\frac{5}{6}\) of an hour.

\(\frac{2}{3}\) + \(\frac{5}{6}\)

LCD of 3, 6 is 6.

\(\frac{4}{6}\) + \(\frac{5}{6}\) = \(\frac{4+5}{6}\) = \(\frac{9}{6}\) = 3 hours

Question 3.

On Wednesday, Abby and Lauren could not practice together, so they practiced separately. Abby practiced for \(\frac{11}{12}\) of an hour and Lauren practiced for \(\frac{2}{3}\) of an hour. How long did they practice on Wednesday?

Answer:

Given,

On Wednesday, Abby and Lauren could not practice together, so they practiced separately.

Abby practiced for \(\frac{11}{12}\) of an hour and Lauren practiced for \(\frac{2}{3}\) of an hour.

\(\frac{11}{12}\) + \(\frac{2}{3}\)

LCD is 12

\(\frac{11}{12}\) + \(\frac{8}{12}\) = \(\frac{11+8}{12}\) = \(\frac{19}{12}\)

Question 4.

**CHALLENGE** If you are adding two fractions that are both greater than \(\frac{1}{2}\), what must be true about the sum? Give three examples to support your thinking.

The sum must be:

Answer:

\(\frac{1}{2}\) + \(\frac{1}{4}\) = \(\frac{3}{4}\)

\(\frac{3}{4}\) is greater than \(\frac{1}{2}\)

Question 5.

**CHALLENGE** If you are adding two fractions that are both less than \(\frac{1}{2}\), what must be true about the sum? Give three examples to support your thinking.

The sum must be:

Answer:

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

\(\frac{2}{3}\) is less than \(\frac{1}{2}\)