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

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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.
$$\frac{1}{2}$$

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

b.
$$\frac{1}{4}$$

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

c.
$$\frac{3}{10}$$

d.
$$\frac{16}{10}$$

$$\frac{16}{10}$$ = $$\frac{8}{5}$$

e.
$$\frac{6}{4}$$

$$\frac{6}{4}$$ = $$\frac{3}{2}$$ = 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$$\frac{1}{2}$$
From the above figure we can say that,

$$\frac{6}{4}$$ = 1$$\frac{1}{2}$$

b.
$$\frac{6}{10}$$ $$\frac{3}{4}$$
$$\frac{6}{10}$$ = 0.6
$$\frac{3}{4}$$ = 0.75
$$\frac{6}{10}$$ < $$\frac{3}{4}$$

c.
$$\frac{16}{10}$$ 1$$\frac{1}{2}$$
$$\frac{16}{10}$$ = 1$$\frac{6}{10}$$
1$$\frac{1}{2}$$
1$$\frac{6}{10}$$ > 1$$\frac{1}{2}$$
$$\frac{16}{10}$$ > 1$$\frac{1}{2}$$

d.
$$\frac{6}{10}$$ $$\frac{6}{4}$$
$$\frac{6}{10}$$ = 0.6
$$\frac{6}{4}$$ = 1$$\frac{1}{2}$$
0.6 < 1$$\frac{1}{2}$$
$$\frac{6}{10}$$ < $$\frac{6}{4}$$

e.
$$\frac{3}{10}$$ $$\frac{1}{4}$$
$$\frac{3}{10}$$ = 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.
$$\frac{1}{2}$$ + $$\frac{1}{4}$$ = __________
$$\frac{1}{2}$$ + $$\frac{1}{4}$$
LCD of 2, 4 = 4
$$\frac{2}{4}$$ + $$\frac{1}{4}$$ = $$\frac{2+1}{2}$$ = $$\frac{3}{4}$$

b.
1$$\frac{1}{2}$$ + $$\frac{3}{4}$$ = __________
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.
$$\frac{1}{2}$$ + $$\frac{1}{10}$$ = __________
$$\frac{1}{2}$$ + $$\frac{1}{10}$$
LCD of 2, 10 is 10.
$$\frac{5}{10}$$ + $$\frac{1}{10}$$ = $$\frac{5+1}{10}$$ = $$\frac{6}{10}$$ = $$\frac{3}{5}$$

d.
$$\frac{3}{10}$$ + $$\frac{1}{4}$$ = __________
$$\frac{3}{10}$$ + $$\frac{1}{4}$$
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.
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
$$\frac{1}{2}$$ + $$\frac{2}{4}$$ = 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.

$$\frac{4}{2}$$ = 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.

Given,
1$$\frac{1}{4}$$
$$\frac{1}{4}$$ can be written as $$\frac{3}{12}$$
1$$\frac{1}{4}$$ = 1$$\frac{3}{12}$$

c.

$$\frac{16}{32}$$ = $$\frac{1}{2}$$
$$\frac{3}{8}$$
$$\frac{1}{2}$$ < $$\frac{3}{8}$$
$$\frac{16}{32}$$ < $$\frac{3}{8}$$

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

Question 1.
Show the fractions on the strips or clocks. Then add them and report the sum.

$$\frac{1}{2}$$ + $$\frac{3}{8}$$ = $$\frac{7}{8}$$

$$\frac{3}{4}$$ + $$\frac{3}{8}$$ = $$\frac{9}{8}$$

$$\frac{5}{8}$$ + $$\frac{1}{2}$$ = 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?
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?
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:
$$\frac{1}{2}$$ + $$\frac{1}{4}$$ = $$\frac{3}{4}$$
$$\frac{3}{4}$$ is greater than $$\frac{1}{2}$$
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.
$$\frac{1}{3}$$ + $$\frac{1}{3}$$ = $$\frac{2}{3}$$
$$\frac{2}{3}$$ is less than $$\frac{1}{2}$$