Math in Focus Grade 5 Chapter 4 Practice 7 Answer Key Real-World Problems: Multiplying and Dividing with Fractions

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Math in Focus Grade 5 Chapter 4 Practice 7 Answer Key Real-World Problems: Multiplying and Dividing with Fractions

Question 1.
Evan typed 72 pages of notes one day. He typed $$\frac{1}{2}$$ of the pages in the morning and $$\frac{1}{3}$$ of the pages in the afternoon. He typed the rest of the pages in the evening. How many pages of notes did he type in the morning and afternoon?
48 pages of notes that he typed in the morning and afternoon
24 pages he typed in the evening.
Explanation:
Evan typed 72 pages of notes one day.
$$\frac{1}{2}$$ of the pages in the morning  72 ÷ 2 = 36
$$\frac{1}{3}$$ of the pages in the afternoon 36 ÷  3 = 12
36 + 12 = 48
He typed the rest of the pages in the evening. 72 – 48 = 24

Question 2.
Last Saturday, Jay spent 6 hours playing games, studying and talking with his friends. He spent $$\frac{2}{5}$$ of the time playing games and $$\frac{1}{2}$$ of the time studying. How many minutes did he spend talking with his friends?
36 minutes
Explanation:
To find $$\frac{2}{5}$$ of the time, all you have to do is multiply is by the time!!!
$$\frac{2}{5}$$   x 360 = 144 minutes
6 x 60 = 360
1 hour has 60 minutes.
Studying:
$$\frac{1}{2}$$ x 360 = 180 minutes

Talking with friends = Total time – playing games – studying
360 – 144 – 180 = 36 minutes

Question 3.
Joanne earns $720 a week. She spends $$\frac{1}{3}$$ of her money on groceries and household goods and $$\frac{3}{4}$$ of the remaining money on rent. How much money does she spend on rent, groceries and household goods? Answer:$600
Explanation:
720 x $$\frac{1}{3}$$ = 240 for Groceries and home goods.
then 720 – 240 = 480 reaming
then 480 x  $$\frac{3}{4}$$ = 360 for rent
total amount spent= 240 + 360 = 600 dollar total

Question 4.
During a triathlon, Sharon swims $$\frac{1}{4}$$ of the total route and cycles $$\frac{3}{5}$$ of the remaining route. She runs the rest of the route. If she runs 3,600 meters, find the total distance of the triathlon route.
6km swimming, 14.4km cycling and 3.6km running

Explanation:
x is the total route in kilometers
(3600m = 3.6km)
we know that
x =3 . 6+ ( $$\frac{1}{4}$$ ) x + ( $$\frac{3}{5}$$)x
multiplying both sides with 20, gives
20 x = 72 + 5x + 12x
or (moving all terms with x to the same side)
3x=72
meaning x =($$\frac{72000}{3}$$ ) = 24000
The triathlon route is 24km long

Question 5.
Victoria has a 2-pound package of flour. She uses $$\frac{2}{5}$$ of the flour to make a pizza. She then uses $$\frac{3}{10}$$ of the remaining flour to make bread. Find the weight of the package of flour that she has left. Express your answer as a decimal.
$$\frac{9}{25}$$ lb. left = 0.36 in decimal.
Explanation:
Victoria has a 2-pound package of flour.
$$\frac{2}{5}$$ of the flour to make a pizza.  $$\frac{3}{5}$$ x 2 = $$\frac{6}{5}$$lb.
She then uses $$\frac{3}{10}$$ of the remaining flour to make bread $$\frac{3}{10}$$ x $$\frac{6}{5}$$
= $$\frac{18}{50}$$ = $$\frac{9}{25}$$ lb. left = 0.36

Question 6.
Karen collects $$\frac{6}{7}$$ quart of rainwater. She uses $$\frac{1}{2}$$ of the water to clean her bicycle and uses the remaining water equally for 3 houseplants. What volume of water does she use for each houseplant?
$$\frac{1}{9}$$ quart volume of water that she use for each houseplant
Explanation:
Karen collects $$\frac{6}{7}$$ quart of rainwater.
$$\frac{1}{2}$$ of the water to clean her bicycle ( $$\frac{1}{2}$$ ) x ($$\frac{6}{7}$$) = $$\frac{6}{14}$$= $$\frac{3}{7}$$ quart
$$\frac{3}{7}$$ x ( $$\frac{1}{3}$$ ) = $$\frac{3}{21}$$ = $$\frac{1}{9}$$ quart

Question 7.
Ricardo spends $$\frac{8}{9}$$ hour reading the newspaper. He spends $$\frac{1}{4}$$ of the time reading the world news and splits the remaining time equally between the sports news and the comics. How much time does he spend reading the comics?
$$\frac{1}{3}$$  time that he spend reading the comics
Explanation:
Ricardo spends $$\frac{8}{9}$$ hour reading the newspaper.
latex]\frac{1}{4}[/latex] x $$\frac{8}{9}$$ = $$\frac{24}{36}$$ =  $$\frac{2}{3}$$ hour
He spends $$\frac{1}{4}$$ of the time reading the world news and splits the remaining time equally between the sports news and the comics.
$$\frac{2}{3}$$ x $$\frac{1}{2}$$ – $$\frac{2}{6}$$ = $$\frac{1}{3}$$ hour reading comics

Question 8.
A square foot of wall space needs $$\frac{1}{8}$$ quart of paint. Terrence has 7 quarts of paint, but uses 2 quarts to paint a pipe. How many square feet of wall can he paint with the rest of the paint?
40 square feet of wall that he can he paint with the rest of the paint
Explanation:
Terrence has 7 quarts of paint, but uses 2 quarts to paint a pipe.
7 – 2 = 5
fifths of ( $$\frac{1}{8}$$ )
5 x 8 = 40 square feet

Question 9.
Mary spends $$\frac{1}{6}$$ hour to make a friendship bracelet. She spends 3 hours before lunch and 2 hours after lunch making the bracelets. How many bracelets does she make in all?
30 bracelets that she make in all
Explanation:
1 hour = 60 minutes
Mary spends $$\frac{1}{6}$$ hour to make a friendship bracelet.
60 ÷ 6 = 10
She spends 3 hours before lunch and 2 hours after lunch making the bracelets.
3 + 2 = 5
5 x 60 = 300
300  ÷  10 = 30

Question 10.
Clayton wants to be a musician. After school one afternoon, he spends half his time practicing his drums and $$\frac{3}{4}$$ of the remaining time on homework and dinner. He spends the remaining $$\frac{3}{4}$$ hour talking with and texting his friends. How long did he practice the drums?
Julia spends $$\frac{5}{9}$$ of her vacation at summer camp. She spends $$\frac{3}{4}$$ of the remaining time at her grandparent’s home. The remaining 7 days she spends at the seashore with her family. How many days of summer vacation does she get each summer.