# McGraw Hill My Math Grade 5 Chapter 10 Lesson 12 Answer Key Problem-Solving Investigation: Draw a Diagram

All the solutions provided in McGraw Hill Math Grade 5 Answer Key PDF Chapter 10 Lesson 12 Problem-Solving Investigation: Draw a Diagram will give you a clear idea of the concepts.

## McGraw-Hill My Math Grade 5 Answer Key Chapter 10 Lesson 12 Problem-Solving Investigation: Draw a Diagram

Learn the Strategy
Jaheim visited an aquarium over the weekend and saw 35 species of fish. This was $$\frac{1}{5}$$ the total number of species of fish. How many total species of fish are at the aquarium?

1. Understand
What facts do you know?
Jaheim saw ____ species of fish, which is _____ of the total number of species.
What do you need to find?
• the total number of species of ____ in the aquarium
By reading the question, we get to know some hints.
The facts we know:
The number of species of fish Jaheim saw = 35
The amount of the total number of species = 1/5
We need to find out the total number of species of fish in the aquarium.
2. Plan
I can solve the problem by drawing a diagram.

We can draw a model to represent the total number of species in the aquarium.
– A bar model can be defined as a pictorial representation of a number in the form of bars or boxes used to solve number problems. Bar models help us to attain an understanding of how a problem needs to be solved and calculated.
– Bar models help us to understand what operations, whether addition, subtraction, multiplication or/and division should be used to solve a word problem.

Each box represents 35.
so, the 35 x 5 = 175
3. Solve
The model is divided into fifths. Since each part represents 35 species, there is a total of 35 × 5, or ____ species of fish at the aquarium.
The model is divided into fifths
each box represents 35
to find out the total numbers of species of fishes we need to multiply.
so, 35 x 5 = 175
Therefore, the total number of species of fishes are 175.
4. Check
Is my answer reasonable? ____ ÷ 5 = 35
To check whether the answers are reasonable or not we need to divide
175 ÷ 5 = 35

Practice the Strategy

Victor has $18 in a piggy bank. He spends $$\frac{2}{3}$$ of the money on a video game and $$\frac{1}{6}$$ on candy. How much money will Victor have left? 1. Understand What facts do you know? ____________________ ____________________ What do you need to find? ____________________ Answer: Above-given facts: The total money Victor has in the piggy bank =$18
The amount he spends on video games = 2/3
The amount he spends on candy = 1/6
After spending all the amount of money we need to find out the amount he left.
2. Plan
____________________
We can solve the problem by using the diagram.
By using the bar model we can solve.
We can draw a model to represent the total number of species in the aquarium.
– A bar model can be defined as a pictorial representation of a number in the form of bars or boxes used to solve number problems. Bar models help us to attain an understanding of how a problem needs to be solved and calculated.
– Bar models help us to understand what operations, whether addition, subtraction, multiplication or/and division should be used to solve a word problem.
3. Solve
The above-given:
2/3 and 1/6
2/3 + 1/6 (take LCM as 6)
4 + 1/6 = 5/6
Now we need to calculate 5/6 of 18
The total amount Victor spend = 5/6
Now divide the bar diagram into six equal parts. There would be $3 in each section. Therefore, Victor has$3 left.

4. Check
____________________
To check whether the answer is reasonable or not. we need to divide and check
18 ÷ 6 = 3

Apply the Strategy

Solve each problem by drawing a diagram.

Question 1.
Mrs Vallez purchased sand toys that were originally $20. She received $$\frac{1}{4}$$ off of the total price. How much did she save? Answer: The above-given: The original amount of sand toys purchased by Vallez = 20 The amount she received = 1/4 The amount she saves = X We can solve the problem by using the diagram Now we have to divide the bar diagram into four equal parts. In each section, we have to write 5. Therefore, she saves$5.
To check whether the answer is reasonable or not.
20 ÷ 5 = 4

Question 2.
Sue has four DVDs and Terry has six DVDs. They put all their DVDs together and sold them for $10 for two DVDs. How much money will they earn if they sell all of their DVDs? Answer: The above-given The number of DVDs Sue has = 4 The number of DVDs Terry has = 6 The total number of DVDs they have together = 6 + 4 = 10 The money they want to earn = X X = 10/2 x 10 X = 5 x 10 X = 50 Therefore, they will earn$50 if they sell all of their DVDs.

Question 3.
Mathematical PRACTICE 4 Model Math Jacinda is decorating cookies for a class party. She can decorate $$\frac{2}{3}$$ of a cookie per minute. At this rate, how many cookies can she decorate in 15 minutes?
The above-given
The time she can decorate a cookie per minute = 2/3
The number of cookies she can decorate in 15 minutes = C
for 1 minute – 2/3 of the cookie
for 15 minutes – how many cookies? (C)
C x 1 = 15 x 2/3
C = 30/3
C = 10
Therefore, she can decorate 10 cookies within 15 minutes.

Question 4.
At a bird sanctuary, Ricky counted 80 birds. Of the birds he counted, $$\frac{1}{4}$$ were baby birds.
If he counted an equal number of adult males r and females, how many adult female birds did Ricky count?
The number of birds counted by Ricky = 80
Out of 80 birds, the number of baby birds = 1/4
We can write in mathematical form as:
1/4 of 80
We need to find out the number of adult female birds.
from the above-given conditions, we have to calculate
1/4 x 80 = 20
The total number of baby birds = 20
Now subtract the total number of birds and a total number of baby birds. Let it be A.
A = 80 – 20
A = 60
Now we got the adult birds (female and male).
Here we have to find out about the female birds. Let it be F
F = 60/2
F = 30
Therefore, the number of female birds is 30.
And finally, we can summarize that the baby birds are 20; female birds are 30; male birds are 30.

Question 5.
Mathematical PRACTICE 5 Use Math Tools To make chocolate ice cream, you need about $$\frac{3}{8}$$ pound of chocolate. How many pounds of chocolate will you need to make 4 batches of ice cream?
The amount of chocolate we need to make a chocolate Ice-cream = 3/8
The number of pounds of chocolate we need to make 4 batches of ice cream = C
C = 3/8 x 4
C = 12/8
C = 3/2
Therefore, 3/2 pounds of chocolate is needed.

Review the Strategies

Use any strategy to solve each problem.

• Draw d diagram.
• Work backwards.
• Guess, check, and revise.
• Act it out.

Question 6.
A cook needs 12 pounds of flour. He wants to spend the least amount of money. If a 2-pound bag costs $1.59 and a 5-pound bag costs$2.89, how many bags of each type of flour should he buy? What will be the total cost?
The pounds of flour a cook needs = 12
The cost of a 2-pound bag  is $1.59 The cost of a 5-pound bag is$2.89
we can buy two 5-pound bags and one 2-pound bag
The total cost can be:
2.89 x 2 = 5.78 (the total cost of 5-pound bags)
1.59 x 1 = 1.59 (the total cost of 2-pound bags)