All the solutions provided in McGraw Hill Math Grade 5 Answer Key PDF Chapter 9 Lesson 6 Use Models to Subtract Unlike Fractions will give you a clear idea of the concepts.
McGraw-Hill My Math Grade 5 Answer Key Chapter 9 Lesson 6 Use Models to Subtract Unlike Fractions
Build It
Akio lives \(\frac{4}{5}\) mile from school. Bianca lives \(\frac{3}{10}\) mile from school. How much farther from school does Akio live than Bianca?
1. Model each fraction using fraction tiles.
Place the \(\frac{1}{10}\)-tiles below the \(\frac{1}{5}\)-tiles.
2. Find which fraction tiles will fill in the area of the dotted box. Try \(\frac{1}{3}\)-tiles. Do they fill the dotted box? _____
Try \(\frac{1}{2}\)-tiles. Do they fill the dotted box? ____
How many \(\frac{1}{2}\)-tiles fill the dotted box? ____
Since 
fills in the area of the dotted box, \(\frac{4}{5}\) – \(\frac{3}{10}\) = 
.
Akio lives mile farther from school than Bianca.
Answer:
The above-given:
The number of miles from the school Akio lives = 4/5
The number of miles from the school Bianca lives = 3/10
The number of miles farther from school Akio lives than Bianca = x
x = 4/5 – 3/10
Find the common denominator
10 is the least common multiple of denominators 5 and 10. Use it to convert to equivalent fractions with this common denominator.
x = 4 x 2/5 x 2 – 3 x 1/10 x 1
x = 8/10 – 3/10
x = 5/10
x = 1/2
The model is:
2. \(\frac{1}{2}\)-tiles. Do they fill the dotted box? NO
How many \(\frac{1}{2}\)-tiles fill the dotted box? YES
since 
fills in the area of the dotted box, \(\frac{4}{5}\) – \(\frac{3}{10}\) =
Akio lives mile farther from school than Bianca.
Try It
Find \(\frac{3}{4}\) – \(\frac{1}{6}\).
1. Model each fraction using fraction tiles. Place the \(\frac{1}{6}\)-tiles below the \(\frac{1}{4}\)-tiles.
2. Find which fraction tiles will fill in the area of the dotted box.
Try \(\frac{1}{3}\)-tiles. Do they fill the dotted box? NO
Try \(\frac{1}{12}\)-tiles. Do they fill the dotted box? YES
How many \(\frac{1}{12}\)-tiles fill the dotted box? 7
Since 
fills in the area of the dotted box, \(\frac{3}{4}\) – \(\frac{1}{6}\) =
So, \(\frac{3}{4}\) – \(\frac{1}{6}\) = .
Talk About It
Question 1.
Would any of the other fraction tiles fit inside the dotted box for the first activity? Explain.
Answer:
a sample answer is given:
Yes, 2/4, 3/6, 4/8, 5/10, and 6/12 would work because they are all equivalent to 1/2.
Question 2.
Mathematical PRACTICE 2 Stop and Reflect Describe how you would use fraction tiles to find \(\frac{1}{2}\) – \(\frac{1}{3}\).
Answer:
Line up the 1/3-fraction tile below the 1/2 – fraction tile. Use a 1/6-fraction tile to fill in the remaining space.
Practice It
Find each difference using fraction tiles. Draw the models.
Question 3.
\(\frac{2}{3}\) – \(\frac{1}{6}\) = ____
Answer:
The above-given unlike fractions:
2/3 – 1/6
Model:
1. First separate the 2/3 into two one-thirds.
2. Each 1/3-fraction is 2 tiles of 1/6-fraction.
3. we want three sets so we have to take 3 tiles of 1/6-fraction.
1/6 + 1/6 + 1/6 = 3/6 = 1/2
4. Therefore, 2/3 – 1/6 = 1/2
The model is shown below:
and we can check the answer by making the denominators equal.
2/3 – 1/6
step 1: Find the common denominators.
6 is the least common multiple of denominators 3 and 6. Use it to convert to equivalent fractions with this common denominator.
= 2 x 2/3 x 2 – 1 x 1/6 x 1
= 4/6 – 1/6
= (4 – 1)/6 = 3/6
– 3 is the greatest common divisor of 3 and 6. Reduce by dividing both the numerator and denominator by 3.
3/6 = 3 ÷ 3/6 ÷ 3
. = 1/2
Hence the answer is proven.
Question 4.
\(\frac{5}{8}\) – \(\frac{1}{4}\) = ____
Answer:
The above-given unlike fractions:
5/8 – 1/4
1. First separate the 5/8 into five one-eighths
2. Here, two tiles of one-eighths are equal to one-fourth (1/8 + 1/8 = 2/8 = 1/4)
3. Here we got 1/4-fraction. Now we need to subtract 1/4 from 5/8.
4. From the 5 tiles of 1/8 we got two tiles equal to 1/4 and the remaining three tiles are 1/8 each.
5. So, 1/8 + 1/8 +1/8 = 3/8. Therefore, the remaining tiles are 3/8.
Model:
and we can check the answer by making the denominators equal.
5/8 – 1/4
step 1: Find the common denominators.
8 is the least common multiple of denominators 8 and 4. Use it to convert to equivalent fractions with this common denominator.
= 5 x 1/8 x 1 – 1 x 2/4 x 2
= 5/8 – 2/8
= (5 – 2)/8
= 3/8
Question 5.
\(\frac{1}{2}\) – \(\frac{1}{6}\) = ____
Answer:
The above-given unlike fractions:
1/2 – 1/6
Model:
and we can check the answer by making the denominators equal.
1/2 – 1/6
step 1: Find the common denominators.
6 is the least common multiple of denominators 2 and 6. Use it to convert to equivalent fractions with this common denominator.
= 1 x 3/2 x 3 – 1 x 1/6 x 1
= 3/6 – 1/6
= (3 – 1)/6
= 2/6 = 1/3
Question 6.
\(\frac{3}{5}\) – \(\frac{1}{2}\) = ____
Answer:
The above-given unlike fractions:
3/5 – 1/2
Model:
1. Separate 3/5 into 3 tiles of 1/5-fraction.
2. Each 1/5 can be written as two tiles of one-tenth (1/10). Likewise, we get six tiles of one-tenths.
3. Here we need to subtract 1/2 from 3/5. In the model we represented 1/2 (1/10 + 1/10 +1/10 + 1/10 + 1/10 = 5/10 = 1/2).
4. And the remaining part is 1/10. Therefore, that would be the answer.
and we can check the answer by making the denominators equal.
3/5 – 1/2
step 1: Find the common denominators.
10 is the least common multiple of denominators 5 and 2. Use it to convert to equivalent fractions with this common denominator.
= 3 x 2/5 x 2 – 1 x 5/2 x 5
= 6/10 – 5/10
= (6 – 5)/10
= 1/10
Hence, the answer is proven.
Question 7.
\(\frac{3}{4}\) – \(\frac{3}{8}\) = ____
Answer:
The above-given unlike fractions:
3/4 – 3/8
Model:
1. 3/4th was separated into 3 tiles of one-fourths
2. each 1/4th is separated into 2 tiles of 1/8.
3. We need to subtract 3/8 from 3/4 and the remaining tiles were added and we get 3/8.
4. Finally, the answer is 3/8.
and we can check the answer by making the denominators equal.
3/4 – 3/8
step 1: Find the common denominators.
8 is the least common multiple of denominators 4 and 8. Use it to convert to equivalent fractions with this common denominator.
= 3 x 2/4 x 2 – 3 x 1/8 x 1
= 6/8 – 3/8
= 3/8
Question 8.
\(\frac{5}{6}\) – \(\frac{1}{4}\) = ____
Answer:
The above-given unlike fractions:
5/6 – 1/4
Model:
and we can check the answer by making the denominators equal.
5/6 – 1/4
step 1: Find the common denominators.
12 is the least common multiple of denominators 6 and 4. Use it to convert to equivalent fractions with this common denominator.
= 5 x 2/6 x 2 – 1 x 3/4 x 3
= 10/12 – 3/12
= 7/12.
Apply It
Mathematical PRACTICE 5 Use Math Tools Draw fraction tiles to help you solve Exercises 9 and 10.
Question 9.
Missy ran \(\frac{5}{8}\) mile to warm up for softball practice, while Farrah only ran \(\frac{1}{2}\) mile. How much farther did Missy run?
Answer:
The above-given:
The number of miles run by Missy = 5/8
The number of miles run by Farrah = 1/2
The number of miles farther Missy ran = r
r = 5/8 – 1/2
step 1: Find the common denominators.
8 is the least common multiple of denominators 8 and 2. Use it to convert to equivalent fractions with this common denominator.
r = 5 x 1/8 x 1 – 1 x 4/2 x 4
r = 5/8 – 4/8
5 = 1/8
Therefore, Missy ran 1/8 mile.
Question 10.
Pablo used \(\frac{1}{2}\) of an oxygen tank while scuba diving. He used another \(\frac{1}{6}\) of the tank exploring underwater. How much oxygen is left in the tank?
Answer:
The above-given:
The oxygen used from the tank by Pablo = 1/2
The oxygen used from the tank exploring underwater = 1/6
The amount of oxygen left = x
x = 1/2 – 1/6
step 1: Find the common denominators.
6 is the least common multiple of denominators 2 and 6. Use it to convert to equivalent fractions with this common denominator.
x = 1 x 3/2 x 3 – 1 x 1/6 x 1
x = 3/6 – 1/6
x = (3 – 1)/6
x = 2/6 = 1/3
Therefore, 1/3rd of amount of the oxygen was left.
Question 11.
Mathematical PRACTICE 4 Model Math Write a real-world problem that could be represented by the fraction tiles shown.
Answer:
a sample answer is given here:
Pablo used \(\frac{3}{4}\) of an oxygen tank while scuba diving. He used another \(\frac{7}{12}\) of the tank exploring underwater. How much oxygen is left in the tank?
The equation can be written based on the model:
The equation is 3/4 – 7/12
step 1: Find the common denominators.
12 is the least common multiple of denominators 4 and 12. Use it to convert to equivalent fractions with this common denominator.
= 3 x 3/4 x 3 – 7 x 1/12 x 1
= 9/12 – 7/12
= (9 – 7)/12
= 2/12 = 1/6
Therefore, 1/6th of the oxygen is left in the tank.
Write About It
Question 12.
How do fraction tiles help me subtract, unlike fractions?
Answer:
– First of all, we have to see how one fraction compares to another for one. Say we had 2/5 and 3/7 it might be confusing for someone to tell which is bigger, but having the tiles will remove their confusion and they can easily say that 3/7 is slightly bigger. Moreover, there are various complicated examples. If we know which is bigger then we will know that subtracting the smaller one which will keep it positive, while if we subtract the larger one from the smaller one it gets negative.
McGraw Hill My Math Grade 5 Chapter 9 Lesson 6 My Homework Answer Key
Practice
Find each difference using the fraction tiles.
Question 1.
\(\frac{7}{8}\) – \(\frac{1}{2}\) = ____
Answer:
The above-given:
7/8 – 1/2
The above model can be explained as:
1. 7/8 is divided into 7 tiles of 1/8
2. The shaded part is written 1/2 (1/8 + 1/8 + 1/8 + 1/8 = 4/8 = 1/2)
3. We need to subtract 1/2 from 7/8. If we remove 1/2 then the remaining space is the answer.
3. And the remaining part is 3/8.
Question 2.
\(\frac{2}{3}\) – \(\frac{1}{4}\) = ____
Answer:
The above-given:
2/3 – 1/4
The above model can be explained as:
1. 2/3 is divided into 2 tiles of 1/3
2. The shaded part is written 1/4 (1/12 + 1/12 + 1/12 = 3/12 = 1/4)
3. We need to subtract 1/4 from 2/3. If we remove 1/4 then the remaining space is the answer.
3. And the remaining part is 5/12.
Problem Solving
Mathematical PRACTICE 5 Use Math Tools Draw fraction tiles to help you solve Exercises 3-6.
Question 3.
Noah bought \(\frac{1}{2}\)– pound of candy to share with his friends. They ate \(\frac{3}{8}\) pound of the candy. How much candy does Noah have left?
Answer:
The above-given:
The number of pounds of candy Noah bought = 1/2
The number of pounds of candy they ate = 3/8
The candy left = c
c = 1/2 – 3/8
1/2 is divided into four tiles of 1/8 and we need to subtract 3/8 from 1/2. And the remaining part is 1/8.
Therefore, the candy left is 1/8.
Question 4.
Mr. Corwin gave his students \(\frac{3}{4}\) an hour to study for a test. After \(\frac{1}{3}\) hour, he played a review game for the remaining time. How much time did Mr. Corwin spend playing the review game?
Answer:
The above-given:
The number of hours Corwin gave his students for a test = 3/4
The number of hours Corwin played a review game for the remaining time = 1/3
The number of hours Corwin spends playing the review game = r
r = 3/4 – 1/3
12 is the least common multiple of denominators 4 and 3. Use it to convert to equivalent fractions with this common denominator.
r = 3 x 3/4 x 3 – 1 x 4/3 x 4
r = 9/12 – 4/12
r = 5/12
Question 5.
Mrs Washer filled the gas tank of her car. She used \(\frac{2}{3}\) of a tank of gasoline while driving to the beach. She used another \(\frac{1}{6}\) of the tank driving to her hotel. How much gasoline is left in the tank?
Answer:
The above-given:
The gasoline she used while driving to the beach = 2/3
The gasoline she used while driving to her hotel = 1/6
The gasoline left in the tank = t
t = 2/3 – 1/6
6 is the least common multiple of denominators 3 and 6. Use it to convert to equivalent fractions with this common denominator.
t = 2 x 2/3 x 2 – 1 x 1/6 x 1
t = 4/6 – 1/6
t = 3/6 = 1/2
Therefore, 1/2 gasoline left in the tank.
Question 6.
Starting from her hotel, Angie walked \(\frac{2}{3}\) mile along the beach in one direction. She turned around and walked \(\frac{1}{2}\) mile toward her hotel. How much farther does she need to walk to get to the hotel?
Answer:
The above-given:
The number of miles Angie walked on the beach in one direction = 2/3
The number of miles she walked toward her hotel = 1/2
The number of miles she needs to walk to get to her hotel = h
h = 2/3 – 1/2
6 is the least common multiple of denominators 3 and 2. Use it to convert to equivalent fractions with this common denominator.
t = 2 x 2/3 x 2 – 1 x 3/2 x 3
t = 4/6 – 3/6
t = 1/6
Therefore, she needs to walk 1/6 mile.