McGraw Hill My Math Grade 5 Chapter 9 Lesson 13 Answer Key Subtract with Renaming

All the solutions provided in McGraw Hill Math Grade 5 Answer Key PDF Chapter 9 Lesson 13 Subtract with Renaming will give you a clear idea of the concepts.

McGraw-Hill My Math Grade 5 Answer Key Chapter 9 Lesson 13 Subtract with Renaming

Math in My World

Example 1
Black sea cucumber has an average length of 2 feet. Spotted sea cucumber has an average length of 1\(\frac{1}{3}\) feet. How much longer is the average black sea cucumber than the average spotted sea cucumber?
McGraw Hill My Math Grade 5 Chapter 9 Lesson 13 Answer Key Subtract with Renaming 1
Find 2 – 1\(\frac{1}{3}\).
Estimate 2 – 1 = ____
You cannot subtract \(\frac{1}{3}\) from 0 thirds.
Rename 2 as 1\(\frac{3}{3}\) to show more thirds.
McGraw Hill My Math Grade 5 Chapter 9 Lesson 13 Answer Key Subtract with Renaming 3

McGraw Hill My Math Grade 5 Chapter 9 Lesson 13 Answer Key Subtract with Renaming 2
The average black sea cucumber is McGraw Hill My Math Grade 5 Chapter 9 Lesson 13 Answer Key Subtract with Renaming 4 foot longer than the average spotted sea cucumber.

Check for Reasonableness 1 ≈ \(\frac{2}{3}\)
Answer:
All the explanation is given above:
McGraw Hill My Math Grade 5 Chapter 9 Lesson 13 Answer Key Subtract with Renaming_1
The average black sea cucumber is McGraw Hill My Math Grade 5 Chapter 9 Lesson 13 Answer Key Subtract with Renaming_2foot longer than the average spotted sea cucumber.

Example 2
Find 4\(\frac{1}{4}\) – 2\(\frac{5}{8}\).
Write equivalent fractions. The LCD is 8.
McGraw Hill My Math Grade 5 Chapter 9 Lesson 13 Answer Key Subtract with Renaming 5
= 4\(\frac{2}{8}\) – 2\(\frac{5}{8}\)

Helpful Hint
You can always check by using fraction tiles or drawing a picture.

You cannot subtract \(\frac{5}{8}\) from \(\frac{2}{8}\). So, rename 4\(\frac{2}{8}\) to show more eighths.
McGraw Hill My Math Grade 5 Chapter 9 Lesson 13 Answer Key Subtract with Renaming 6
Answer:
4 2/8 – 2 5/8
as the fraction is larger we cannot subtract 5/8 from 2/8 so we take borrow
* to take (one) from a digit of the minuend in subtraction in order to add as 10 to the digit holding the next lower place.
here 4 becomes 3 because we take borrow from 4.
3 10/8 – 2 5/8
= 3 – 2 – 10/8 – 5/8
= 1 – 5/8
= 1 5/8
McGraw Hill My Math Grade 5 Chapter 9 Lesson 13 Answer Key Subtract with Renaming_3

Guided Practice

Question 1.
Estimate, then subtract. Write each difference in simplest form.
McGraw Hill My Math Grade 5 Chapter 9 Lesson 13 Answer Key Subtract with Renaming 7
Answer:
The above-given mixed fractions:
5 2/5 – 3 4/5
Here 2/5 is less than 4/5 so we cannot subtract. In this case, we have to regroup the fractions.
Take borrow ‘1’ from 5 so 5 becomes 4. And add the denominator and numerator ( 5 + 2 = 7) now the numerator becomes 7. And the denominator remains the same.
Now the equation is:
4 7/5 – 3 4/5
Step 1: We will subtract the whole numbers of both fractions. i.e., 4 – 3 = 1.
Step 2: Now we will subtract the fractional parts. i.e., (7/5 – 4/5) = 3/5
Step 3: We will combine the result of the last two steps to get the result. i.e., 1 + (3/5) = 1 3/5.
McGraw Hill My Math Grade 5 Chapter 9 Lesson 13 Answer Key Subtract with Renaming_4

 

Talk Math
Describe the steps you would use to find 3\(\frac{2}{7}\) – 1\(\frac{4}{7}\).
Answer:
The above-given mixed fractions:
3 2/7 – 1 4/7
Here 2/7 is less than 4/7 so we cannot subtract. In this case, we have to regroup the fractions.
Take borrow ‘1’ from 3 so 3 becomes 2. And add the denominator and numerator ( 7 + 2 = 9) now the numerator becomes 9. And the denominator remains the same.
Now the equation is:
2 9/7 – 1 4/7
Step 1: We will subtract the whole numbers of both fractions. i.e., 2 – 1 = 1.
Step 2: Now we will subtract the fractional parts. i.e., (9/7 – 4/7) = 5/7
Step 3: We will combine the result of the last two steps to get the result. i.e., 1 + (5/7) = 1 5/7.
McGraw Hill My Math Grade 5 Chapter 9 Lesson 13 Answer Key Subtract with Renaming 8

Independent Practice

Estimate, then subtract. Write each difference in simplest form.

Question 2.
McGraw Hill My Math Grade 5 Chapter 9 Lesson 13 Answer Key Subtract with Renaming 9
Answer:
The above-given mixed fractions:
4 3/8 – 1 5/8
Here 3/8 is less than 5/8 so we cannot subtract. In this case, we have to regroup the fractions.
Take borrow ‘1’ from 4 so 4 becomes 3. And add the denominator and numerator ( 8 + 3 = 11) now the numerator becomes 11. And the denominator remains the same.
Now the equation is:
3 11/8 – 1 5/8
Step 1: We will subtract the whole numbers of both fractions. i.e., 3 – 1 = 2.
Step 2: Now we will subtract the fractional parts. i.e., (11/8 – 5/8) = 6/8 = 3/4
Step 3: We will combine the result of the last two steps to get the result. i.e., 2 + (3/4) = 2 3/4.
Therefore, McGraw Hill My Math Grade 5 Chapter 9 Lesson 13 Answer Key Subtract with Renaming_5

Question 3.
McGraw Hill My Math Grade 5 Chapter 9 Lesson 13 Answer Key Subtract with Renaming 10
Answer:
Fractions with unequal denominators are known as, unlike fractions.
The above-given fractions:
3 1/6 – 1 1/3
Here 1/6 is less than 1/3 so we cannot subtract. In this case, we have to regroup the fractions.
Take borrow ‘1’ from 3 so 3 becomes 2. And add the denominator and numerator ( 6 + 1 = 7) now the numerator becomes 7. And the denominator remains the same.
Now the equation is:
2 7/6 – 1 1/3
– separate the whole numbers and fractions. Now make the denominators equal by taking the LCM.
Step 1: We will subtract the whole numbers of both fractions. i.e., 2 – 1 = 1.
Step 2: Now we will subtract the fractional parts. i.e., (7/6 – 1/3)
6 is the least common multiple of denominators 6 and 3. Use it to convert to equivalent fractions with this common denominator.
7 – 2/6 = 5/6
Step 3: We will combine the result of the last two steps to get the result. i.e., 1 + (5/6) = 1 5/6.
Therefore, McGraw Hill My Math Grade 5 Chapter 9 Lesson 13 Answer Key Subtract with Renaming_6

Question 4.
McGraw Hill My Math Grade 5 Chapter 9 Lesson 13 Answer Key Subtract with Renaming 11
Answer:
Fractions with unequal denominators are known as, unlike fractions.
The above-given mixed fractions:
5 1/4 – 4 1/2
Here 1/4 is less than 1/2 so we cannot subtract. In this case, we have to regroup the fractions.
Take borrow ‘1’ from 5 so 5 becomes 4. And add the denominator and numerator ( 4 + 1 = 5) now the numerator becomes 5. And the denominator remains the same.
Now the equation is:
4 5/4 – 4 1/2
– separate the whole numbers and fractions. Now make the denominators equal by taking the LCM.
Step 1: We will subtract the whole numbers of both fractions. i.e., 4 – 4 = 0
Step 2: Now we will subtract the fractional parts. i.e., (5/4 – 1/2)
4 is the least common multiple of denominators 4 and 2. Use it to convert to equivalent fractions with this common denominator.
(5 – 2)/4 = 3/4
Step 3: We will combine the result of the last two steps to get the result. i.e., 0 + (3/4) = 3/4
Therefore, McGraw Hill My Math Grade 5 Chapter 9 Lesson 13 Answer Key Subtract with Renaming_7

Question 5.
McGraw Hill My Math Grade 5 Chapter 9 Lesson 13 Answer Key Subtract with Renaming 12
Answer:
Fractions with unequal denominators are known as, unlike fractions.
The above-given mixed fractions:
7 1/2 – 3 4/5
We have two ways to perform the subtraction.
Method I: By subtracting the whole numbers and the fractions by making their denominators equal.
Method II: By converting them into improper fractions, followed by subtracting them by making their denominators equal.
We go for the second method:
– Convert mixed numbers to improper fraction
7 1/2 = (7 x 2)/2 + 1/2 = 14/2 + 1/2 = 15/2
3 4/5 = (3 x 5)/5 + 4/5 = 15/5 + 4/5 = 19/5
Now find the common denominator:
– 10 is the least common multiple of denominators 2 and 5. Use it to convert to equivalent fractions with this common denominator.
15/2 – 19/5
= (15 x 5)/(2 x 5) – (19 x 2)/(5 x 2)
= 75/10 – 38/10
= (75 – 38)/10
= 37/10
Now simplify for the mixed number:
– Reduce the fraction to the lowest terms.
– 1 is the greatest common divisor of 37 and 10. The result can’t be further reduced.
– Convert improper fractions to mixed number
37 ÷ 10 = 3 remainder 7
The mixed fraction is 3 7/10.
Therefore, McGraw Hill My Math Grade 5 Chapter 9 Lesson 13 Answer Key Subtract with Renaming_8

Question 6.
McGraw Hill My Math Grade 5 Chapter 9 Lesson 13 Answer Key Subtract with Renaming 13
Answer:
The above-given:
4 – 1 1/8
Here 4 is an integer.
Now convert the integer to a fraction.
4 = 4/1
– Convert mixed numbers to improper fraction
1 1/8 = (1 x 8)/8 + 1/8 = (8 + 1)/8 = 9/8
– Now find the common denominator:
4/1 – 9/8 = (4 x 8)/(1 x 8) – (9 x 1)/(8 x 1) = 32/8 – 9/8
.              = (32 – 9)/8
.              = 23/8
Now simplify for the mixed fraction:
– Reduce the fraction to the lowest terms
23 ÷ 8 = 2 remainder 7
The mixed number is 2 7/8

 

Question 7.
McGraw Hill My Math Grade 5 Chapter 9 Lesson 13 Answer Key Subtract with Renaming 14
Answer:
The above-given:
12 – 5 1/6
Here 12 is an integer so convert the integer into a fraction.
12 = 12/1
– Now convert mixed numbers to improper fractions.
5 1/6 = 6 x 5/6 + 1/6 = 30/6 + 1/6 = 31/6
– Now find the common denominator
– 6 is the least common multiple of denominators 1 and 6. Use it to convert to equivalent fractions with this common denominator.
12/1 – 31/6 = 12 x 6/1 x 6 – 31 x 1/6 x 1 = 72/6 – 31/6
.                                                                = 72 – 31/6
.                                                                = 41/6
Now simplify the 41/6 to make it a mixed number.
41/6: Reduce the fraction to the lowest terms
– 1 is the greatest common divisor of 41 and 6. The result can’t be further reduced.
– Convert improper fractions to mixed number
41 ÷ 6 = 6 remainder 5
The mixed fraction can be written as 6 5/6.

Question 8.
7\(\frac{2}{7}\) – 6\(\frac{4}{7}\) = _____
Answer:
The above-given:
7 2/7 – 6 4/7
Here 2/7 is less than 4/7 so we cannot subtract In this case, we have to regroup the fractions.
Take borrow ‘1’ from 7 so 7 becomes 6. And add the denominator and numerator ( 7 + 2 = 9) now the numerator becomes 9. And the denominator remains the same.
Now the equation is:
6 9/7 – 6 4/7
– separate the whole numbers and fractions. Denominators are equal so we can subtract directly.
Step 1: We will subtract the whole numbers of both fractions. i.e., 6 – 6 = 0
Step 2: Now we will subtract the fractional parts. i.e., 9/7 – 4/7
= ( 9 – 4)/7 = 5/7
Step 3: We will combine the result of the last two steps to get the result. i.e., 0 + (5/7) = 5/7.

Question 9.
9\(\frac{3}{10}\) – 5\(\frac{7}{10}\) = _____
Answer:
The above-given fractions:
9 3/10 – 5 7/10
Here 3/10 is less than 7/10 so we cannot subtract In this case, we have to regroup the fractions.
Take borrow ‘1’ from 9 so 9 becomes 8. And add the denominator and numerator ( 10 + 3 = 13) now the numerator becomes 13. And the denominator remains the same.
Now the equation is:
8 13/10 – 5 7/10
– separate the whole numbers and fractions. Denominators are equal so we can subtract directly.
Step 1: We will subtract the whole numbers of both fractions. i.e., 8 – 5 = 3
Step 2: Now we will subtract the fractional parts. i.e., 13/10 – 7/10
= ( 13 – 7)/10 = 6/10 = 3/5
Step 3: We will combine the result of the last two steps to get the result. i.e., 3 + (3/5) = 3 3/5.

Question 10.
10\(\frac{1}{3}\) – 3\(\frac{2}{3}\) = _____
Answer:
The above-given:
10 1/3 – 3 2/3
Here 1/3 is less than 2/3 so we cannot subtract In this case, we have to regroup the fractions.
Take borrow ‘1’ from 10 so 10 becomes 9. And add the denominator and numerator ( 3 + 1 = 4) now the numerator becomes 4. And the denominator remains the same.
Now the equation is:
9 4/3 – 3 2/3
– separate the whole numbers and fractions. Denominators are equal so we can subtract directly.
Step 1: We will subtract the whole numbers of both fractions. i.e., 9 – 3 = 6
Step 2: Now we will subtract the fractional parts. i.e., 4/3 – 2/3
= ( 4 – 2)/3 = 2/3
Step 3: We will combine the result of the last two steps to get the result. i.e., 6 + 2/3 = 6 2/3.

Question 11.
18 – 9\(\frac{1}{4}\) = _____
Answer:
The above-given:
18 – 9 1/4
Here 12 is an integer so convert the integer into a fraction.
18 = 18/1
– Now convert mixed numbers to improper fractions.
9 1/4 = 9 x 4/4 + 1/4 = 36/4 + 1/4 = 37/4
– Now find the common denominator
– 4 is the least common multiple of denominators 1 and 4. Use it to convert to equivalent fractions with this common denominator.
18/1 – 37/4 = 18 x 4/1 x 4 – 37 x 1/4 x 1 = 72/4 – 37/4
.                                                                = 72 – 37/4
.                                                                = 35/4
Now simplify the 35/4 to make it a mixed number.
35/4: Reduce the fraction to the lowest terms
– 1 is the greatest common divisor of 35 and 4. The result can’t be further reduced.
– Convert improper fractions to mixed number
35 ÷ 4 = 8 remainder 3
The mixed fraction can be written as 8 3/4

Question 12.
13 – 4\(\frac{1}{3}\) = _____
Answer:
The above-given:
13 – 4 1/3
Here 12 is an integer so convert the integer into a fraction.
13 = 13/1
– Now convert mixed numbers to improper fractions.
4 1/3 = 4 x 3/3 + 1/3 = 12/3 + 1/3 = 13/3
– Now find the common denominator
– 3 is the least common multiple of denominators 1 and 3. Use it to convert to equivalent fractions with this common denominator.
13/1 – 13/3 = 13 x 3/1 x 3 – 13 x 1/3 x 1 = 39/3 – 13/3
.                                                                = 39 – 13/3
.                                                                = 26/3
Now simplify the 26/3 to make it a mixed number.
26/3: Reduce the fraction to the lowest terms
– 1 is the greatest common divisor of 26 and 3. The result can’t be further reduced.
– Convert improper fractions to mixed number
26 ÷ 3 = 8 remainder 2
The mixed fraction can be written as 8 2/3

Question 13.
5\(\frac{1}{4}\) – 1\(\frac{1}{2}\) = _____
Answer:
The above-given fractions:
5 1/4 – 1 1/2
Here 1/4 is less than 1/2 so we cannot subtract. In this case, we have to regroup the fractions.
Take borrow ‘1’ from 5 so 5 becomes 4. And add the denominator and numerator ( 4 + 1 = 5) now the numerator becomes 5. And the denominator remains the same.
Now the equation is:
4 5/4 – 1 1/2
– separate the whole numbers and fractions. Now make the denominators equal by taking the LCM.
Step 1: We will subtract the whole numbers of both fractions. i.e., 4 – 1 = 3
Step 2: Now we will subtract the fractional parts. i.e., (5/4 – 1/2)
4 is the least common multiple of denominators 4 and 2. Use it to convert to equivalent fractions with this common denominator.
(5 – 2)/4 = 3/4
Step 3: We will combine the result of the last two steps to get the result. i.e., 3 + (3/4) = 3 3/4

Problem Solving

Use the table for Exercises 14 and 15. The table shows the average lengths of some insects in the United States.

Question 14.
Mathematical PRACTICE 2 Reason Is the difference in length between a Monarch butterfly and a bumble bee greater or less than the difference in length between a walking stick and a grasshopper? Explain your reasoning.
McGraw Hill My Math Grade 5 Chapter 9 Lesson 13 Answer Key Subtract with Renaming 15
Answer:
The above-given:
The length of the Monarch butterfly = 3 1/2
The length of the walking stick = 4
The length of the grasshopper = 1 3/4
The length of the Bumble Bee = 5/8
The difference between the Monarch butterfly and the Bumble Bee is 3 1/2 – 5/8
convert mixed fraction into an improper fraction:
3 1/2 = 7/2
Now the equation is 7/2 – 5/8
Make the denominators equal.
8 is the least common multiple of denominators 8 and 2. Use it to convert to equivalent fractions with this common denominator.
28/8 – 5/8 = (28 – 5)/8 = 23/8
Now simplify the fraction for mixed numbers:
– Reduce the fraction to lowest terms: 1 is the greatest common divisor of 23 and 8. The result can’t be further reduced.
– Convert improper fractions to mixed numbers: 23 ÷ 8 = 2 remainder 7
The mixed number is 2 7/8.
The difference between the walking stick and a grasshopper = 4 – 1 3/4
convert the integer into a fraction: 4 = 4/1
1 3/4 = 7/4
now the equation is 4/1 – 7/4
Make the denominators equal:
4 is the least common multiple of denominators 1 and 4. Use it to convert to equivalent fractions with this common denominator.
4/1 – 7/4 = 4 x 4/1 x 4 – 7 x 1/4 x 1 = 16/4 – 7/4 = 9/4
– Convert improper fractions to mixed numbers: 9 ÷ 4 = 2 remainder 1
The mixed number is 2 1/4.
Now compare:
2 7/8 and 2 1/4
7/8 is greater than 1/4
Hence, we can say that the difference in length between a Monarch butterfly and a bumble bee is greater than the difference in length between a walking stick and a grasshopper.

Question 15.
Find the difference in length between a walking stick and a bumble bee.
Answer:
The length of the walking stick = 4
The length of the Bumble Bee = 5/8
The difference = 4 – 5/8
step 1: convert an integer into a fraction: 4 as 4/1
step 2: find the common denominator
– 8 is the least common multiple of denominators 1 and 8. Use it to convert to equivalent fractions with this common denominator.
4/1 – 5/8 = 32/8 – 5/8 = 27/8
Now simplify the 27/8 for mixed number
– Convert improper fractions to mixed number
– 27 ÷ 8 = 3 remainder 3
The mixed number is 3 3/8.

Question 16.
Arlo had 5 gallons of paint. He used 2\(\frac{5}{8}\) gallons. How much paint does he have left?
McGraw Hill My Math Grade 5 Chapter 9 Lesson 13 Answer Key Subtract with Renaming 16
Answer:
The above-given:
The number of gallons of paint Arlo had = 5
The number of gallons he used = 2 5/8
The number of gallons left = x
x = 5 – 2 5/8
step 1: convert an integer into a fraction: 5 as 5/1
step 2: Convert mixed numbers to improper fraction
2 5/8 = 21/8
step 3: find the common denominator
– 8 is the least common multiple of denominators 1 and 8. Use it to convert to equivalent fractions with this common denominator.
5/1 – 21/8 = 40/8 – 21/8 = 19/8
Now simplify the 19/8 for mixed number
– Convert improper fractions to mixed number
– 19 ÷ 8 = 2 remainder 3
The mixed number is 2 3/8.

HOT Problems

Question 17.
Mathematical PRACTICE 1 Plan Your Solution Write a subtraction problem in which you have to rename a fraction whose solution is between 3 and 4.
Answer:
x – y = 3.5
for example,
7 7/8 – 4 1/2
= 7 – 4 – 7/8 – 1/2
= 3 – 7/8 – 1/2
here the denominators are not equal so we have to make the denominators equal.
– Find the common denominator.
– 8 is the least common multiple of denominators 8 and 2. Use it to convert to equivalent fractions with this common denominator.
= 3 – (7 – 4)/8
= 3 – 2/8
= 3 – 1/4
This can also be written as 3 1/4

Question 18.
? Building on the Essential Question How are equivalent fractions used in renaming when subtracting?
Answer:
When subtracting one fraction from another, one or both fractions are renamed so that they have the same denominators. Then the result of the subtraction is equal to the subtraction of the numerators divided by the common denominator.

McGraw Hill My Math Grade 5 Chapter 9 Lesson 13 My Homework Answer Key

Practice

Estimate, then subtract. Write each difference in simplest form.

Question 1.
McGraw Hill My Math Grade 5 Chapter 9 Lesson 13 Answer Key Subtract with Renaming 17
Answer:
The above-given:
2 1/8 – 1 7/8
step1: convert mixed numbers to improper fractions.
2 1/8 = 2 x 8/8 + 1/8 = 16/8 + 1/8 = 17/8
1 7/8 = 1 x 8/8 + 7/8 = 8/8 + 7/8 = 15/8
now subtract,
17/8 – 15/8 = 2/8 = 1/4

Question 2.
McGraw Hill My Math Grade 5 Chapter 9 Lesson 13 Answer Key Subtract with Renaming 18
Answer:
The above-given:
12 1/4 – 5 2/3
convert mixed numbers to improper fractions.
12 1/4 = 12 x 4/4 + 1/4 = 48/4 + 1/4 = 49/4
5 2/3 = 5 x 2/3 + 2/3 = 10/3 + 2/3 = 12/3
Now subtract:
49/4 – 12/3
– Make the denominators equal.
49/4 – 12/3 :
12 is the least common multiple of denominators 4 and 3. Use it to convert to equivalent fractions with this common denominator.
49 x 3/4 x 3 – 17 x 4/3 x 4 = 147/12 – 68/12 = 79/12
Now simplify for the mixed number.
79/12:
– Reduce the fraction to the lowest terms
– 1 is the greatest common divisor of 79 and 12. The result can’t be further reduced.
– convert improper fractions to mixed number
79 ÷ 12 = 6 remainder 7
Therefore, the mixed number is 6 7/12.

Question 3.
8\(\frac{1}{6}\) – 3\(\frac{5}{6}\) = ____
Answer:
The above-given:
8 1/6 – 3 5/6
– Here 1/6 is less than 5/6 so we cannot subtract directly. In this case, we have to regroup the fractions.
Take borrow ‘1’ from 8 so 8 becomes 7. And add the denominator and numerator ( 6 + 1 = 7) now the numerator becomes 7. And the denominator remains the same.
Now the equation is:
7 7/6 – 3 5/6
– separate the whole numbers and fractions.
Step 1: We will subtract the whole numbers of both fractions. i.e., 7 – 3 = 4
Step 2: Now we will subtract the fractional parts. i.e., (7/6 – 5/6)
Here the denominators are equal so subtract directly.
7/6 – 5/6 = 2/6 = 1/3
Step 3: We will combine the result of the last two steps to get the result. i.e., 4 + 1/3 = 4 1/3.

Problem Solving

Question 4.
Mathematical PRACTICE 1 Make a Plan Sherman’s backpack weighs 6\(\frac{1}{4}\) pounds. Brie’s backpack weighs 5\(\frac{3}{4}\) pounds. How much heavier is Sherman’s backpack than Brie’s backpack?
Answer:
The above-given:
The number of pounds Sherman’s backpack weighs = 6 1/4
The number of pounds Brie’s backpack weighs = 5 3/4
The number of pounds heavier Sherman’s backpack than Brie’s backpack = x
x = 6 1/4 – 5 3/4
– Here 1/4 is less than 3/4 so we cannot subtract directly. In this case, we have to regroup the fractions.
Take borrow ‘1’ from 6 so 6 becomes 5. And add the denominator and numerator ( 4 + 1 = 5) now the numerator becomes 5. And the denominator remains the same.
Now the equation is:
5 5/4 – 5 3/4
– separate the whole numbers and fractions.
Step 1: We will subtract the whole numbers of both fractions. i.e., 5 – 5 = 0
Step 2: Now we will subtract the fractional parts. i.e., (5/4 – 3/4)
Here the denominators are equal so subtract directly.
5/4 – 3/4 = 2/4 = 1/2
Step 3: We will combine the result of the last two steps to get the result. i.e., 0 + 1/2 = 1/2.

Question 5.
Mathematical PRACTICE 2 Use Number Sense Veronica jogged 10\(\frac{3}{16}\) miles in one week The next week she jogged 8\(\frac{7}{16}\) miles. How many more miles did she jog the first week?
Answer:
The above-given:
The number of miles Veronica jogged in one week = 10 3/16
The number of miles she jogged in next week = 8 7/16
The number of more miles she jogs the first week = x
x = 10 3/16 – 8 7/16
– Here 3/16 is less than 7/16 so we cannot subtract directly. In this case, we have to regroup the fractions.
Take borrow ‘1’ from 10 so 10 becomes 9. And add the denominator and numerator ( 16 + 3 = 19) now the numerator becomes 19. And the denominator remains the same.
Now the equation is:
9 19/16 – 8 7/16
– separate the whole numbers and fractions.
Step 1: We will subtract the whole numbers of both fractions. i.e., 9 – 8 = 1
Step 2: Now we will subtract the fractional parts. i.e., (19/16 – 7/16)
Here the denominators are equal so subtract directly.
19/16 – 7/16 = 12/16 = 3/4
Step 3: We will combine the result of the last two steps to get the result. i.e., 1 + 3/4 = 1 3/4.

Question 6.
Mathematical PRACTICE 6 Be Precise Careta swam 7\(\frac{1}{8}\) miles. Joey swam 5\(\frac{5}{8}\) miles. How many more miles did Careta swim than Joey?
McGraw Hill My Math Grade 5 Chapter 9 Lesson 13 Answer Key Subtract with Renaming 19
Answer:
The above-given:
The number of miles Careta swam = 7 1/8
The number of miles Joey swam = 5 5/8
The number of more miles Caretan swim than Joey = x
x = 7 1/8 – 5 5/8
– Here 1/8 is less than 5/8 so we cannot subtract directly. In this case, we have to regroup the fractions.
Take borrow ‘1’ from 7 so 7 becomes 6. And add the denominator and numerator ( 8 + 1 = 9 ) now the numerator becomes 9. And the denominator remains the same.
Now the equation is:
6 9/8 – 5 5/8
– separate the whole numbers and fractions.
Step 1: We will subtract the whole numbers of both fractions. i.e., 6 – 5 = 1
Step 2: Now we will subtract the fractional parts. i.e., (9/8 – 5/8)
Here the denominators are equal so subtract directly.
9/8 – 5/8 = 4/8 = 1/2
Step 3: We will combine the result of the last two steps to get the result. i.e., 1 + 1/2 = 1 1/2.

Test Practice

Question 7.
Ross has 6 yards of material. He bought 2\(\frac{1}{3}\) more yards. Then he used 6\(\frac{5}{6}\) yards. How many yards of material does he have left?
A. 1\(\frac{1}{2}\) yards
B. 3\(\frac{1}{6}\) yards
C. 3\(\frac{2}{3}\) yards
D. 8\(\frac{1}{3}\) yards
Answer:
The above-given:
The number of yards of material Ross has = 6
The number of yards he bought = 2 1/3
The number of yards he used = 6 5/6
The number of yards of material he left = x
x = 6 + 2 1/3 – 6 5/6
convert integer to a fraction.
6 = 6/1
convert mixed numbers to fractions:
2 1/3 = 2 x 3/3 + 1/3 = 6/3 + 1/3 = 7/3
Now add: 6/1 + 7/3
make the denominators equal.
3 is the least common multiple of denominators 1 and 3. Use it to convert to equivalent fractions with this common denominator.
6/1 + 7/3 = 6 x 3/1 x 3 + 7 x 1/3 x 1 = 18/3 + 7/3 = 25/3.
Now subtract:
25/3 – 6 5/6
convert mixed numbers to fractions:
6 5/6 = 41/6
Make the denominators equal:
– 6 is the least common multiple of denominators 3 and 6. Use it to convert to equivalent fractions with this common denominator.
25/3 – 41/6 =  50/6 – 41/6 = 9/6 = 3/2
convert an improper fraction to mixed numbers:
– 3 ÷ 2 = 1 remainder 1
The mixed number is 1 1/2.

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