All the solutions provided in McGraw Hill My Math Grade 5 Answer Key PDF Chapter 9 Review will give you a clear idea of the concepts.

Vocabulary Check

Write each of the following on the lines to make a true sentence.

equivalent fractions least common denominator like fractions
mixed number unlike fractions

Question 1.
Fractions that have the same denominator, such as $$\frac{1}{3}$$ and $$\frac{2}{3}$$, are
___________
The fractions with the same denominator are called like fractions. Here, the denominators of all the fractions are 2. Hence, they are called like fractions.

Question 2.
Fractions that have the same value, such as $$\frac{1}{4}$$ and $$\frac{2}{8}$$, are ______
Equivalent fractions are fractions that have different numerators and denominators but are equal to the same value. For example, 2/4 and 3/6 are equivalent fractions, because they both are equal to 1/2. A fraction is a part of a whole. Equivalent fractions represent the same portion of the whole.

Question 3.
The ____ of $$\frac{5}{6}$$ and $$\frac{7}{12}$$ is 12.
The LCM of any two is the value that is evenly divisible by the two given numbers. The full form of LCM is Least Common Multiple. It is also called the Least Common Divisor (LCD).

Question 4.
A number that has a whole number part and a fraction part is called a ______
A mixed number is a whole number, and a proper fraction is represented together.  It generally represents a number between any two whole numbers.
A mixed number is formed by combining three parts: a whole number, a numerator, and a denominator. The numerator and denominator are part of the proper fraction that makes the mixed number.

Question 5.
An example of two ____ are $$\frac{1}{8}$$ and $$\frac{3}{4}$$.
Fractions with different denominators are called the, unlike fractions. Here the denominators of fractions have different values. For example, 2/3, 4/9, 6/67, 9/89 are unlike fractions. Since the denominators here are different, therefore it is not easy to add or subtract such fractions.

Concept Check

Round each fraction to 0, $$\frac{1}{2}$$, or 1.

Question 6.
$$\frac{4}{7}$$ ≈ ____
The above-given fraction: 4/7
Steps to round fractions:
– Take the above fraction.
– Convert the given fraction into decimals by dividing the numerator by the denominator.
– If the obtained number to the right of the decimal point is 0.5 or more, then add 1 to the left of the decimal point and remove the decimal part.
– If the obtained number to the right of the decimal point is lesser than 0.5, then leave the number to the left of the decimal point and remove the decimal part.
– Write the new number as a rounded number.
4/7 can be rounded to 1
Explanation: The actual value of 4/7 is 0.6 and .6 is greater than .5 so we have to add 1.

Question 7.
$$\frac{9}{10}$$ ≈ ____
The above-given: 9/10
Steps to round fractions:
– Take the above fraction.
– Convert the given fraction into decimals by dividing the numerator by the denominator.
– If the obtained number to the right of the decimal point is 0.5 or more, then add 1 to the left of the decimal point and remove the decimal part.
– If the obtained number to the right of the decimal point is lesser than 0.5, then leave the number to the left of the decimal point and remove the decimal part.
– Write the new number as a rounded number.
9/10 can be rounded to 1
Explanation: The actual value of 9/10 is 0.9 and .9 is greater than .5 so we have to add 1.

Question 8.
$$\frac{2}{9}$$ ≈ ____
The above-given: 2/9
Steps to round fractions:
– Take the above fraction.
– Convert the given fraction into decimals by dividing the numerator by the denominator.
– If the obtained number to the right of the decimal point is 0.5 or more, then add 1 to the left of the decimal point and remove the decimal part.
– If the obtained number to the right of the decimal point is lesser than 0.5, then leave the number to the left of the decimal point and remove the decimal part.
– Write the new number as a rounded number.
2/9 can be rounded to 0
Explanation: The actual value of 2/9 is 0.2 and .2 is less than .5 so we have to leave the number to the left of the decimal point and remove the decimal part.

Add. Write each sum in simplest form.

Question 9.
$$\frac{5}{9}$$ + $$\frac{1}{9}$$ = ____
The above-given fractions;
5/9 + 1/9
Here the denominators are equal so we can add directly.
= 5 + 1/9
= 6/9
We can reduce the lowest terms.
3 is the greatest common divisor of 6 and 9. Reduce by dividing both the numerator and denominator by 3.
6/9 = 6 ÷ 3/9 ÷ 3
= 2/3
Therefore, $$\frac{5}{9}$$ + $$\frac{1}{9}$$ = 2/3

Question 10.
$$\frac{6}{7}$$ + $$\frac{1}{7}$$ = ____
The above-given:
6/7 + 1/7
Here the denominators are equal so we can add directly.
= 6 + 1/7
= 7/7
= 1
Therefore, $$\frac{6}{7}$$ + $$\frac{1}{7}$$ = 1.

Question 11.
$$\frac{5}{8}$$ + $$\frac{1}{8}$$ = ____
The above-given:
5/8 + 1/8
Here the denominators are equal so we can add directly.
= 5 + 1/8
= 6/8
Here we can reduce the fraction to the lowest terms.
2 is the greatest common divisor of 6 and 8. Reduce by dividing both the numerator and denominator by 2.
= 6 ÷ 2/8 ÷ 2
= 3/4
Therefore, $$\frac{5}{8}$$ + $$\frac{1}{8}$$ = 3/4.

Question 12.
$$\frac{3}{5}$$ + $$\frac{1}{10}$$ = ____
The above-given:
3/5 + 1/10
Here the denominators are not equal, so make them equal.
– Find common denominators:
10 is the least common multiple of denominators 5 and 10. Use it to convert to equivalent fractions with this common denominator.
= 3 x 2/5 x 2 + 1 x 1/10 x 1
= 6/10 + 1/10
Now denominators are equal so add:
= (6 + 1)/10
= 7/10
Therefore, $$\frac{3}{5}$$ + $$\frac{1}{10}$$ = 7/10

Question 13.
$$\frac{1}{2}$$ + $$\frac{1}{8}$$ = ____
The above-given:
1/2 + 1/8
Here the denominators are not equal, so make them equal.
– Find common denominators:
8 is the least common multiple of denominators 2 and 8. Use it to convert to equivalent fractions with this common denominator.
= 1 x 4/2 x 4 + 1 x 1/8 x 1
= 4/8 + 1/8
= (4 + 1)/8
= 5/8
Therefore, $$\frac{1}{2}$$ + $$\frac{1}{8}$$ = 5/8

Question 14.
$$\frac{2}{7}$$ + $$\frac{5}{14}$$ = ____
The above-given:
2/7 + 5/14
Here the denominators are not equal, so make them equal.
– Find common denominators:
14 is the least common multiple of denominators 7 and 14. Use it to convert to equivalent fractions with this common denominator.
= 2 x 2/7 x 2 + 5 x 1/14 x 1
= 4/14 + 5/14
= (4 + 5)/14
= 9/14
Therefore, $$\frac{2}{7}$$ + $$\frac{5}{14}$$ = 9/14

Question 15.
6$$\frac{3}{4}$$ + 2$$\frac{2}{4}$$ = ____
The above-given:
6 3/4 + 2 2/4
– Convert mixed numbers into an improper fraction
6 3/4 = 6 x 4/4 + 3/4 = 24/4 + 3/4 = 27/4
2 2/4 = 2 x 4/4 + 2/4 = 8/4 + 2/4 = 10/4
27/4 + 10/4 = 27 + 10/4 = 37/4
Here we can reduce fractions to the lowest terms.
1 is the greatest common divisor of 37 and 4. The result can’t be further reduced.
– Convert improper fractions to mixed number
37 ÷ 4 = 9 remainder 1
Therefore, the mixed number is 9 1/4.
Therefore, 6$$\frac{3}{4}$$ + 2$$\frac{2}{4}$$ = 9 1/4

Question 16.
1$$\frac{1}{12}$$ + 3$$\frac{2}{12}$$ = ____
The above-given:
1 1/12 + 3 2/12
– Convert mixed numbers into an improper fraction
1 1/12 = 1 x 12/12 + 1/12 = 12/12 + 1/12 = 13/12
3 2/12 = 3 x 12/12 + 2/12 = 36/12 + 2/12 = 38/12
13/12 + 38/12 = 13 + 38/12 = 51/12
Here we can reduce the fractions into the lowest terms:
3 is the greatest common divisor of 51 and 12. Reduce by dividing both the numerator and denominator by 3.
51 ÷ 3/12 ÷ 3 = 17/4
– Convert improper fractions to mixed number
17 ÷ 4 = 4 remainder 1
Therefore, the mixed number is 4 1/4.
Hence, 1$$\frac{1}{12}$$ + 3$$\frac{2}{12}$$ = 4 1/4.

Question 17.
12$$\frac{1}{3}$$ + 6$$\frac{2}{6}$$ = ____
The above-given:
12 1/3 + 6 2/6
– Convert mixed numbers into an improper fraction
12 1/3 = 12 x 3/3 + 1/3 = 36/3 + 1/3 = 37/3
6 2/6 = 6 x 6/6 + 2/6 = 36/6 + 2/6 = 38/6
Now we have to find the common denominator:
6 is the least common multiple of denominators 3 and 6. Use it to convert to equivalent fractions with this common denominator.
= 37 x 2/3 x 2 + 38 x 1/6 x 1
= 74/6 + 38/6
= 74 + 38/6
= 112/6
Reduce the fraction to the lowest terms
2 is the greatest common divisor of 112 and 6. Reduce by dividing both the numerator and denominator by 2.
= 112 ÷ 2/6 ÷ 2
= 56/3
– Convert improper fractions to mixed number
56 ÷ 3 = 18 remainder 2
The mixed number is 18 2/3.
Therefore, 12$$\frac{1}{3}$$ + 6$$\frac{2}{6}$$ = 18 2/3

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

Question 18.
$$\frac{7}{16}$$ – $$\frac{3}{16}$$ = ____
The above-given:
7/16 – 3/16
Here the denominators are equal so we can subtract directly.
= 7 – 3/16
= 4/16
= 1/4
Therefore, $$\frac{7}{16}$$ – $$\frac{3}{16}$$ = 1/4

Question 19.
$$\frac{11}{12}$$ – $$\frac{7}{12}$$ = ____
The above-given:
11/12 – 7/12
Here the denominators are equal so we can subtract directly.
= 11 – 7/12
= 4/12
= 1/3
Therefore, $$\frac{11}{12}$$ – $$\frac{7}{12}$$ = 1/3

Question 20.
$$\frac{4}{5}$$ – $$\frac{2}{5}$$ = ____
The above-given:
4/5 – 2/5
Here the denominators are equal so we can subtract directly.
= 4 – 2/5
= 2/5
Therefore, $$\frac{4}{5}$$ – $$\frac{2}{5}$$ = 2/5

Question 21.
$$\frac{8}{9}$$ – $$\frac{5}{6}$$ = ____
The above-given:
8/9 – 5/6
– Find the common denominator:
18 is the least common multiple of denominators 9 and 6. Use it to convert to equivalent fractions with this common denominator.
= 8 x 2/9 x 2 – 5 x 3/6 x 3
= 16/18 – 15/18
Now subtract:
= 16 -15/16
= 1/18

Question 22.
$$\frac{11}{12}$$ – $$\frac{7}{8}$$ = ____
The above-given:
11/12 – 7/8
– Find the common denominator:
24 is the least common multiple of denominators 12 and 8. Use it to convert to equivalent fractions with this common denominator.
= 11 x 2/12 x 2 – 7 x 3/8 x 3
= 22/24 – 21/24
Now subtract:
= 22 – 21/24
= 1/24
Therefore, $$\frac{11}{12}$$ – $$\frac{7}{8}$$ = 1/24

Question 23.
$$\frac{7}{10}$$ – $$\frac{1}{5}$$ = ____
The above-given:
7/10 – 1/5
– Find the common denominator:
10 is the least common multiple of denominators 10 and 5. Use it to convert to equivalent fractions with this common denominator.
= 7 x 1/10 x 1 – 1 x 2/5 x 2
= 7/10 – 2/10
Now subtract:
= 7 – 2/10
= 5/10
= 1/2
Therefore, $$\frac{7}{10}$$ – $$\frac{1}{5}$$ = 1/2

Problem Solving

Question 24.
Russ is putting his vacation photographs in an album that is 12$$\frac{1}{8}$$– inches long and 10$$\frac{1}{4}$$ inches wide. Should he trim the edges of the photographs to 12 inches long and 10 inches wide or to 12$$\frac{1}{2}$$– inches long and 10$$\frac{1}{2}$$ inches wide?

The above-given:
The number of inches long Russ put his photos in an album = 12 1/8
The width is 10 1/4 inches
Now what we do is round off the values and check:
12 1/8: 1/8 can be rounded to 0
10 1/4: 1/4 can be rounded to 0
12 + 0 = 12
10 + 0 =10
Finally, he can trim the photographs to 12 inches long and 10 inches width.

Question 25.
Steve watched television for $$\frac{3}{4}$$ hour on Monday and $$\frac{5}{6}$$ hour on Tuesday. How much longer did he watch television on Tuesday than on Monday?
The above-given:
The number of hours Steve watched television on Monday = 3/4
The number of hours Steve watched television on Tuesday = 5/6
The number of more hours he watched on Tuesday than Monday = x
x = 5/6 – 3/4
Now make the denominators equal
12 is the least common multiple of denominators 6 and 4. Use it to convert to equivalent fractions with this common denominator.
x = 5 x 2/6 x 2 – 3 x 3/4 x 3
x = 10/12 – 9/12
x = 10 – 9/12
x = 1/12
Therefore, he watched 1/12 hour more on Tuesday than the Monday.

Question 26.
When Ricki walks to school on the sidewalk, she walks $$\frac{7}{10}$$ mile. She then takes a shortcut across the field, which is $$\frac{1}{4}$$ mile long. How long is Ricki’s route to school?
The above-given:
The number of miles she walked = 7/10
The number of miles long the short cut = 1/4
The number of miles she travelled to school = x
x = 7/10 + 1/4
– Make the denominators equal
20 is the least common multiple of denominators 10 and 4. Use it to convert to equivalent fractions with this common denominator.
x = 7 x 2/10 x 2 + 1 x 5/4 x 5
x = 14/20 + 5/20
x = 19/20
Therefore, she walks 19/20 miles to school.

Test Practice

Question 27.
Peta was swimming with stingrays. The first stingray she swam with was 5$$\frac{1}{4}$$– feet long. The second one she swam with was 4$$\frac{3}{4}$$– feet long. How much longer was the first stingray?
A. $$\frac{1}{2}$$ foot
B. $$\frac{3}{4}$$ foot
C. 1$$\frac{1}{4}$$ feet
D. 1$$\frac{1}{2}$$ feet
Explanation:
The above-given:
The number of feet she swims on the first day = 5 1/4
The number of feet she swims on the second day = 4 3/4
The number of feet long was the first stingray = x
x = 5 1/4 – 4 3/4
Now convert them into improper fractions:
5 1/4 = 5 x 4/4 + 1/4 = 20/4 + 1/4 = 21/4
4 3/4 = 4 x 4/4 + 3/4 = 16/4 + 3/4 = 19/4
x = 21/4 – 19/4
x = 2/4
x = 1/2
Therefore, 1/2 foot long.

Reflect

Use what you learned about fraction operations to complete the graphic organizer.