Relationships to Divide Whole Numbers by Fractions
Key Concepts
■ Divide whole number by fractions
■ Divide fractions by whole numbers
Introduction:
We already know that a fraction is a part of a whole.
Let us consider an example of a watermelon cut into 5 equal parts and out of which 3 parts are left.
The fraction can be represented as 3/5
.
The above figure can be divided into 3 equal parts and each part can be represented into one part out of the 5 parts as shown.
i.e.,1/5× 3 =3/5
1.4.1 Divide whole number by fractions
How to divide whole numbers by fractions?
The following steps explains division of a whole number by a fraction:
Step 1: First, write the fraction and the whole number.
Step 2: Write the reciprocal of the fraction.
Step 3: Multiply the whole number with reciprocal and the required product is the answer.
Example 1: A cardboard is 3 feet long. If the board is cut into pieces and each piece is 3/4 feet long to make shelves. How many shelves can be made from the board?
Solution:
Repeated subtraction method:
If we write the given whole number 3 as a fraction with denominator 4.
Then the total board measure can be written as
12/4feet.
Given that each shelf is 3/4 feet.
Use repeated subtraction to divide until remainder becomes zero.
12/4 − 3/4 = 9/4
9/4 − 3/4 = 6/4
6/4 − 3/4 = 3/4
3/4 −3/4 = 0
∴4 shelves can be made from the board.
Number line method:
Using number line to divide 3 by 3/4
Reciprocal of 3/4 is 4/3
3 ÷ 3/4 = 3 × 4/3 = 4
∴4 shelves can be made from the board.
1.4.2 Divide fractions by whole numbers
How to divide fractions by whole numbers?
The following steps explain division of a fraction by a whole number:
Step 1: First, write the fraction and the whole number.
Step 2: Convert the whole number into fraction.
Step 3: Write the reciprocal of the fraction.
Step 4: Multiply the whole number with reciprocal of the fraction and the required product is the answer.
Example 1: Divide 4/6÷2
Solution:
Division of fractions can be explained using the following area model.
From the above area model, 4/6 can be represented using a rectangle. 4 parts out of 6, shaded in blue, represents the fraction 4/6.
The given fraction 4/6 when divided by a whole number 2, gives the result 2/ 6 as shown above in the rectangle shaded by yellow.
i.e., 4 / 6÷2=4/6×1/2=2/6
(since, reciprocal of 2 is 1 / 2)
Example 2: Divide 1/4÷3
Solution:
Division of fractions can be explained using the following area model.
From the above figure,
The reciprocal of 3 is 1/3
1 / 4÷3 =
1/4 ×1/3 = 1/2
1.4.3 Divide fractions by whole numbers
Reciprocal of a number:
Two numbers whose product is one are known as reciprocal of each other.
How to find the reciprocal of a fraction?
The reciprocal of a fraction is the interchange of numerator and denominator of the other fraction.
Example 1: Divide 4 ÷ 2/3
Solution:
Use patterns of division and multiplication to divide the given whole number by a fraction.
4÷2/3=4×3/2
=4 / 1×3 / 2
=12 / 2 or 6
Example 2: Divide 14 ÷ 4/7
Solution:
14 ÷ 4/7 =14 / 1÷4 / 7
=14 / 1×7 / 4
=98 / 4
Exercise:
1. Henrieta prepared 60 donuts for a party.The donuts are divided equally among 14 guests, how many donuts will each guest have? Also find the leftover donuts.
2. A container has 12 boxes of Oranges.Total boxes costs $184. How much each box cost?
3. A farmer is shipping 2,384 bananas. There are 70 crates in total, each crate has equal number of bananas. Find the number of bananas in each crate.
4. Divide 86 + 4.
5. Divide 232 + 40.
6. Use the division algorithm to divide 809.40 4. 8.
7. Divide 140 + S to find the decimal quotient
8. Divide 128.8 ÷ 1.4.
9. Divide 14.7 ÷ 2.1.
10. Divide 1.296 ÷ 0.108.
What have we learned:
■ Understand fraction division using area models.
■ Understand fraction division using number line.
■ Divide whole number by fractions.
■ Divide fractions by whole numbers.
■ Use relationships to divide whole numbers by fractions.
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