8 4/7 Divided By 15

Dividing Fractions

We will discuss here about dividing fractions by a whole number, past a fractional number or by another mixed partial number.

Commencement let united states recall how to find reciprocal of a fraction, we interchange the numerator and the denominator.

For case, the reciprocal of ¾ is four/3.

Discover the reciprocal of iii ¾

The reciprocal of 3 ¾ is iv/15.

I. Partitioning of a Fraction past a Whole Number:

4 ÷ two = ii ways, there are 2 2'due south in 4.

6 ÷ two = iii means, there are two 2's in 6.

Similarly 5 ÷ \(\frac{1}{two}\) means, how many halves are there in five?

We know that \(\frac{1}{2}\) + \(\frac{1}{ii}\) = one

\(\frac{1}{two}\) + \(\frac{1}{2}\)+	\(\frac{1}{2}\) + \(\frac{one}{2}\)+	\(\frac{one}{ii}\) + \(\frac{1}{2}\)+	\(\frac{1}{two}\) + \(\frac{1}{2}\)+	\(\frac{ane}{2}\) + \(\frac{ane}{2}\)
1+	1+	1+	1+	i	=   5

i.e. there are 10 halves in 5.

5 ÷ \(\frac{i}{2}\) = 5 × \(\frac{2}{1}\) = \(\frac{10}{ane}\) = 10

For Case:

i. \(\frac{seven}{ten}\) ÷ 5 = \(\frac{7}{10}\) ÷ \(\frac{5}{1}\)

= \(\frac{7}{10}\) × \(\frac{one}{5}\)

= \(\frac{vii × ane}{ten × v}\)

= \(\frac{7}{50}\)

2.  What is \(\frac{10}{15}\) ÷ 5? \(\frac{10}{15}\) ÷ \(\frac{5}{1}\) = \(\frac{ten}{15}\) × \(\frac{i}{5}\) = \(\frac{2 × \not 5 × one}{3 × \non five × 5}\) = \(\frac{ii}{15}\)

10 = 2 × 5               15 = three × v                 5 = 1 × 5

To separate a fraction past a number, multiply the fraction with the reciprocal of the number.

For example:

iii. Divide iii/5 by 12

Solution: 3/5 ÷ 12 = 3/5 ÷ 12/1 = three/5 × 1/12 = (3 × ane)/(5 × 12) = 3/60 = 1/20

Step I: Notice the reciprocal of the whole number and multiply with the partial number as usual. Pace II: Limited the product in its lowest terms.

iv. Solve: 5/7 ÷ ten

= 5/7 ÷ ten/one = 5/7 × 1/10 = (5 × 1)/(7 × 10) = 5/70

Step I: Find the reciprocal of the whole number and multiply with the partial number as usual. Pace II: Express the product in its everyman terms.

2. Division of a Fractional Number by a Fractional Number:

For instance:

1. Split 7/8 by 1/5

Solution: 7/8 ÷ ane/5 = seven/8 × 5/1 = (seven × 5)/(8 × 1) = 35/8 = four three/eight

Stride I: Notice reciprocal of 1/5. Step II: Multiply 7/8 by it. Step Iii: Express the product in its simplest form.

2. Carve up: v/ix ÷ 10/18

Solution: 5/9 ÷ 10/xviii = five/9 × 18/ten = (five × xviii)/(9 × 10) = 90/xc = ane

Step I: Find reciprocal of 1/5. Step II: Multiply 7/8 by it. Stride III: Express the product in its simplest form.

Segmentation of a Fraction by a Fraction:

three. Split \(\frac{3}{4}\) ÷ \(\frac{5}{3}\)

Stride I: Multiply the showtime fraction with the reciprocal of the second fraction.

Reciprocal of \(\frac{5}{3}\) = \(\frac{iii}{5}\)

Therefore, \(\frac{three}{4}\) ÷ \(\frac{five}{3}\)  = \(\frac{3}{iv}\) × \(\frac{iii}{5}\)

                           = \(\frac{3 × 3}{iv × 5}\)

                           = \(\frac{9}{20}\)

Step Two: Reduce the fraction to the everyman terms. (if necessary)

4. Divide \(\frac{16}{27}\) ÷ \(\frac{4}{9}\) Therefore, \(\frac{xvi}{27}\) ÷ \(\frac{4}{ix}\) = \(\frac{xvi}{27}\) × \(\frac{9}{iv}\); [Reciprocal of \(\frac{4}{9}\) = \(\frac{9}{4}\)]                             = \(\frac{\not two × \not ii × 2 × 2 × \not 3 × \non iii}{\not 3 × \not 3 × 3 × \non 2 × \not 2}\)                             = \(\frac{four}{iii}\)                             = 1\(\frac{1}{3}\)

sixteen = 2 × 2 × two × two             9 = iii × 3             27 = 3 × 3 × three             4 = ii × 2

Iii. Division of a Mixed Number past another Mixed Number:

For example:

ane. Carve up 2 ¾ by 1 2/iii

Solution: two ¾ ÷ i 2/3 = 11/4 ÷ five/3 = 11/four × 3/5 = (11 × 3)/(4 × 5) = 33/20 = one thirteen/20

Express the mixed numbers as improper fractions and multiply every bit usual.

2. Divide: 2  4/17 ÷ 1  four/17

Solution: two  4/17 ÷ one  4/17 = 38/17 ÷ 21/17 = 38/17 × 17/21 = (38 × 17)/(17 × 21) = 646/357 = 38/21 = 1 17/21

Express the mixed numbers as improper fractions and multiply as usual.

Questions and Answers on Dividing Fractions:

I. Divide the post-obit.

(i) \(\frac{2}{half-dozen}\) ÷ \(\frac{1}{3}\)

(ii) \(\frac{5}{8}\) ÷ \(\frac{15}{16}\)

(iii) \(\frac{5}{half-dozen}\) ÷ 15

(iv) \(\frac{7}{viii}\) ÷ 14

(v) \(\frac{2}{iii}\) ÷ 6

(half dozen) 28 ÷ \(\frac{7}{iv}\)

(vii) 2\(\frac{5}{six}\) ÷ 34

(eight) 9\(\frac{ane}{2}\) ÷ \(\frac{38}{2}\)

(9) three\(\frac{1}{iv}\) ÷ \(\frac{26}{28}\)

(x) 7\(\frac{1}{iii}\) ÷ 1\(\frac{5}{6}\)

(xi) 2\(\frac{3}{5}\) ÷ ane\(\frac{11}{15}\)

(xii) 1\(\frac{ane}{2}\) ÷ \(\frac{4}{7}\)

Related Concept

● Fraction of a Whole Numbers

● Representation of a Fraction

● Equivalent Fractions

● Properties of Equivalent Fractions

● Like and Unlike Fractions

● Comparison of Like Fractions

● Comparing of Fractions having the aforementioned Numerator

● Types of Fractions

● Changing Fractions

● Conversion of Fractions into Fractions having Same Denominator

● Conversion of a Fraction into its Smallest and Simplest Class

● Improver of Fractions having the Same Denominator

● Subtraction of Fractions having the Aforementioned Denominator

● Improver and Subtraction of Fractions on the Fraction Number Line

fourth Course Math Activities

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