What Is 6/7 - 2/5 - Smith Trate1937

Multiplying Fractions

Nosotros will discuss here about multiplying fractions by a whole number, by a fractional number or by another mixed partial number.

I. Multiplication of Fractional Number past a Whole Number:

We accept learnt 4 × 5 = 4 times v

= 5 + five + v + 5

= 20

In the same way 6 × $\frac{i}{7}$ = 6 times $\frac{ane}{7}$

= $\frac{1}{7}$ + $\frac{1}{7}$ + $\frac{ane}{7}$ + $\frac{one}{seven}$ + $\frac{ane}{7}$ + $\frac{i}{seven}$

= $\frac{ane + 1 + 1 + 1 + 1 + 1}{7}$

= $\frac{half dozen}{vii}$

i.east., six × $\frac{1}{vii}$ = $\frac{6 × 1}{7}$ = $\frac{six}{7}$

Multiply four × $\frac{3}{five}$

4 × $\frac{3}{five}$ = 4 times 4 × $\frac{three}{five}$

= $\frac{three}{v}$ + $\frac{iii}{5}$ + $\frac{3}{5}$ + $\frac{3}{5}$

= $\frac{12}{5}$

i.due east. four × $\frac{3}{5}$ = $\frac{iv × 3}{5}$ = $\frac{12}{5}$

Production of a whole number and a fractional number =

$\frac{\textrm{Product of Whole Number × Numerator of the Fractional Number}}{\textrm{Denominator of the Partial Number}}$

For examples:

$\frac{three}{iv}$ × 5 = $\frac{3 × 5}{4}$ = $\frac{15}{4}$

$\frac{6}{7}$ × 2 = $\frac{half-dozen × ii}{7}$ = $\frac{12}{7}$

7 × $\frac{4}{5}$ = $\frac{7 × 4}{5}$ = $\frac{28}{5}$

iv × $\frac{three}{11}$ = $\frac{4 × 3}{11}$ = $\frac{12}{eleven}$

Permit united states of america multiply $\frac{1}{4}$ by 3. We utilise the rule of repeated improver to discover the product.

$Multiplying Fractions$

We can say that $\frac{1}{iv}$ of 3 = $\frac{iii}{4}$

To multiply a fraction by a whole number, nosotros multiply the numerator of the fraction past the whole number and reduce the fraction to the lowest terms, if and so required.

For example:

(i) Multiply 1$\frac{2}{9}$ by 25

Solution:

1$\frac{2}{9}$ × 25

= $\frac{ane × ix + ii}{9}$

= $\frac{11}{9}$ × 25

= $\frac{11 × 25}{9}$

= $\frac{275}{nine}$

= xxx$\frac{five}{ix}$

(2) Multiply 2/3 by vii

Solution:

two/3 × 7

= (2 × vii)/3

= 14/3

= 4 2/3

We simply multiply the numerator of the fractional number past the whole number. The denominator remains the aforementioned.

(iii) Multiply xx × $\frac{4}{5}$

20 × $\frac{iv}{5}$ = $\frac{20 × iv}{5}$

= $\frac{2 × 2 × \not five × 2 × 2}{\not 5}$

= 16

$Prime Factors of 20, 4 and 5$

xx = 2 × 2 × 5

4 = 2 × ii

five = five × 1

(iv) Multiply ii$\frac{3}{5}$ by 6

Solution:

2$\frac{3}{5}$ × 6

= (2 × 5 + 3)/v × 6

= (10 + iii)/v × 6

= xiii/five × six

= (13 × half dozen)/5

= 78/five

= 15$\frac{3}{5}$

We modify the mixed numbers into improper fractions and then just multiply the numerator of the fractional number by the whole number. The denominator remains the same.

Ii. Multiplication of Fractional Number past Another Fractional Number:

For example:

(i) Multiply 2/five past four/5

Solution:

two/5 × four/5

= (2 × 4)/(5 × v)

= 8/25

Step I: We multiply the numerators.

Step Two: We multiply the denominators.

Footstep III: We write the fraction in the simplest course.

(ii) Multiply 8/ix by 7/10

Solution:

8/9 × 7/ten

= (viii × vii)/(9 × 10)

= 56/90

We simply multiply the numerators of the fractional numbers and and then multiply the denominators of the fractional numbers. Write the fraction in the simplest form.

(iii)Multiply $\frac{four}{7}$ × $\frac{2}{5}$

Multiply the numerators to get the numerator of the product and

Multiply the denominators to get the denominator of the product.

Reduce the product to the lowest terms.

Therefore, $\frac{iv}{7}$ × $\frac{two}{v}$ = $\frac{4 × two}{seven × 5}$ = $\frac{8}{35}$

Iii: Production of More than 2 Fractions:

For examples:

(i) Multiply $\frac{9}{x}$ × $\frac{2}{5}$ × $\frac{3}{vii}$

$H.C.F. of 54 and 350$

Method I: $\frac{9}{10}$ × $\frac{2}{5}$ × $\frac{3}{seven}$ = $\frac{9 × 2 × 3}{10 × 5 × 7}$ = $\frac{54}{350}$

H.C.F. of 54 and 350 is 2

$\frac{54 ÷ 2}{350 ÷ 2}$ = $\frac{27}{175}$

Therefore, $\frac{nine}{10}$ × $\frac{2}{5}$ × $\frac{three}{7}$ = $\frac{27}{175}$

Method II: $\frac{9}{x}$ × $\frac{ii}{5}$ × $\frac{iii}{seven}$ = ?

9 = 3 × 3

2 = 2 × 1

3 = 3 × 1

10 = 2 × 5

five = v × 1

7 = 7 × 1

$Prime Factors of 9, 2, 3, 10, 5 and 7$

Write the numbers as the products of prime factors.

Cancel the numbers mutual in numerator and denominator.

Therefore, $\frac{9}{10}$ × $\frac{2}{5}$ × $\frac{3}{seven}$ = $\frac{3 × three × \not 2 × 1 × 3 × i}{\not ii × five × 5 × ane × 7 × i}$

= $\frac{27}{175}$

(v) Multiply $\frac{4}{seven}$, $\frac{three}{xi}$ and $\frac{five}{8}$.

Solution:

To multiply 2 or more fractions, we multiply the numerators of given fractions to find the new numerator of the product and multiply the denominators to get the denominator of the product.

Hence, $\frac{4}{vii}$ × $\frac{3}{11}$ × $\frac{five}{8}$ = $\frac{four × 3 × 5}{7 × xi × eight}$

= $\frac{lx}{616}$

(vi) Multiply $\frac{ten}{21}$ × $\frac{5}{24}$ × $\frac{iii}{50}$

$\frac{10}{21}$ × $\frac{v}{24}$ × $\frac{iii}{50}$

=$\frac{x × v × 3}{21 × 24 × l}$

= $\frac{\non two × \not v × \non 5 × \not 3}{\non three × 7 × iii × \not 2 × two × 2 × two × \not v × \not 5}$

=$\frac{1}{168}$

$Prime Factors of 10, 5, 3, 21, 24 and 50$

10 = ii × 5

v = v × 1

3 = iii × 1

21 = 3 × 7

24 = three × 2 × 2 × two

50 = two× five × five

3. Multiplication of a Mixed Number past Another Mixed Number:

For Example:

(i) Multiply 2 1/three by 1 ¾

Solution:

2 1/3 × 1 ¾

= seven/3 × seven/4

= 49/12

= iv 1/12

We change the mixed numbers into improper fractions and so nosotros multiply as usual.

(ii) Multiply i 7/9 past three 5/11

Solution:

1 7/9 × three 5/eleven

= 16/9 × 38/eleven

= (16 × 38)/(nine × 11)

= 608/99

= 6 14/99

Nosotros change the mixed numbers into improper fractions and and then nosotros multiply as usual.

(iii) Multiply xi$\frac{7}{8}$ past three$\frac{1}{24}$

Solution:

Let u.s. first convert mixed numbers into improper fractions.

11$\frac{7}{viii}$ = $\frac{11 × 8 + 7}{eight}$ = $\frac{95}{8}$

3$\frac{1}{24}$ = $\frac{3 × 24 + 1}{24}$ = $\frac{73}{24}$

At present, $\frac{95}{8}$ × $\frac{73}{24}$ = $\frac{95 × 73}{8 × 24}$

= $\frac{6935}{192}$

= 36$\frac{23}{192}$

(iv) Multiply 3$\frac{1}{2}$ × 2$\frac{1}{5}$

three$\frac{ane}{ii}$ × 2$\frac{ane}{5}$ = $\frac{7}{two}$ × $\frac{11}{5}$

= $\frac{7 × 11}{ii × five}$

= $\frac{77}{10}$

= vii$\frac{7}{10}$

$Mixed to Improper$

Questions and Answers on Multiplying Fractions:

I. Find the product:

(i) $\frac{five}{xix}$ × ane

(2) $\frac{half-dozen}{7}$ × 5

(iii) $\frac{9}{14}$ × 6

(4) $\frac{4}{13}$ × 0

(5) $\frac{1}{7}$ × $\frac{5}{vi}$

(six) 1$\frac{ane}{x}$ × 8

(vii) $\frac{1}{7}$ × $\frac{8}{1}$

(8) $\frac{1}{3}$ × $\frac{7}{5}$ × $\frac{2}{nine}$

(nine) $\frac{four}{15}$ × $\frac{10}{21}$

(ten) $\frac{one}{2}$ of 100

(xi) $\frac{1}{3}$ of 60

(xii) $\frac{iv}{5}$ of $\frac{8}{11}$

Answers:

I. (i) $\frac{5}{19}$

(two) four$\frac{2}{7}$

(three) 3$\frac{6}{7}$

(4) 0

(v) $\frac{5}{42}$

(half-dozen) 8$\frac{4}{5}$

(vii) 1$\frac{1}{seven}$

(eight) $\frac{fourteen}{135}$

(nine) $\frac{8}{63}$

(ten) 50

(xi) 20

(xii) $\frac{32}{55}$

Two. Multiply and write the product in lowest terms.

(i) $\frac{1}{2}$ × 40

(ii) $\frac{1}{3}$ × 150

(iii) $\frac{2}{seven}$ × 21

(iv) $\frac{7}{38}$ × 0

(5) $\frac{31}{65}$ × ane

(vi) 8 × $\frac{17}{24}$

(vii) $\frac{three}{7}$ × $\frac{vii}{15}$

(8) $\frac{9}{32}$ × $\frac{8}{36}$

(ix) $\frac{eleven}{15}$ × $\frac{45}{88}$

(x) $\frac{ii}{ten}$ ×$\frac{3}{22}$ ×$\frac{twoscore}{30}$

(xi) $\frac{1}{6}$ ×$\frac{ii}{5}$ ×$\frac{iii}{iv}$

(xii) 3$\frac{i}{7}$ ×$\frac{21}{44}$

Answers:

II. (i) 20

(ii) fifty

(three) half dozen

(four) 0

(v) $\frac{31}{65}$

(6) $\frac{17}{3}$

(vii) $\frac{1}{v}$

(viii) $\frac{1}{xvi}$

(ix) $\frac{3}{eight}$

(10) $\frac{2}{55}$

(eleven) $\frac{ane}{twenty}$

(xii) 1$\frac{one}{2}$

3. Discover the Product and Reduce it the Lowest Terms:

(i) 4$\frac{1}{iii}$ × 2$\frac{1}{3}$

(2) six × v$\frac{1}{ii}$

(three) 1$\frac{1}{7}$ × 2$\frac{1}{4}$

(4) $\frac{3}{4}$ × $\frac{ane}{three}$ × $\frac{ii}{vi}$

(v) 1$\frac{one}{two}$ × 5$\frac{2}{three}$ × 4$\frac{i}{v}$

(vi) $\frac{vii}{9}$ × $\frac{10}{15}$ × $\frac{3}{21}$

(vii) $\frac{16}{48}$ × $\frac{12}{24}$ × $\frac{fifteen}{xxx}$

(eight) $\frac{19}{38}$ × $\frac{2}{4}$ × $\frac{8}{20}$

(ix) $\frac{vi}{42}$ × one$\frac{i}{five}$ × $\frac{xv}{fifty}$

Answer:

III.(i) 10$\frac{1}{9}$

(ii) 33

(iii) two$\frac{4}{seven}$

(iv) $\frac{1}{12}$

(v) 35$\frac{7}{x}$

(vi) $\frac{2}{27}$

(vii) $\frac{1}{12}$

(viii) $\frac{1}{ten}$

(ix) $\frac{9}{175}$

IV. Simplify. (employ Prime Factorisation)

(i) $\frac{7}{9}$ × $\frac{18}{21}$ × $\frac{6}{10}$

(two) $\frac{24}{36}$ × $\frac{81}{27}$ × $\frac{5}{10}$

(iii) $\frac{x}{12}$ × $\frac{12}{14}$ × $\frac{14}{twenty}$

(iv) $\frac{xv}{16}$ × $\frac{32}{30}$ × $\frac{one}{4}$

(five) $\frac{one}{2}$ × $\frac{4}{8}$ × $\frac{16}{6}$

(half dozen) $\frac{13}{22}$ × $\frac{xi}{26}$ × $\frac{4}{half-dozen}$

Answer:

Iv. (i) $\frac{2}{5}$

(ii) 1

(iii) $\frac{ane}{2}$

(four) $\frac{1}{4}$

(five) $\frac{two}{3}$

(half dozen) $\frac{1}{6}$

V. Multiply:

(i) iv × $\frac{six}{11}$

(two) $\frac{8}{thirteen}$ × 3

(iii) $\frac{2}{v}$ × 10

(four) $\frac{5}{7}$ × 5

(five) 8 × $\frac{v}{6}$

(vi) $\frac{7}{12}$ × 2

(seven) 15 × $\frac{1}{4}$

(viii) 19 × $\frac{1}{3}$

Respond:

5. (i) 2$\frac{two}{11}$

(ii) 1$\frac{eleven}{13}$

(3) 4

(4) three$\frac{4}{seven}$

(five) 6$\frac{two}{3}$

(vi) i$\frac{ane}{6}$

(vii) 3$\frac{3}{4}$

(viii) 6$\frac{one}{iii}$

VI. Find the given quantity.

(i) $\frac{1}{7}$ of 28 kg apples

(ii) $\frac{2}{15}$ of $300

(iii) $\frac{v}{9}$ of 54 km

(iv) $\frac{2}{5}$ of 70 chairs

Answers:

Vi. (i) 4 kg apples

(ii) $40

(three) xxx km

(iv) 28 chairs

$Multiplying Fractions Examples$

Seven: Word issues on Multiplying Fractions:

1. 2$\frac{ane}{5}$ m of fabric is required to make a shirt. Ron wants to make 25 shirts, what length of cloth does he need?

Answer: 55 grand of material

two. $\frac{3}{4}$ cups of milk is required to brand a block of ane kg. How many cups of milk is required to make a cake of 4$\frac{one}{2}$ kg?

Answer: 3$\frac{3}{8}$ cups

3. Shelly bought 16$\frac{3}{4}$ liters of juice. If the cost of 1 liter juice is $8, detect the total toll of juice?

Answer: $134

4. The weight of each bag is 4$\frac{1}{4}$ Kg. What would exist the weight of 36 such bags?

Answer: 153 kg

five. Sam works for six$\frac{2}{8}$ hours each day. For how much time will she work in a calendar month if she works for 24 days in a month?

Respond: 150 hours

●Related Concepts

Fraction of a Whole Numbers
Representation of a Fraction
Equivalent Fractions
Properties of Equivalent Fractions
Finding Equivalent Fractions
Reducing the Equivalent Fractions
Verification of Equivalent Fractions
Finding a Fraction of a Whole Number
Like and Unlike Fractions
Comparison of Like Fractions
Comparison of Fractions having the same Numerator
Comparison of Dissimilar Fractions
Fractions in Ascending Social club
Fractions in Descending Guild
Types of Fractions
Changing Fractions
Conversion of Fractions into Fractions having Aforementioned Denominator
Conversion of a Fraction into its Smallest and Simplest Class
Add-on of Fractions having the Same Denominator
Addition of Unlike Fractions
Addition of Mixed Fractions
Discussion Problems on Addition of Mixed Fractions
Worksheet on Word Problems on Improver of Mixed Fractions
Subtraction of Fractions having the Same Denominator
Subtraction of Different Fractions
Subtraction of Mixed Fractions
Word Issues on Subtraction of Mixed Fractions
Worksheet on Give-and-take Problems on subtraction of Mixed Fractions
Addition and Subtraction of Fractions on the Fraction Number Line
Word Issues on Multiplication of Mixed Fractions
Worksheet on Word Problems on Multiplication of Mixed Fractions
Multiplying Fractions
Dividing Fractions
Discussion Bug on Division of Mixed Fractions
Worksheet on Discussion Problems on Division of Mixed Fractions

4th Class Math Activities

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