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Multiplying Fractions

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


I. Multiplication of Fractional Number by a Whole Number:

We have learnt             4 × 5                 =          4 times 5

                                                            =          5 + 5 + 5 + 5

                                                            =          20

In the same way 6 × 17 = 6 times 17

                                  = 17 + 17 + 17 + 17 + 17 + 17

                                  = 1+1+1+1+1+17

                                  = 67

        i.e., 6 × 17 = 6×17 = 67

Multiply 4 × 35

           4 × 35 = 4 times 4 × 35

                     = 35 + 35 + 35 + 35

                     = 125

        i.e. 4 × 35 = 4×35 = 125


Product of a whole number and a fractional number =

Product of Whole Number × Numerator of the Fractional NumberDenominator of the Fractional Number


For examples:

34 × 5 = 3×54 = 154

67 × 2 = 6×27 = 127

7 × 45 = 7×45 = 285

4 × 311 = 4×311 = 1211


Let us multiply 14 by 3. We use the rule of repeated addition to find the product.

Multiplying Fractions

We can say that 14 of 3 = 34

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


For example:

(i) Multiply 129 by 25

Solution:

129 × 25

= 1×9+29

= 119 × 25

= 11×259

= 2759

= 3059


(ii) Multiply 2/3 by 7

Solution:

2/3 × 7

= (2 × 7)/3

= 14/3

= 4 2/3


We simply multiply the numerator of the fractional number by the whole number. The denominator remains the same.


(iii) Multiply 20 × 45

20 × 45 = 20×45

           = 2×2×5×2×25

           = 16

Prime Factors of 20, 4 and 5

20 = 2 × 2 × 5

 4 = 2 × 2

 5 = 5 × 1


(iv) Multiply 235 by 6

Solution:

235 × 6

= (2 × 5 + 3)/5 × 6

= (10 + 3)/5 × 6

= 13/5 × 6

= (13 × 6)/5

= 78/5

= 1535



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


II. Multiplication of Fractional Number by Another Fractional Number:

For example:

(i) Multiply 2/5 by 4/5

Solution:

2/5 × 4/5

= (2 × 4)/(5 × 5)

= 8/25


Step I: We multiply the numerators.

Step II: We multiply the denominators.

Step III: We write the fraction in the simplest form.



(ii) Multiply 8/9 by 7/10

Solution:

8/9 × 7/10

= (8 × 7)/(9 × 10)

= 56/90

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


(iii) Multiply 47 × 25

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, 47 × 25 = 4×27×5 = 835


III: Product of More than Two Fractions:

For examples:

(i) Multiply 910 × 25 × 37

H.C.F. of 54 and 350

Method I: 910 × 25 × 37 = 9×2×310×5×7 = 54350

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

54÷2350÷2 = 27175

Therefore, 910 × 25 × 37 = 27175


Method II: 910 × 25 × 37 = ?

9 = 3 × 3 

2 = 2 × 1

3 = 3 × 1   

10 = 2 × 5

 5 = 5 × 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 common in numerator and denominator.

Therefore, 910 × 25 × 37 = 3×3×2×1×3×12×5×5×1×7×1

                                    = 27175


(v) Multiply 47, 311 and 58.

Solution:

To multiply two 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, 47 × 311 × 58 = 4×3×57×11×8

                             = 60616


(vi) Multiply 1021 × 524 × 350


1021 × 524 × 350


10×5×321×24×50


2×5×5×33×7×3×2×2×2×2×5×5


1168

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

10 = 2 × 5

5 = 5 × 1

3 = 3 × 1

21 = 3 × 7

24 = 3 × 2 × 2 × 2

50 = 2 × 5 × 5


III. Multiplication of a Mixed Number by Another Mixed Number:

For Example:

(i) Multiply 2 1/3 by 1 ¾

Solution:

2 1/3 × 1 ¾

= 7/3 × 7/4

= 49/12

= 4 1/12


We change the mixed numbers into improper fractions and then we multiply as usual.



(ii) Multiply 1  7/9 by 3 5/11

Solution:

1  7/9 × 3 5/11

= 16/9 × 38/11

= (16 × 38)/(9 × 11)

= 608/99

= 6 14/99



We change the mixed numbers into improper fractions and then we multiply as usual.


(iii) Multiply 1178 by 3124

Solution:

Let us first convert mixed numbers into improper fractions.

1178 = 11×8+78 = 958

3124 = 3×24+124 = 7324

Now, 958 × 7324 = 95×738×24

                     = 6935192

                     = 3623192


(iv) Multiply 312 × 215

312 × 215 = 72 × 115

              = 7×112×5

              = 7710

              = 7710

Mixed to Improper


Questions and Answers on Multiplying Fractions:

I. Find the product:

(i) 519 × 1

(ii) 67 × 5

(iii) 914 × 6

(iv) 413 × 0

(v) 17 × 56

(vi) 1110 × 8

(vii) 17 × 81

(viii) 13 × 75 × 29

(ix) 415 × 1021

(x) 12 of 100

(xi) 13 of 60

(xii) 45 of 811


Answers:

I. (i) 519

(ii) 427

(iii) 367

(iv) 0

(v) 542

(vi) 845

(vii) 117

(viii) 14135

(ix) 863

(x) 50

(xi) 20

(xii) 3255


II. Multiply and write the product in lowest terms.

(i) 12 × 40

(ii) 13 × 150

(iii) 27 × 21

(iv) 738 × 0

(v) 3165 × 1

(vi) 8 × 1724

(vii) 37 × 715

(viii) 932 × 836

(ix) 1115 × 4588

(x) 210 ×322 ×4030

(xi) 16 ×25 ×34

(xii) 317 ×2144


Answers:

II. (i) 20

(ii) 50

(iii) 6

(iv) 0

(v) 3165

(vi) 173

(vii) 15

(viii) 116

(ix) 38

(x) 255

(xi) 120

(xii) 112


III. Find the Product and Reduce it the Lowest Terms:

(i) 413 × 213

(ii) 6 × 512

(iii) 117 × 214

(iv) 34 × 13 × 26

(v) 112 × 523 × 415

(vi) 79 × 1015 × 321

(vii) 1648 × 1224 × 1530

(viii) 1938 × 24 × 820

(ix) 642 × 115 × 1550


Answer:

III. (i) 1019

(ii) 33

(iii) 247

(iv) 112

(v) 35710

(vi) 227

(vii) 112

(viii) 110

(ix) 9175


IV. Simplify. (use Prime Factorisation)

(i) 79 × 1821 × 610

(ii) 2436 × 8127 × 510

(iii) 1012 × 1214 × 1420

(iv) 1516 × 3230 × 14

(v) 12 × 48 × 166

(vi) 1322 × 1126 × 46


Answer:

IV. (i) 25

(ii) 1

(iii) 12

(iv) 14 

(v) 23

(vi) 16


V. Multiply:

(i) 4 × 611

(ii) 813 × 3

(iii) 25 × 10

(iv) 57 × 5

(v) 8 × 56

(vi) 712 × 2

(vii) 15 × 14

(viii) 19 × 13


Answer:

V. (i) 2211

(ii) 11113

(iii) 4

(iv) 347

(v) 623

(vi) 116

(vii) 334

(viii) 613


VI. Find the given quantity.

(i) 17 of 28 kg apples

(ii) 215 of $300

(iii) 59 of 54 km

(iv) 25 of 70 chairs


Answers:

VI. (i) 4 kg apples

(ii) $40

(iii) 30 km

(iv) 28 chairs

Multiplying Fractions Examples

VII: Word problems on Multiplying Fractions:

1. 215 m of cloth is required to make a shirt. Ron wants to make 25 shirts, what length of cloth does he need?

Answer: 55 m of cloth


2. 34 cups of milk is required to make a cake of 1 kg. How many cups of milk is required to make a cake of 412 kg?

Answer: 338 cups


3. Shelly bought 1634 liters of juice. If the cost of 1 liter juice is $8, find the total cost of juice?

Answer:  $134


4. The weight of each bag is 414 Kg. What would be the weight of 36 such bags?

Answer: 153 kg


5. Sam works for 628 hours each day. For how much time will she work in a month if she works for 24 days in a month?

Answer: 150 hours

 Related Concepts






4th Grade Math Activities

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