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

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I. Multiplication of fractional number by a whole number:

Let us multiply (frac14) by 3. We use the rule ofrepeated addition to find the product.


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

For example:

(i) Multiply 1(frac29) by 25

Solution:

1(frac29) × 25

= (frac1 × 9 + 29)

= (frac119) × 25

= (frac11 × 259)

= (frac2759)

= 30(frac59)


(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 bythe whole number. The denominator remains the same.


(iii) Multiply2  3/5 by 6

Solution:

2  3/5 × 6

= (2 ×5 + 3)/5 × 6

= (10 +3)/5 × 6

= 13/5× 6

= (13 ×6)/5

= 78/5

= 153/5

Wechange the mixed numbers into improper fractions and then simply multiply thenumerator of the fractional number by the whole number. The denominator remainsthe same.


(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 numbersand then multiply the denominators of the fractional numbers. Write thefraction in the simplest form.


(iii) Multiply (frac47), (frac311) & (frac58).

Solution:

To multiply two or more fractions, we multiply thenumerators of given fractions to find the new numerator of the hàng hóa andmultiply the denominators lớn get the denominator of the product.

Hence, (frac47) × (frac311) × (frac58)= (frac4 × 3 × 57 × 11 × 8)

                             =(frac60616)

III. Multiplication of a mixed number by another mixednumber:

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 & thenwe multiply as usual.


(ii) Multiply1  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 & thenwe multiply as usual.


(iii) Multiply 11(frac78) by 3(frac124)

Solution:

Let us first convert mixed numbers into improper fractions.

11(frac78) = (frac11 × 8 + 78) = (frac958)

3(frac124) = (frac3 × 24 + 124) = (frac7324)

Now, (frac958) × (frac7324) = (frac95 × 738× 24)

                      =(frac6935192)

                      =36(frac23192)

Questions and Answers on Multiplying Fractions:

I. Find the product:

(i) (frac519) × 1

(ii) (frac67) × 5

(iii) (frac914) × 6

(iv) (frac413) × 0

(v) (frac17) × (frac56)

(vi) 1(frac110) × 8

(vii) (frac17) × (frac81)

(viii) (frac13) × (frac75) × (frac29)

(ix) (frac415) × (frac1021)

(x) (frac12) of 100

(xi) (frac13) of 60

(xii) (frac45) of (frac811)

Answers:

(i) (frac519)

(ii) 4(frac27)

(iii) 3(frac67)

(iv) 0

(v) (frac542)

(vi) 8(frac45)

(vii) 1(frac17)

(viii) (frac14135)

(ix) (frac863)

(x) 50

(xi) 20

(xii) (frac3255)

II. Multiply và write the product in lowest terms.

(i) (frac12) × 40

(ii) (frac13) × 150

(iii) (frac27) × 21

(iv) (frac738) × 0

(v) (frac3165) × 1

(vi) 8 × (frac1724)

(vii) (frac37) × (frac715)

(viii) (frac932) × (frac836)

(ix) (frac1115) × (frac4588)

(x) (frac210) ×(frac322) ×(frac4030)

(xi) (frac16) ×(frac25) ×(frac34)

(xii) 3(frac17) ×(frac2144)

Answers:

(i) 20

(ii) 50

(iii) 6

(iv) 0

(v) (frac3165)

(vi) (frac173)

(vii) (frac15)

(viii) (frac116)

(ix) (frac38)

(x) (frac255)

(xi) (frac120)

(xii) 1(frac12)

III. Find the given quantity.

(i) (frac17) of 28 kg apples

(ii) (frac215) of $300

(iii) (frac59) of 54 km

(iv) (frac25) of 70 chairs

Answers:

(i) 4 kilogam apples

(ii) $40

(iii) 30 km

(iv) 28 chairs


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Word problems on Multiplying Fractions:

1. 2(frac15) m of cloth is required lớn make a shirt. Ron wants to lớn make 25 shirts, what length of cloth does he need?

Answer: 55 m of cloth

2. (frac34) cups of milk is required lớn make a cake of 1 kg. How many cups of milk is required lớn make a cake of 4(frac12) kg?

Answer: 3(frac38) cups

3. Shelly bought 16(frac34) liters of juice. If the cost of 1 liter juice is $8, find the total cost of juice?

Answer:  $134

4.

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 The weight of each bag is 4(frac14) Kg. What would be the weight of 36 such bags?

Answer: 153 kg

5. Sam works for 6(frac28) hours each day. For how much time will she work in a month if she works for 24 days in a month?