By what fraction should we multiply 4/5 to get 16 3/5 ?
Answers
Answer:
Let us multiply 14 by 3. We use the rule of repeated addition to find the product.
Multiplying Fractions
1Save
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 2 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
= 15 3/5
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, 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
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
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) 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:
(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 given quantity.
(i) 17 of 28 kg apples
(ii) 215 of $300
(iii) 59 of 54 km
(iv) 25 of 70 chairs
Answers:
(i) 4 kg apples
(ii) $40
(iii) 30 km
(iv) 28 chair
Correct Question:-
By what fraction should we multiply 4/5 to get 16/35 ?
Solution:-
4×4=16
5×7=35
we have to multiply 4/7 to 4/5 to get 16/35